US20070273097A1

US20070273097A1 - Method of playing blackjack with an innovative side wager

Info

Publication number: US20070273097A1
Application number: US11/439,840
Authority: US
Inventors: Michael A. Kirkutis
Original assignee: Individual
Current assignee: Individual
Priority date: 2006-05-24
Filing date: 2006-05-24
Publication date: 2007-11-29

Abstract

This invention presents methods for playing live and electronic Blackjack-style games with an optional side wager incorporating a bonus or Jackpot feature. The essence of the instant invention is the making of a side bet in the game of Blackjack where the player making the side bet is wagering that he or she will be dealt two Aces, which will then be split and (depending upon casino rules and State Gaming Commission regulations) re-split as additional Aces are dealt, with the ultimate goal of subsequently being dealt Ten value cards that will result in “21” when paired with previously dealt Aces. Additional payouts are available if the “21's” are of a specified rank, suit, and color. This invention presents the opportunity for a unique combination of significant payouts for the player, increased revenue for the casino, and relative simplicity while retaining the basic nature of Blackjack.

Description

CROSS REFERENCE TO RELATED APPLICATIONS

None

FEDERAL RESEARCH STATEMENT

None

FIELD OF THE INVENTION

This invention relates to Blackjack-style games and more particularly to methods for playing live and electronic Blackjack-style games with an optional side wager incorporating a bonus or Jackpot feature.

BACKGROUND OF THE INVENTION

The prior art reveals a multitude of live and electronic casino card games wherein one or more players are dealt or assemble hands of cards and compete against a hand representing a dealer's hand. One of the most common and popular of such casino card games is the game of Blackjack, which is also referred to as “21.” In the card game of Blackjack, each player makes a wager and the dealer deals two cards to each player to define an initial holding and two cards to himself defining a dealer's initial holding. The cards may be dealt from a single, standard deck of fifty-two playing cards, or from a “shoe” containing multiple decks of cards. The cards to the player(s) may be dealt face up or face down. For the dealer, in the traditional game, one of the dealer's cards in his initial holding is turned face up, which is often referred to as the “up” card, and the other card is dealt face down, which is often referred to as the “hole” card. In the traditional game of Blackjack, the cards have the following arithmetic value:

	TABLE 1

	Card	Value

	Ace	1 or 11 (at player's option)
	King	10
	Queen	10
	Jack	10
	2-10	card face value

Each player, in turn, has the opportunity to complete his or her hand in a manner well known in the prior art. The object of the game is for the player to assemble a final hand which (1) has a higher numerical count value than the dealer's final hand without the value exceeding a predetermined target value which, in traditional Blackjack, is 21. In this regard each player may generally exercise the following options:
1. Receiving no additional cards (i.e. “stand”) thereby making the value of the initial holding the player's final holding;
2. Being dealt additional cards (taking “hits”) in order to attempt to achieve or come close to the predetermined target value but at the same time not exceeding the predetermined target value;
3. Doubling the value of his or her initial wager (i.e. “doubling down”) in accordance with the casino's rules;
4. Splitting card pairs of the initial holding into two hands and playing each hand separately;
5. Stopping play of his or her hand (i.e. “surrendering”) and giving up half their wager as permitted and governed by casino rules; and/or.
6. Taking insurance by wagering an amount equal to their game wager and if the dealer has a “Blackjack” or “natural” (initial holding composed of an Ace and a Ten-value card), the player wins 2:1 and therefore, basically, does not win or lose.
Once all the players have completed their hands, the dealer does so as well by taking hits or standing according to the house rules. A variation included in those rules is that the dealer may be required to stand on a “soft 17” (i.e., a hand numerical count of 17 including an Ace which counts as a 1 or an 11). Other rules require the dealer to hit a soft 17.
If a player exceeds the target value of “21”, he or she loses the wager regardless of whether the dealer also exceeds the target value. This is so because the players complete their hands first. If the player's hand does not exceed the target value and (1) his hand has a value exceeding the dealer or (2) the dealer exceeds the target value, the player wins and is paid 1:1 on his or her game wager. If the dealer does not exceed the target value and his hand has a greater value than the player's final hand, the player loses his or her wager. If the player's and the dealer's final hand values are the same, it is a tie (or “push”) and the player neither wins nor loses.
The prior art also reveals computerized games wherein the computer generally assumes the role of the dealer and competes against a player or players. The prior art also reveals hand held, electronic Blackjack.
The rules of traditional Blackjack are somewhat limiting in that the most a player can win is a 3:2 award (i.e. 150% of original wager) which occurs when the player has a natural (i.e. Ace and a Ten value card) and the dealer does not have a natural. Therefore, several variations of traditional Blackjack have been developed whereby the potential payouts for players have been increased (thereby making the games more attractive to players) while at the same time increasing potential revenue for the casino.
For example, in U.S. Pat. No. 6,845,981 to Ko, a method for playing Blackjack with a side wager is disclosed. The player wins or loses based upon (1) the dealer's hand exceeding the target value and (2) various parameters involving the dealer's hand and/or the player's hand.
Another example is shown in Griffiths, U.S. Pat. No. 5,174,579. In Griffiths, there is disclosed a Blackjack side wager “21 or over”. The player making this side wager is betting that the dealer will either “bust” (i.e. exceed the value of 21) or achieve exactly a hand count of 21 with 3 or more cards. When the dealer has either busted or achieved an exact hand count of 21, the player is paid according to predetermined odds of 1:1, 3:2 or 2:1. A significant drawback to this wager is the low payoff odds which limit the attractiveness of the game to the player.
There are many Blackjack side wagers that pay much higher payoffs. One such game is known as Lucky Ladies where the top payoff odds are 1000:1 if the player has a hand of Queens of the same suit. Thus “21 or over” won't be enticing or exciting enough for the players. The reason “21 or over” cannot pay odds more than 2:1 is that its hit frequency (probability of the occurrence during play) of 36% is too high. In a “Blackjack game dealt from 6 decks with the “dealer hits a soft 17” rule, a dealer will bust 28.58% of his hands and achieve a count of 21 7.49% of the time. Since the odds are only 1.78:1 against winning a bet with a hit frequency of 36%, there is no way the casino can pay odds higher than 1.78:1, and even with a dealer hand count of 21 being a push, 2.24:1 would be the highest odds the casino can pay without incurring a loss.
Another example is shown in Keller, U.S. Pat. No. 5,816,575, where several side wagers are disclosed, one of which allows the player to bet that the dealer will go bust. When the dealer busts, the player is paid at 5:2 (i.e., 2.5:1) odds. Again, like “21 or over”, the payoff odds for the side wager are unattractive. Furthermore, since the odds against the dealer going bust are only 2.499:1, the casino won't have an advantage if the side wager is paid 2.5:1. Thus the casino would not have a profit motive for hosting a game with such a side wager.
In Forte, U.S. Pat. No. 5,934,998, there is disclosed a side wager that rewards the player if the number of consecutive dealer bust hands has exceeded a predetermined dealer bust event threshold of 5. The drawback to such a wager is that it not only requires additional equipment such as electronic displays and counters to tally the dealer bust event for every player, but once the dealer starts to bust, the player has to stay and continue to play until the dealer either stops busting or reaches the predetermined threshold. Hence side wagers that cannot be resolved in one single hand or round of play require more supervision and cause inconveniences for the players. Further, because new players may enter the game during the dealer busting sequence, maintaining the tally for each player is difficult and likely to lead to disputes.
In Vancura, U.S. Pat. No. 5,673,917, there is disclosed a side wager for the player to make in addition to his or her base game wager in Blackjack. One embodiment describes the player as making a side wager based upon the number of “hits” the player will take in completing his or her hand. Players are paid for their side wager according to one of several suggested pay tables. One drawback to this game embodiment is that the side wager is either fixed, a percentage of the base wager, or confined within strict limits to counteract the effect of an advantage obtained by professional card counters. When the outcome of a side wager depends on the base wager or is confined within limits determined by the possible effects of card counting in a game where skill can impact the frequency and amount won such as Blackjack, most players will, with respect to the side wager, lose a disproportionate amount of the time. The strategy for this side wager will presumably comprise a set of 2- to N-card strategies, where N equals the maximum winning number of successful hits minus 1 and each multi-card strategy is a matrix composed of “hit or stand” rules based on the player's current hand total of 12 through 20 versus the Ten dealer up cards for a total of 90 rules times (N.times.2)!
Furthermore, since the base wager and the side wager are paid at different odds, the optimal strategy will vary with the ratio of the base wager to the side wager, thereby necessitating memorizing many more strategy deviations if the player wants to vary their wager size, which they often do. Thus the size of the side wager had better be a fixed amount or fraction of the base wager as stated in his claims 20 to 23.
Another embodiment described in Vancura is that the player may make one or more side wagers where he or she is attempting to predict the exact number of hits the dealer or player will take. If the player incorrectly predicts the exact number, e.g., the player wagers on two hits and the dealer only takes no hits, one hit or three or more hits, the player loses their side wager. There are several drawbacks to this side wager. First, the player must accurately and precisely predict the number of the dealer hits. If he does not so predict, the player loses their side wager. Second, the outcome of the side wager is also dependent upon the player hand. For the side wager where the player is predicting the number of dealer hits, exact prediction is required for the player to win their side wager. For the side wager on the number of player hits there is disclosed an “over” wager, i.e. three or more hits. Second, the outcome of the side wager is also dependent upon the player hand. Also, according to certain disclosed embodiments, if the player receives a natural Blackjack, the side wager is a push. This means the player will not have a chance to win the bet an additional 4.7% of the time (the statistical frequency of player Blackjack(s)). Also, the side wager either pushes or loses if the player exercises one of such options as surrender, double down and splitting. This further deprives the player of their chances to win the side wager an additional 12% of the time. The requirement to precisely predict the dealer's hits and the dependency of the outcome of the side wager on the player hand Reduce the frequency that the player will win their side wager. If players do win or see other side wagers won relatively frequently, they may abandon the game or at least the side wager. Further, since precise prediction is required for side wagers based on the dealer's hand, players may become frustrated by infrequent wins of the side wager. As for wagers on the player's hand, often the player will be put into a situation where they must choose between winning their base wager and trying to win their side wager. This creates a stressful situation which may cause casual players to shun the side wager altogether. It is further noted that limiting the side the side wager to ⅕ of the base game wager not only Reduces both the excitement and betting action for the player and the revenue for the casino, but it also creates difficulties in calculating the exact bet amount for the player and in calculating and making the payment for the dealer as well when the bet amount is not a multiple of 5. Imagine a player making a base wager of $17.
Yet another Blackjack-style game is known as “No Bust 21” or “21.sup.st Century Blackjack” where no hands can “bust.” If the player hand goes over 21, instead of losing their wager immediately as in traditional Blackjack, the player's wager remains in effect until the dealer plays out his hand. Unless the dealer's hand also goes over 21 and is closer to 21 than is the player hand, the player won't lose the wager.
Some Blackjack-style games have been adopted and played which provide for a side (“bonus”) wager that (1) the dealer will have a Blackjack, (2) the dealer's hand will have a certain combination of cards such as suited Queens, or (3) the dealer will take a certain number of hits, or (4) the dealer will bust.
A more recently disclosed method of play is presented in Patent Application No. US2003/0218303 by Walker, et al. The Walker application discloses games whereby a player can make side wagers on future hands.
Another recently disclosed method of play is presented in U.S. Patent Application No. US2003/0222400 by Collins, et al. In Collins, the casino makes the determination which cards may be split. In this case, the player splits Ace—eight hands.
None of the games, patents, or patent applications described above presents the opportunity for the unique combination of significant payouts for the player, increased revenue for the casino, and relative simplicity while retaining the basic nature of Blackjack that the present invention comprises.

DETAILED DESCRIPTION OF THE INVENTION

The present invention comprises a method of playing Blackjack with an innovative optional side wager. The side bet is made before the dealer begins dealing cards. The side bet is made once at the beginning of the hand and no further side bet is collected. The side bet game is essentially a play for a specific predetermined card combination of cards a player has the possibility of receiving in the normal play of Blackjack utilizing split Aces as the foundation. The side bet game does not incite the player to make abnormal decisions in the game of Blackjack. The side bet game follows basic strategy of always splitting Aces.
The essence of the instant invention is the making of a side bet in the game of Blackjack where the player making the side bet is wagering that he or she will be dealt two Aces, unsuited or suited, which will then be split and (depending upon casino rules and State Gaming Commission regulations) re-split as additional Aces, either unsuited or suited, are dealt with the ultimate goal of subsequently being dealt Ten value cards (i.e. Tens, jacks, Queens or Kings), either unsuited or suited that will result in “21s” when paired with previously dealt Aces. Three side bet games have been created, Game A. and Game B. and Game C. These games differ in the defined Aces and Ten value cards which the player is seeking. Game A involves matching Ten value cards. Game B involves suited Ten value cards on suited Aces. Game C seeks same color Ten value cards on same color Aces.
Embodied within each game there are two options. These options are governed by how many times the house (or casino) will allow Aces to be split. The side bet games created account for a one split and three split option.

Suited Cards and the Minimum Number of Decks Needed for a Created Side Bet Game.

This side bet game begins with the player's goal of being dealt two Aces. These Aces can be unsuited (which would require a minimum of one deck) or suited (which would require a minimum of two decks). In either case, there is no maximum number of decks. As the process of continuing to allow Aces to be split moves forward, additional decks are required in order to present the possibility of obtaining suited Aces.
For example, consider a Blackjack game which allows Aces to be split three times for a total of four hands. In order for a player to start with suited Aces, split once, split twice and split three times as additional suited Aces are received, this would require a minimum of four decks of cards to a maximum of ad infinitum.
Similarly, in considering the Ten value hit cards to be received on these Aces, they can be of a specified rank (for example, jacks) and possibly suited. Because there are choices to be made in this side bet game as to the payout hands and progression of hands, each created side bet game will define, in itself, the minimum number of decks to be used in conjunction with the goal hands to be achieved.
This side bet game in Blackjack has been developed for commercial play in a casino environment. One main issue has been to consider the underlying game rules (which vary from casino to casino) of allowing Aces to be split once only or multiple times. Commonplace is one split yet some casinos allow multiple splits. These games have been created for one split and three splits.
Game A. The first side bet game has two options (A1 and A2) to play depending on how many times a casino will allow Aces to be split.

Game A1.

For one split maximum, A1 envisions the goal of getting Aces to start, split, followed by matching Ten value cards (Ace, Ace split hit cards Queen, Queen for example), with the ultimate goal of getting suited Aces to start, split, followed by suited matching Ten value cards in the same suit as beginning suited Aces (Ace Hearts, Ace Hearts, Split, hit cards King Hearts, King Hearts for example). This game assumes only one split with at least two decks.

Game A2

For multiple splits on a pair of Aces, a casino will typically allow for a maximum of three splits for a total of four hands. Since, probabilities for split Aces beyond three times are extremely small, game (A2) has been created for Aces to be split a maximum of three times.
A2 envisions the goal of getting Aces to start, split, followed by additional Aces and matching Ten value cards (as the hit cards on the Aces), split 2 and split 3 with additional matching Ten value cards as the hit cards thus achieving four 21s with matching Ten value cards (Ace, Ace, Split 1, Ten, Ace, Split 2, King, Ace, Split 3, Jack, Queen). This side bet game assumes three splits with at least one deck.
Game B. The second side bet game has two options again, B1 and B2, depending on how many times a casino will allow Ace to be split.

Game B1

For one split maximum, B1 envisions the goal of getting Aces to start, split, followed by Ten value cards (Ace, Ace Split, Jack, King), with the ultimate goal of getting suited Aces to start, split, followed by suited Ten value cards that follow in the same suit as beginning two suited Aces (Ace Diamonds, Ace Diamonds, Split, hit cards, Jack Diamonds, Ten Diamonds for example). This game assumes only one split with at least two decks.

Game B2

For multiple splits on a pair of Aces a casino will typically allow for a maximum of three times for a total of four hands. Since probabilities for split Aces beyond three times are extremely small, game (B2) has been created for Aces to be split a maximum of three times.
B2 envisions the goal of getting Aces to start, split, followed by additional Aces and/or Ten value cards (as the hit cards on the Aces), split 2 and split 3 thus achieving four 21 value hands (Ace, Ace, Split 1, Ten, Ace, Split 2, King, Ace, Split 3, Jack, Queen). The ultimate goal would be to start with suited Aces, split and receive additional suited Aces, split 2 and split 3 with suited Ten value cards as the hit cards, in the same suite as the Aces (for example, Ace Spades, Ace Spades, split 1, hit cards Ten Spades, Aces Spades, Split 2, hit cards King Spades, Ace Spades, Split 3 hit cards Jack Spades, Queen Spades thus achieving four 21s all cards suited). This side bet game assumes three splits with at least four decks.
One embodiment of the present invention is to allow the Aces to be split once only as disclosed in Game A1 and B1 above. The second embodiment of the invention is to allow multiple splits of Aces, which if allowed typically follows that Aces be split a maximum of three times for a total of four hands, Game A2 and B2.
Game A1. The side bet game begins with the assumption that Aces are allowed to be split once only. The goal of this side bet game A1 is to be a dealt a pair of Aces, either suited or unsuited, split them and the receive two matching Ten value cards (Tens, Jacks, Queens or Kings), either suited or unsuited.
The initial goal of a player who places this side bet is to be dealt two Aces (either suited or unsuited) in the initial two cards. If a player receives the sought after two Aces, the player then automatically splits the two cards (which requires an additional regular wager) and receives only one card per Ace (in most casinos) with the goal of obtaining two 21's with two matching Ten value cards (Tens, Jacks, Queens, Kings), either suited or unsuited thus getting two 21 value hands (otherwise known as Blackjack except these hands receive payouts in the ratio of 1 to 1 instead of payouts of 3 to 2 as in normal Blackjack). The ultimate goal is getting suited Aces (in hearts for example), splitting them, and getting two matching Ten value cards (Kings for instance) which are suited and in the same suit as the Aces (i.e. two King of Hearts).
The present invention furthermore anticipates payouts could be made upon attainment of the following:
Game A1. Aces are allowed to be split once only.

- 1. Being dealt 1^stcard Ace and 2^ndcard non-Ace.
- 2. Being dealt two unsuited Aces.
- 3. Being dealt two suited Aces (this requires the use of at least two card decks).
- 4. Upon either 2. or 3. above occurring, splitting the Aces and being dealt two Ten value cards, preferably matching Ten value cards(i.e. Tens, Jacks, Queens, or Kings) suited or unsuited, equaling two 21 value hands.
- 5. A Jackpot hand which for instance could require suited Aces and two suited matching Ten value cards (in the same suit as the Aces) For example, player dealt Ace of hearts, Ace of hearts, Split, dealt King of hearts, King of hearts which results in a Jackpot Hand).

The method of playing this unique game is exemplified by the following typical example:

Supersplit DoubleMatch 21 or Mirror 21s

Assumptions:
Playing Blackjack with 6 decks
Dealer allows maximum of 1 split on pair of Aces for a total of 2 hands.
6 Decks=312 Cards, Aces=24, Kings(K), Queens(Q), Jacks(J), Tens(N)=24, Ten Value card(T)=96, Y=216=non TVC, AA=Playable Aces(dealer does not have Blackjack) s=suited


1^stCard Ace: Ace and non Ace
= 24/312 × 288/311
= .076923077 × .926045016
= .071234232 or 1 in 14.04 hands
Pair of Aces(dealer gets Blackjack): Ace, Ace, Ace, TVC or Ace, TVC,
Ace, Ace
= (24/312 × 23/311 × 22/310 × 96/309) × 2
= (.076923077 × .073954984 × .070967742 × .310679612) × 2
= ( [.005688845] × .070967742 × .310679612) × 2
[1 in 175.78 hands]
= (.000125429) × 2
= .000250858

So, Playable Aces(AA)=0.005688845−0.000250858=0.005437987 Or 1 in 183.89 hands.


Pair of playable Aces split with no 2 TVCs:
AAY1 + AATY
= (.005437987 × 214/310 × 1) + (.005437987 × 96/310 × 214/309)
= (.005437987 × .690322581) + (.005437987 × .309677419 × .692556634)
= (.003753965) + (.001166280)
= .004920245
Payout for AA = Pair of Aces where dealer gets Blackjack + playable Aces with no 2 TVCs =
.000250858 + .004920245 = .005171103 or 1 in 193.38 hands.
Pair of Suited Aces(dealer gets Blackjack):
AAAsT + ATAsA
= (24/312 × 31/311 × 5/310 × 96/309) × 2
= (.076923077 × .099678457 × .016129032 × .310679612) × 2
= (.000038422) × 2
= .000076844 or 1 in 13,013.38 hands.

So, Playable Suited Aces(AAs)	= (24/312 × 5/311) − .000076844
	= (.076923077 × .016077170) − .000076844
	= .001236705 − .000060222

[So suited Aces comes up every 1 in 808.60 hand]

= .001176483 or 1 in 849.99 hands.

Pair of playable suited Aces split with no 2 TVCs:

AAsY1 + AAsTY

= (.001176483 × 214/310 × 1) + (.001176483 × 96/310 × 214/309)

= (.001176483 × .690322581) + (.001176483 × .309677419 × .692556634)

= (.000812153) + (.000252319)

= .001064472

Or 1 in 939.43 hands.

Payout for AAs = Pair of suited Aces where dealer gets Blackjack + playable suited Aces with no

2 TVCs = .000076844 + .001064472 = .001141316.

Two 21s

AATT - two double match 21s

= (.005437987 × 96/310 × 95/309) − .000125348

= (.005437987 × .309677419 × .307443366) − .000125348

= .000517741 − .000125348

= .000392393 or 1 in 2,548.47 hands.

Two DoubleMatch 21s

AATT(match) =

= (AAKK + AAQQ + AAJJ + AANN) − two suited double match 21s

= (.005437987 × 96/310 × 23/309) − .000001474

= (.005437987 × .309677419 × .074433657) − .000001474

= .000125348 − .000001474

= .000123874 or 1 in 8,072.72 hands.

Two Suited DoubleMatch 21s, all cards suited (requires AAs to start)

AAsTTs(match)=

= AAsKKs + AAsQQs + AAsJJs + AAsNNs

= .001176483 × 24/310 × 5/309

= .001176483 × .077419355 × .016181230

= .000001474 or 1 in 678,426.05 hands.

SUPERSPLIT DOUBLEMatch 21 or Mirror 21s

- Side bet game in Blackjack
- Aces allowed to be split once for a total of 2 hands.


Side Bet $1

Initial two cards:	Payouts	Probability =	$Per Hand to payout

1^stCard Ace	$3	.071234232 =	$.2137
Pair of Aces	$25	.005171103 =	$.1293
Pair of Aces Suited	$50	.001141316 =	$.0571

Pair of Aces split (requires additional regular bet) with additional hit cards.

Two 21s

$500

.000392393 =

$.1962

DoubleMatch Hands

Two DoubleMatch (AJ AJ mixed suits, AK AK mixed suits for example)

21s

$1000

.000123874 =

$.1239

Two Suited DoubleMatch 21s (AT AT all cards suited, AQ AQ all cards

suited for example), requires AA suited.

$50,000.00	.000001474 =	$.0737
		$.7939

All payout are non cumulative. Player is paid out at highest payout achieved.
A pair of Aces split once is required for all 21 payouts.
$1−0.7939=$0.2061

- or
- House makes 20.61% on each dollar wagered.

Game A2. The side bet game begins with the assumption that Aces are allowed to be split three times for a total of four hands. The goal of this side bet game A2 is to be a dealt a pair of Aces, split them(for the first time) and get additional Aces and matching Ten value cards, whereby any additional pair of Aces are split for a second and third time for a total of four hands with the end goal of receiving matching Ten value cards, for a total of four 21 value hands(i.e. end hands, Ace, King-Ace, King-Ace, King-Ace, King)
The present invention furthermore anticipates payouts could be made upon attainment of the following:
Game A2. Aces are allowed to be split three times for a total of four hands.

- 1. Being dealt 1^stcard Ace and 2^ndcard non-Ace.
- 2. Being dealt two Aces (no regard to suit).
- 3. Upon 2 above occurring, splitting the Aces for the 1^sttime and being dealt additional Aces, split for the 2^ndand 3^rdtime and matching Ten value cards, (matching the previous dealt Ten value cards), for a goal of four 21 value hands.
- 4. A Jackpot hand which for instance could be four 21 value hands with matching Ten value cards( Ace, Ten-Ace, Ten-Ace, Ten-Ace, Ten for example)

Supersplit QuadrupleMatch 21

Assumptions:
Playing Blackjack with 6 decks
Dealer allows maximum of 3 splits on pair of Aces for a total of 4 hands.
6 Decks=312 Cards, Aces=24, Kings(K), Queens(Q), Jacks(J), Tens(N)=24, Ten Value card(T)=96, Y=216=non TVC, AA=Playable Aces(dealer does not have Blackjack) s=suited, X=non TVC and non Ace=192

So, Playable Aces(AA)=0.005688845−0.000250858=0.005437987

- Or 1 in 183.89 hands.


Pair of playable Aces split with no Aces and no 2 TVCS:
AA((No Ace and No TVC) and no Ace) + AA(T and (no TVC and no Ace))
= (.005437987 × 192/310 × 287/309) + (.005437987 × 96/310 × 192/309)
= (.005437987 × .619354839 × .928802589) + (.005437987 × .309677419 × .621359223)
= (.003128248) + (.001046382)
= .004174630
Payout for AA = Pair of Aces where dealer gets Blackjack + playable Aces with no Aces or 2
TVCs = .000250858 + .004174630 = .004425488 or 1 in 225.96 hands.
Two 21s
= AATT + (AATATX × 6) + (AAAATTXX × 12) + (AATAXATX × 48)
= AATT + (AATATX × 6) + (AAAATTXX × 60)
= .000517741 + .000138771 + .000059639
= .000716151 Or 1 in 1,396.35 Hands.
So Part 1, AATT is
= (.005437987 × 96/310 × 95/309)
= (.005437987 × .309677419 × .307443366)
Part 2, (AATATX × 6)
= ((.005437987 × 96/310 × 22/309 × 95/308 × 192/307) × 6)
= ((.005437987 × .309677419 × .071197411 × .308441558 × .625407166) × 6)
= .000023129 × 6
= .000138771
Part 3, (AAAATTXX × 60)
= ((.005437987 × 22/310 × 21/309 × 96/308 × 95/307 × 192/306 × 191/305) × 12)
= ((.005437987 × .070967742 .067961165 × .311688312 × .309446254 .627450980 × .626229508) × 12) × 5
= .000011928 × 5
= .000059639
Two DoubleMatch 21s
= AATTm + (AATATmX × 6) + (AAAATTmXX × 12) + (AATAXATmX × 48)
= AATTm + (AATATmX × 6) + (AAAATTmXX × 60)
= .000125348 + .000033601 + .000014440
= .000173389 Or 1 in 5,767.38 Hands.
So Part 1, AATTm is
= (.005437987 × 96/310 × 23/309)
= (.005437987 × .309677419 × .074433657)
= .000125348 or 4.13 times harder than just AATT
Part 2, (AATATmX × 6)
= ((.005437987 × 96/310 × 22/309 × 95/308 × 192/307) × 6)
= ((.005437987 × .309677419 × .071197411 × .308441558 × .625407166) × 6)
= .000023129 × 6
= .000138771 divided by 4.13
= .000033601
Part 3, (AAAATTmXX × 60)
= ((.005437987 × 22/310 × 21/309 × 96/308 × 95/307 × 192/306 × 191/305) × 12)
= ((.005437987 × .070967742 .067961165 × .311688312 × .309446254 .627450980 × .626229508) × 12) × 5
= .000011928 × 5
= .000059639 divided by 4.13
= .000014440
Three 21s
= (AAATTT × 2) + (AAAATTTX × 4) + (AATAATTX × 16)
= .000022647 + .000001957 + .000008642
= .000033246 Or 1 in 30,078.81 Hands.
So Part 1, (AAATTT × 2)
= (.005437987 × 22/310 × 96/309 × 95/308 × 94/307) × 2
= (.005437987 × .070967742 × .310679612 × .308441558 × .306188925) × 2
= .000011323 × 2
= .000022647
Part 2, (AAAATTTX × 4)
= ((.005437987 × 22/310 × 21/309 × 96/308 × 95/307 × 94/306 × 192/305) × 4)
= ((.005437987 × .070967742 × .067961165 × .311688312 × .309446254 × .307189543 ×
.629508197) × 4)
= .000000489 × 4
= .000001957
Part 3, (AATAATTX × 16)
= ((.005437987 × 96/310 × 22/309 × 21/308 × 95/307 × 94/306 × 212/305) × 16)
= ((.005437987 × .309677419 × .071197411 × .068181818 × .309446254 × .307189543 ×
.695081967) × 16)
= .000000540 × 16
= .000008642
Three TripleMatch 21s(17.65 times harder than Three 21s)
= (AAATTmTm × 2) + (AAAATTmTmX × 4) + (AATAATmTmX × 16)
= .000001283 + .000000111 + .000000490
= .000001884 Or 1 in 530,785.56 Hands.
So Part 1, (AAATTmTm × 2)
= (.005437987 × 22/310 × 96/309 × 23/308 × 22/307) × 2
= (.005437987 × .070967742 × .310679612 × .074675325 × .071661238) × 2
= .000000642 × 2
= .000001283
Part 2, (AAAATTmTmX × 4)
= ((.005437987 × 22/310 × 21/309 × 96/308 × 23/307 × 22/306 × 192/305) × 4)
= ((.005437987 × .070967742 × .067961165 × .311688312 × .074918567 × .071895425 ×
.629508197) × 4)
= .000000028 × 4
= .000000111
Part 3, (AATAATmTmX × 16)
= ((.005437987 × 96/310 × 22/309 × 21/308 × 23/307 × 22/306 × 212/305) × 16)
= ((.005437987 × .309677419 × .071197411 = .068181818 × .074918567 × .071895425 ×
.695081967) × 16)
= .000000031 × 16
= .000000490
Four 21s
= (AAAATTTT) + (AAATATTT × 4)
= .000000237 + .000000948
= .000001185 Or 1 in 843,881.86 Hands.
So Part 1, (AAAATTTT)
= (.005437987 × 22/310 × 21/309 × 96/308 × 95/307 × 94/306 × 93/305)
= (.005437987 × .070967742 × .067961165 × .311688312 × .309446254 × .307189543 ×
.304918033)
= .000000237
Part 2, + (AAATATTT × 4)
= ((.005437987 × 22/310 × 96/309 × 21/308 × 95/307 × 94/306 × 93/305) × 4)
= ((.005437987 × .070967742 × .310679612 × .068181818 × .309446254 × .307189543 ×
.304918033) × 4)
= .000000237 × 4
= .000000948
Four QuadrupleMatch 21s
= (AAAATTmTmTm) + (AAATATmTmTm × 4)
So Part 1, (AAAATTmTmTm) × 5
= (.005437987 × 22/310 × 21/309 × 96/308 × 23/307 × 22/306 × 21/305)
= (.005437987 × .070967742 × .067961165 × .311688312 × .074918567 × .071895425 ×
.068852459) × 5
= .000000003 × 5
= .000000015 or 1 in 66,666,666.67 hands

SUPERSPLIT QuadrupleMatch 21

- Side bet game in Blackjack
- Aces allowed to be split three times for a total of 4 hands.


Side Bet $1

Initial two cards:	Payouts	Probability =	$Per Hand to payout

1^stCard Ace	$3	.071234232 =	$.2137
Pair of Aces	$25	.004425488 =	$.1106

Pair of Aces split(requires additional regular bet) with additional

hit cards being Aces, additionally split and matching Ten value cards.

Two 21s

$100

.000716151 =

$.0716

Two DoubleMatch (AJ AJ mixed suits, AK AK mixed suits for examples)

21s	$1,000	.000173389 =	$.1734
Three 21s	$3,000	.000033246 =	$.0997

Three TripleMatch (AQ AQ AQ mixed suits for example)

21s	$30,000	.000001884 =	$.0471
Four 21s	$50,000	.000001185 =	$.0593

Four Quadruple Match (AK AK AK AK mixed suits for example)

21s	$1,000,000	.000000015 =	$.0150
			$.7904

All payout are non cumulative. Player is paid out at highest payout achieved.
A pair of Aces split once is required for all 21 payouts.
$1−0.7904=$0.2096

- or
- House makes 20.96% on each dollar wagered.

Game B1. The side bet game begins with the assumption that Aces are allowed to be split once only. The goal of this side bet game B1 is to be a dealt a pair of Aces, either suited or unsuited, split them and the receive two Ten value cards (Tens, Jacks, Queens or Kings), either suited or unsuited.
The initial goal of a player who places this side bet is to be dealt two Aces (either suited or unsuited) in the initial two cards. If a player receives the sought after two Aces, the player then automatically splits the two cards (which requires an additional regular wager) and receives only one card per Ace (in most casinos) with the goal of obtaining two 21's with two Ten value cards(Tens, Jacks, Queens, Kings), either suited or unsuited thus getting two 21 value hands (otherwise known as Blackjack except these hands receive payouts in the ratio of 1 to 1 instead of payouts of 3 to 2 as in normal Blackjack). The ultimate goal is getting suited Aces, splitting them, and getting two suited Ten value cards (Ace Hearts, Ace Hearts, Split, King Hearts, Jack Hearts)
The present invention furthermore anticipates payouts could be made upon attainment of the following:
Game B1. Aces are allowed to be split once only.

- 1. Being dealt 1^stcard Ace and 2^ndcard non-Ace.
- 2. Being dealt two unsuited Aces.
- 3. Being dealt two suited Aces (this requires the use of at least two card decks).
- 4. Upon either 2. or 3. above occurring, splitting the Aces and being dealt two Ten value cards(i.e. Tens, Jacks, Queens, or Kings) suited or unsuited, equaling two 21 value hands.
- 5. A Jackpot hand which for instance could require suited Aces and two suited Ten value cards (in the same suit as the Aces) For example, player dealt Ace of hearts, Ace of hearts, Split, dealt Queen of hearts, Ten of hearts which results in a Jackpot Hand).

Suited Supersplit 21


1^stCard Ace: Ace and non Ace
= 24/312 × 288/311
= .076923077 × .926045016
= .071234232 or 1 in 14.04 hands
Pair of Aces (dealer gets Blackjack): Ace, Ace, Ace, TVC or Ace, TVC,
Ace, Ace
= (24/312 × 23/311 × 22/310 × 96/309) × 2
= (.076923077 × .073954984 × .070967742 × .310679612) × 2
= ( [.005688845] × .070967742 × .310679612) × 2
[1 in 175.78 hands]
= (.000125429) × 2
= .000250858

So, Playable Aces(AA)=0.005688845−0.000250858=0.005437987

- Or 1 in 183.89 hands.


Pair of playable Aces split with no TVCs:
AAYY
= .005437987 × 214/310 × 213/309
= .005437987 × .690322581 × .689320388
= .002587685
Payout for AA = Pair of Aces where dealer gets Blackjack + playable
Aces with no TVCs = .000250858 + .002587685 = .002838543 or 1
in 352.29 hands.
Pair of Suited Aces(dealer gets Blackjack):
AAAsT + ATAsA
= (24/312 × 31/311 × 5/310 × 96/309) × 2
= (.076923077 × .099678457 × .016129032 × .310679612) × 2
= (.000038422) × 2
= .000076844 or 1 in 13,013.38 hands.

[So suited Aces comes up every 1 in 808.60 hand]

= .001176483 or 1 in 849.99 hands.

Pair of playable suited Aces split with no TVCs:

AAsYY

= .001176483 × 214/310 × 213/309

= .001176483 × .690322581 × .689320388

= .000559833 or 1 in 1,786.25 hands.

Payout for AAs = Pair of suited Aces where dealer gets Blackjack +

playable suited Aces with no

TVCs = .000076844 + .000559833 = .000636677.

One 21

AATY + AAYT

= (.005437987 × 96/310 × 214/309) × 2

= (.005437987 × .309677419 × .692556634) × 2

= .001166280 × 2

= .002332560 or 1 in 428.71 hands.

Two 21s

AATT-two suited 21s

= (.005437987 × 96/310 × 95/309) − .000006780

= (.005437987 × .309677419 × .307443366) − .000006780

= .000517741 − .000006780

= .000510961 or 1 in 1,957.10 hands.

Two Suited 21s, all cards suited(requires AAs to start)

AAsTTs

= .001176483 × 24/310 × 23/309

= .001176483 × .077419355 × .074433657

= .000006780 or 1 in 147,492.63 hands

SUITED SUPERSPLIT 21


Side Bet $1

Initial two cards:	Payouts	Probability =	$Per Hand to payout

1^stCard Ace	$3	.071234232 =	$.2137
Pair of Aces	$25	.002838543 =	$.0710
Pair of Aces Suited	$50	.000636677 =	$.0318

Pair of Aces split(requires additional regular bet) with additional hit cards.

One 21	$100	.002332560 =	$.2333
Two 21s	$400	.000510961 =	$.2044

Two Suited 21s (AK AT all cards suited, AJ AQ all cards

suited for example), requires AA suited.

$10,000.00	.000006780 =	$.0678
		$.8220

All payout are non cumulative. Player is paid out at highest payout achieved.
A pair of Aces split once is required for all 21 payouts.
$1−0.8220=$0.1780

- or
- House makes 17.80% on each dollar wagered.

Game B2. The side bet game begins with the assumption that Aces are allowed to be split three times and that four decks are being played. The goal of Game B2 is getting Aces to start, split, followed by additional Aces, split 2 and split 3 and/or Ten value cards (as the hit cards on the Aces), thus achieving four 21 value hands (Ace, Ace, Split 1, Ten, Ace, Split 2, King, Ace, Split 3, Jack, Queen). The ultimate goal would be to start with suited Aces, split and receive additional suited Aces, split 2 and split 3 with suited Ten value cards as the hit cards, in the same suite as the Aces (for example, Ace Spades, Ace Spades, split 1, hit cards Ten Spades, Aces Spades, Split 2, hit cards King Spades, Ace Spades, Split 3 hit cards Jack Spades, Queen Spades thus achieving four 21s all cards suited)
The present invention furthermore anticipates payouts could be made upon attainment of the following:
Game B1. Aces are allowed to be split three times.

- 1. Being dealt 1^stcard Ace and 2^ndcard non-Ace.
- 2. Being dealt two unsuited Aces.
- 3. Being dealt two suited Aces.
- 4. Upon either 2. or 3. above occurring, splitting the Aces for the 1^sttime and being dealt additional Aces, split for the 2^ndand 3^rdtime and Ten value cards(i.e. Tens, Jacks, Queens, or Kings) suited or unsuited.
- 5. A Jackpot hand which for instance could require suited Aces, split, hit cards additional suited Aces, split 2 and split 3, with suited Ten value cards (in the same suit as the Aces) For example, player dealt Ace of hearts, Ace of hearts, Split 1, dealt Queen of hearts, Ace of hearts, Split 2, dealt Jack of Hearts, Ace of Hearts, Split 3, dealt King Hearts, Ten Hearts which results in a Jackpot Hand).

Suited Supersplit 21

Assumptions:
Playing Blackjack with 6 decks
Dealer allows maximum of 1 split on pair of Aces for a total of 2 hands.
6 Decks=312 Cards, Aces=24, Kings(K), Queens(Q), Jacks(J), Tens(N)=24, Ten Value card(T)=96, Y=216=non TVC, AA=Playable Aces(dealer does not have Blackjack) s=suited, X=non Ten and non Ace=192

So, Playable Aces(AA)=0.005688845−0.000250858=0.005437987

- Or 1 in 183.89 hands.

[So suited Aces comes up every 1 in 808.60 hand]

= .001176483 or 1 in 849.99 hands.

Pair of playable suited Aces split with no TVCs:

AAsYY

= .001176483 × 214/310 × 213/309

= .001176483 × .690322581 × .689320388

= .000559833 or 1 in 1,786.25 hands.

TVCs = .000076844 + .000559833 = .000636677.

One 21

(AATX × 2) + (AAXATX × 6) + (AAAATYYY × 4) + (AAXAXAYT × 16)

= .002332561 + .000279000 + .000010721 + .000078005

= .002700287

Part 1

= (AATY × 2)

= (.005437987 × 96/310 × 214/309) × 2

= (.005437987 × .309677419 × .692556634) × 2

= .001166280 × 2

= .002332561

Part 2

(AAXATX × 6)

= (.005437987 × 192/310 × 22/309 × 96/308 × 191/307) × 6

= (.005437987 × .619354839 × .071197411 × .311688312 × .622149837) × 6

= .000046500 × 6

= .000279000

Part 3

(AAAATYYY × 4)

= (.005437987 × 22/310 × 21/309 × 96/308 × 212/307 × 211/306 × 210/305) × 4

= (.005437987 × .070967742 × .067961165 × .311688312 × .690553746 × .689542484 ×

.688524590) × 4

= .000002680 × 4

= .000010721

Part 4

= AAXAXAYT × 16

= (.005437987 × 192/310 × 22/309 × 191/308 × 21/307 × 212/306 × 211/305) × 16

= (.005437987 × .619354839 × .071197411 × .620129870 × .068403909 × .692810458 ×

.691803279) × 16

= .000004875 × 16

= .000078005

Two 21s

AATT-two suited 21s

= .000510961 or 1 in 1,957.10 hands.

= (AATT) + (AATATX × 6) + (AAAATTYY × 6) + (AAXAXATT × 24)

= .000517741 + .000138048 + .000007275 + .000023856

= .000686920

= Part 1

= (AATT)

= (.005437987 × 96/310 × 95/309)

= (.005437987 × .309677419 × .307443366)

= .000517741

Part 2

(AATATX × 6)

= (.005437987 × 96/310 × 22/309 × 95/308 × 191/307) × 6

= (.005437987 × .309677419 × .071197411 × .308441558 × .622149837) × 6

= .000023008 × 6

= .000138048

Part 3

(AAAATTYY × 6)

= (.005437987 × 22/310 × 21/309 × 96/308 × 95/307 × 212/306 × 211/305) × 6

= (.005437987 × .070967742 × .067961165 × .311688312 × .309446254 × .692810458 ×

.691803279) × 6

= .000001212 × 6

= .000007275

Part 4

= AAXAXATT × 24

= (.005437987 × 192/310 × 22/309 × 191/308 × 21/307 × 96/306 × 95/305) × 24

= (.005437987 × .619354839 × .071197411 × .620129870 × .068403909 × .313725490 ×

.311475410) × 24

= .000000994 × 24

= .000023856

Two Suited 21s, all cards suited(requires AAs to start)

AAsTTs

= .001176483 × 24/310 × 23/309

= .001176483 × .077419355 × .074433657

= .000006780 or 1 in 147,492.63 hands

Three 21s

= (AAATTT × 2) + (AAAATTTX × 4) + (AATAATTX × 16)

= .000022647 + .000001957 + .000008642

= .000033246 Or 1 in 30,078.81 Hands.

So Part 1, (AAATTT × 2)

= (.005437987 × 22/310 × 96/309 × 95/308 × 94/307) × 2

= (.005437987 × .070967742 × .310679612 × .308441558 × .306188925) × 2

= .000011323 × 2

= .000022647

Part 2, (AAAATTTX × 4)

= ((.005437987 × 22/310 × 21/309 × 96/308 × 95/307 × 94/306 × 192/305) × 4)

= ((.005437987 × .070967742 × .067961165 × .311688312 × .309446254 × .307189543 ×

.629508197) × 4)

= .000000489 × 4

= .000001957

Part 3, (AATAATTX × 16)

= ((.005437987 × 96/310 × 22/309 × 21/308 × 95/307 × 94/306 × 212/305) × 16)

= ((.005437987 × .309677419 × .071197411 × .068181818 × .309446254 × .307189543 ×

.695081967) × 16)

= .000000540 × 16

= .000008642

= .000510961 or 1 in 1,957.10 hands.

Three 21s All Cards Suited

= (AAsAsTsTsTs × 2) + (AAsAsAsTsTsTsX × 4) + (AAsTsAsAsTsTsX × 16)

= .000000058 + .000000001 + .000000016

= .000000075 Or 1 in 13,333,333.33 Hands.

So Part 1, (AAsAsTsTsTs × 2)

= (.005437987 × 4/310 × 24/309 × 23/308 × 22/307) × 2

= (.005437987 × .012903226 × .077669903 × .074675325 × .071661238) × 2

= .000000029 × 2

= .000000058

Part 2, (AAsAsAsTsTsTsY × 4 )

= ((.005437987 × 4/310 × 3/309 × 24/308 × 23/307 × 22/306 × 216/305) × 4)

= ((.005437987 × .012903226 × .009708738 × .077922078 × .074918567 × .071895425 ×

.708196721) × 4)

= .000000001

Part 3, (AAsTssAAsTsTsX × 16)

= ((.005437987 × 4/310 × 3/309 × 24/308 × 23/307 × 22/306 × 216/305) × 16)

.708196721) × 16)

= .000000001 × 16

= .000000016

Four 21s

= (AAAATTTT) + (AAATATTT × 4)

= .000000237 + .000000948

= .000001185 Or 1 in 843,881.86 Hands.

So Part 1, (AAAATTTT)

= (.005437987 × 22/310 × 21/309 × 96/308 × 95/307 × 94/306 × 93/305)

= (.005437987 × .070967742 × .067961165 × .311688312 × .309446254 × .307189543 ×

.304918033)

= .000000237

Part 2, + (AAATATTT × 4)

= ((.005437987 × 22/310 × 96/309 × 21/308 × 95/307 × 94/306 × 93/305) × 4)

= ((.005437987 × .070967742 × .310679612 × .68181818 × .309446254 × .307189543 ×

.304918033) × 4)

= .000000237 × 4

= .000000948

Four Suited 21s

= (AAsAsAsTsTsTsTs) × 5

= .000000237

= .000001185 Or 1 in 843,881.86 Hands.

So Part 1, = (AAsAsAsTsTsTsTs) × 5

= (.005437987 × 4/310 × 3/309 × 24/308 × 23/307 × 22/306 × 21/305) × 5

= (.005437987 × .012903226 × .009708738 × .077922078 × .074918567 × .071895425 ×

.068852459) × 5

= 9.843 − 11

SUITED SUPERSPLIT 21

- Side bet game in Blackjack
- Aces allowed to be three times for a total of 4 hands.


Side Bet $1

			$Per Hand
Initial two cards:	Payouts	Probability =	to payout

1^stCard Ace	$3	.071234232 =	$.2137
Pair of Aces	$25	.002838543 =	$.0710
Pair of Aces Suited	$50	.000636677 =	$.0318

Pair of Aces split(requires additional regular bet) with additional

splits/hit cards.

One 21	$75	.002700287 =	$.2025
Two 21s	$200	.000686920 =	$.1374
Three 21s	$1,000	.000033246 =	$.0332
Four 21s	$10,000	.000001185 =	$.0119
Two Suited 21s	$10,000	.000006780 =	$.0678
Three Suited 21s	$500,000	.000000075 =	$.0375
Four Suited 21s	$100,000,000	9.843-11 =	$.0098
			$.8166
			Cost Per Hand

All payout are non cumulative. Player is paid out at highest payout achieved.
A pair of Aces split once and or additional times is required for all 21 payouts.
$1−0.8166=$0.1834

- or
- House makes 18.34% on each dollar wagered.

Game (C1). The side bet game begins with the assumption that Aces are allowed to be split once only. The goal of this side bet game is to be a dealt a pair of Aces, either mixed colors, Red, Black or suited, split them and the receive two Ten value cards(Tens, Jacks, Queens or Kings), either mixed colors, Red, Black, suited in the same color/suit as the colored two Aces, if applicable.
The initial goal of a player who places this side bet is to be dealt two Aces (either Mixed colors, Red, Black, or suited) in the initial two cards. If a player receives the sought after two Aces, the player then automatically splits the two cards (which requires an additional regular wager) and receives only one card per Ace (in most casinos) with the goal of obtaining two 21's with two Ten value cards (Tens, Jacks, Queens, Kings), either mixed colors, Red, Black, or suited, thus getting two 21 value hands (otherwise known as Blackjack except these hands receive payouts in the ratio of 1 to 1 instead of payouts of 3 to 2 as in normal Blackjack). The ultimate goal is getting suited (colored) Aces (in Hearts for example), splitting them, and getting two suited (colored) Ten value cards (King of Hearts and Queen of Hearts) which are suited and in the same suit as the Aces.
The present invention furthermore anticipates payouts could be made upon attainment of the following:
Game C1. Aces are allowed to be split once only.

- 1. Being dealt 1^stcard Ace and 2^ndcard non-Ace.
- 2. Being dealt two Mixed color Aces.
- 3. Being dealt two colored Aces.
- 4. Being dealt two suited Aces
- 5. Upon either 2, 3 or 4 above occurring, splitting the Aces and being dealt two Ten value cards (i.e. Tens, Jacks, Queens, or Kings) either mixed colors, Red, Black, or suited, equaling two 21 value hands.
- 6. A Jackpot hand which for instance could require suited (colored) Aces and two suited Ten value cards (in the same suit as the Aces). For example, player dealt Ace of hearts, Ace of hearts, Split, dealt King of hearts, Queen of hearts which results in a Jackpot Hand.

Supersplit ColorMatch 21

Assumptions

Playing Blackjack with 6 decks
Dealer allows maximum of 1 split on pair of Aces for a total of 2 hands.
6 Decks=312 Cards, Aces=24, Kings(K), Queens(Q), Jacks(J), Tens(N)=24, Ten Value card(T)=96, Y=216=non TVC, AA=Playable Aces(dealer does not have Blackjack) s=suited, c=same color Ten value cards=48


1^stCard Ace: Ace and non Ace
= 24/312 × 288/311
= .076923077 × .926045016
= .071234232 or 1 in 14.04 hands
Pair of Aces(dealer gets Blackjack): Ace, Ace, Ace, TVC or Ace, TVC,
Ace, Ace
= (24/312 × 23/311 × 22/310 × 96/309) × 2
= (.076923077 × .073954984 × .070967742 × .310679612) × 2
= ([.005688845] × .070967742 × .310679612) × 2
[1 in 175.78 hands]
= (.000125429) × 2
= .000250858

So, Playable Aces(AA)=0.005688845−0.000250858=0.005437987

- Or 1 in 183.89 hands.


Pair of playable Aces split with no 2 TVCs:
AAY1 + AATY
= (.005437987 × 214/310 × 1) + (.005437987 × 96/310 × 214/309)
= (.005437987 × .690322581) + (.005437987 × .309677419 ×
.692556634)
= (.003753965) + (.001166280)
= .004920245
Payout for AA = Pair of Aces where dealer gets
Blackjack + playable Aces with no 2 TVCs = .000250858 +
.004920245 = .005171103 or 1 in 193.38 hands.
Pair of colored Aces split with no 1 or 2 TVCs
AAcYY
= 24/312 × 11/311 × 214/310 × 213/309
= .076923077 × .035369775 × .690322581 × .689320388
= .002720752 × .690322581 × .689320388
= .001294679
Pair of Suited Aces (dealer gets Blackjack):
AAAsT + ATAsA
= (24/312 × 31/311 × 5/310 × 96/309) × 2
= (.076923077 × .099678457 × .016129032 × .310679612) × 2
= (.000038422) × 2
= .000076844 or 1 in 13,013.38 hands.

[So suited Aces comes up every 1 in 808.60 hand]

= .001176483 or 1 in 849.99 hands.

Pair of playable suited Aces split with no 1 or 2 TVCs:

AAsYY

= .001176483 × 214/310 × 213/309

= .001176483 × .690322581 × .689320388

= .000559833 Or 1 in 1,786.25 hands.

Payout for AAs = Pair of suited Aces where dealer gets

Blackjack + playable suited Aces with no 1 or 2

TVCs == .000076844 + .000559833 = .000636677

One 21

AATY + AAYT

= (.005437987 × 96/310 × 214/309) × 2

= (.005437987 × .309677419 × .692556634) × 2

= .001166280 × 2

= .002332560 or 1 in 428.71 hands.

Two 21s

AATT-two colored 21s

= (.005437987 × 96/310 × 95/309) − .000064078

= (.005437987 × 309677419 × .307443366) − .000064078

= .000517725 − .000064078

= .000453663 or 1 in 2,204.28 hands.

Two colored Aces split with 2 colored TVCs

AAcTcTc

= 24/312 × 11/311 × 48/310 × 47/309

= .076923077 × .035369775 × .154838710 × .152103560

= .002720752 × .154838710 × .152103560

= .000064078 or 1 in 15,605.98 hands.

Two Suited 21s, all cards suited(requires AAs to start)

AAsTsTs

= .001176483 × 24/310 × 23/309

= .001176483 × .077419355 × .074433657

= .000006780 or 1 in 147,492.63 hands

Supersplit ColorMatch 21

DoubleColor 21


Side Bet $1

Initial two cards:	Payouts	Probability =	$Per Hand to payout

1^stCard Ace	$3	.071234232 =	$.2137
Pair of Mixed	$25	.005171103 =	$.1293
Color Aces
Pair of Colored	$50	.001294679 =	$.0647
Aces
Pair of Suited Aces	$100	.000636677 =	$.0637

Pair of Aces split(requires additional regular bet) with additional hit cards.

Two 21s	$200	.000453663 =	$.0907
Two 21s,	$2000	.000064078 =	$.1282
all cards same color
Two 21s,	$10,000.00	.000006780 =	$.0678
all cards suited
			$.7581

All payout are non cumulative. Player is paid out at highest payout achieved.
A pair of Aces split once is required for all 21 payouts.
$1−0.7581=$0.2419

- or
- House makes 24.19% on each dollar wagered.

Game C2. The side bet game begins with the assumption that Aces are allowed to be split three time for a possible total of four hands. The goal of this side bet game is to be a dealt a pair of Aces, either mixed colors or the same color (Red, Black), split them and the receive additional Aces, split for the 2^ndand 3^rdtime and receive Ten value cards (Tens, Jacks, Queens or Kings), either mixed colors, or the same color (Red, Black) in the same color/suit as the colored two Aces, if applicable.
The initial goal of a player who places this side bet is to be dealt two Aces (either mixed colors, or the same color(Red or Black), in the initial two cards. If a player receives the sought after two Aces, the player then automatically splits the two cards (which requires an additional regular wager) and receives only one card per Ace (in most casinos) with the goal of obtaining additional Aces, split for the 2^ndand 3^rdtime and receiving 21's with Ten value cards (Tens, Jacks, Queens, Kings), either mixed colors, or the same color (Red, Black) in the same suit as the colored Aces, if applicable, thus getting 21 value hands (otherwise known as Blackjack except these hands receive payouts in the ratio of 1 to 1 instead of payouts of 3 to 2 as in normal Blackjack). The ultimate goal is getting colored Aces, splitting them, and getting additional Aces, in the same color as the 1^sttwo Aces, split for the 2^ndand 3^rdtime and receiving colored Ten value cards in the same suit as the Aces. For example, Ace Hearts, Ace Diamonds, split 1, hit cards Ten Diamonds, Ace Hearts, split 2, hit cards, Queen Hearts, Ace Diamonds, split 3, hit cards King Diamond, Jack Hearts thus achieving four 21 value hands with cards all of the same color.
The present invention furthermore anticipates payouts could be made upon attainment of the following:
Game C2. Aces are allowed to be split three time for a total of four hands.

- 1. Being dealt 1^stcard Ace and 2^ndcard non-Ace.
- 2. Being dealt two Mixed color Aces.
- 3. Being dealt two colored Aces.
- 4. Upon either 2 or 3 above occurring, splitting the Aces (split 1) and being dealt additional Aces, split 2, split 3 and receiving Ten value cards (i.e. Tens, Jacks, Queens, or Kings) either mixed colors, or colored (Red, Black), equaling four 21 value hands.
- 5. A Jackpot hand which for instance could require colored Aces, split 1, and getting additional Aces in the same color as the 1^sttwo Aces, split 2 and split 3 and receiving colored Ten value cards (in the same suit as the Aces) which results in a Jackpot Hand. For example, player dealt Ace of Hearts, Ace of Diamonds, Split 1, dealt Queen of Hearts, Ace of Hearts, split 2, dealt Jack of Diamonds, Ace of Diamonds, Split 3, dealt, Ten of Hearts, King of Diamonds which results four 21 all of the cards the same color.

Supersplit ColorMatch 21

Assumptions

So, Playable Aces(AA)=0.005688845−0.000250858=0.005437987

- Or 1 in 183.89 hands.

[So suited Aces comes up every 1 in 808.60 hand]

= .001176483 or 1 in 849.99 hands.

Pair of playable suited Aces split with no 1 or 2 TVCs:

AAsYY

= .001176483 × 214/310 × 213/309

= .001176483 × .690322581 × .689320388

= .000559833 Or 1 in 1,786.25 hands.

1 or 2 TVCs == .000076844 + .000559833 = .000636677

One 21

AATY + AAYT

= (.005437987 × 96/310 × 214/309) × 2

= (.005437987 × .309677419 × .692556634) × 2

= .001166280 × 2

= .002332560 or 1 in 428.71 hands.

Two 21s

AATT-two colored 21s

= (.005437987 × 96/310 × 95/309) − .000064078

= (.005437987 × .309677419 × .307443366) − .000064078

= .000517725 − .000064078

= .000453663 or 1 in 2,204.28 hands.

Two colored Aces split with 2 colored TVCs

AAcTcTc

= 24/312 × 11/311 × 48/310 × 47/309

= .076923077 × .035369775 × .154838710 × .152103560

= .002720752 × .154838710 × .152103560

= .000064078 or 1 in 15,605.98 hands.

Three 21s

= (AAATTT × 2) + (AAAATTTX × 4) + (AATAATTX × 16)

= .000022647 + .000001957 + .000008642

= .000033246 Or 1 in 30,078.81 Hands.

So Part 1, (AAATTT = 2)

= (.005437987 × 22/310 × 96/309 × 95/308 × 94/307) × 2

= (.005437987 × .070967742 × .310679612 × .308441558 × .306188925) × 2

= .000011323 × 2

= .000022647

Part 2, (AAAATTTX × 4)

.629508197) × 4)

= .000000489 × 4

= .000001957

Part 3, (AATAATTX × 16)

.695081967) × 16)

= .000000540 × 16

= .000008642

= .000510961 or 1 in 1,957.10 hands.

Three 21s All Cards Same Color

=AAcAcTcTcTc + (AAcAcAcTcTcTcX × 4) + (AAcTcAcAcTcTcX × 16)

= .000000312 + .000000025 + .000000096

= .000000433 Or 1 in 2,309,468.82 Hands.

So Part 1, AAcAcTcTcTc

= 24/312 × 11/311 × 10/310 × 48/309 × 47/308 × 46/307

= .076932077 × .035369775 × .032258065 × .155339806 × .152597403 × .149837134

= (.076932077 × .035369775) × .032258065 × .155339806 × .15297403 × .149837134

= .002720752 × .032258065 × .155339806 × .152597403 × .149837134

= .000000312

Part 2, (AAcAcAcTcTcTcY × 4)

= ((.002720752 × 10/310 × 9/309 × 48/308 × 47/307 × 46/306 × 212/305) × 4

= ((.002720752 × .032258065 × .029126214 × .155844156 × .153094463 × .150326797 ×

.695081967) × 4)

= .000000006 × 4

= .000000025

Part 3, (AAcTcAcAcTcTcX × 16)

= ((.002720752 × 48/310 × 10/309 × 9/308 × 47/307 × 46/306 × 212/305) × 16)

= ((.002720752 × .154838710 × .032362460 × .029220779 × .153094463 × .150326797 ×

.695081967) × 16)

= .000000006 × 16

= .000000096

Four 21s

= (AAAATTTT) + (AAATATTT × 4)

= .000000237 + .000000948

= .000001185 Or 1 in 843,881.86 Hands.

So Part 1, (AAAATTTT)

= (.005437987 × 22/310 × 21/309 × 96/308 × 95/307 × 94/306 × 93/305)

.304918033)

= .000000237

Part 2, + (AAATATTT × 4)

= ((.005437987 × 22/310 × 96/309 × 21/308 × 95/307 × 94/306 × 93 /305) × 4)

= ((.005437987 × .070967742 × .310679612 × .068181818 × .309446254 × .307189543 ×

.034918033) × 4)

= .000000237 × 4

= .000000948

Four 21s, All cards same color

= (AAcAcAcTcTcTcTc) × 5

= .000000007 Or 1 in 142,857,142.9 Hands.

So Part 1, = (AAcAcAcTcTcTcTc) × 5

= (.002720752 × 10/310 × 9/309 × 48/308 × 47/307 × 46/306 × 45/305) × 5

= (.002720752 × .032258065 × .029126214 × .155844156 .153094463 × .150326797 ×

.147540984) × 5

= .000000001 × 5

= .000000007

Supersplit ColorMatch 21


Side Bet $1

Initial two cards:	Payouts	Probability =	$Per Hand to payout

1^stCard Ace	$3	.071234232 =	$.2137
Pair of Mixed	$25	.005171103 =	$.1293
Color Aces
Pair of Colored	$50	.001294679 =	$.0647
Aces

Pair of Aces split(requires additional regular bet) with additional Aces,

split 2 and split 3 and hit cards.

Two 21s	$200	.000453663 =	$.0907
Two 21s,	$2000	.000064078 =	$.1282
all cards same color
Three 21s	$3,000	.000033246 =	$.0997
Three 21s,	$30,000	.000000433 =	$.0130
all cards same color
Four 21s	$50,000	.000001185 =	$.0593
Four 21s,	$1,000,000	.000000007 =	$.0070
all cards same color
			$.8056

All payout are non cumulative. Player is paid out at highest payout achieved.
A pair of Aces split once and/or twice and/or three times is required for all 21 payouts.
$1−0.8056=$0.1944

- or
- House makes 19.44% on each dollar wagered.

Claims

1. A method of playing a computerized or live card game with a dealer, at least one player, and two or more standard decks of cards comprising the steps of:

a. a player placing a bet for a standard Blackjack game wherein Aces are allowed to be split once only,

b. the same player as in (a) above placing an additional side bet with the goal of being dealt two Aces,

c. if two Aces are dealt to the player in (b), the player splits those two Aces (split no. 1) into two separate hands, and then is dealt an additional card for each of the two split hands and continues playing Blackjack in each of said two separate hands,

d. if Ten value cards are dealt to the player in (c) above, the casino pays off according to a pre-established scheme for the final hands that are created by the split of the initial two Aces.

2. A method of playing a computerized or live card game as in claim 1 where the Ten value cards are matching Ten value cards.

3. A method of playing a computerized or live card game as in claim 1 where the Aces are of the same suit.

4. A method of playing a computerized or live card game as in claim 1 where the matching Ten value cards are of the same suit.

5. A method of playing a computerized or live card game as in claim 1 where the suited Aces and suited matching Ten value cards are of the same suit.

6. A method of playing a computerized or live card game with a dealer, at least one player, and one or more standard decks of cards comprising the steps of:

a. a player placing a bet for a standard Blackjack game wherein Aces are allowed to be split up to three times,

b. the same player as in (a) above placing an additional side bet with the initial goal of being dealt two Aces,

c. if two Aces are dealt to the player in (b), the player splits those two Aces (split no. 1) into two separate hands, and then is dealt an additional card for each of the two split hands and continues playing Blackjack in each of said two separate hands with the additional goal of being dealt additional Aces,

d. if additional Aces are dealt to the player in (c) above, the player splits the hands with the additional Aces (splits 2 and further split 3) and continues playing Blackjack with the additional goal of being dealt Ten value cards on the split Aces.

7. A method of playing a computerized or live card game as in claim 6 where the Ten value cards are matching Ten value cards.

8. A method of playing a computerized or live card game as in claim 6 with at least 4 or more standard decks of cards.

9. A method of playing a computerized or live card game as in claim 6 where the Aces are of the same suit.

10. A method of playing a computerized or live card game as in claim 6 where the matching Ten value cards are of the same suit.

11. A method of playing a computerized or live card game as in claim 6 where the suited Aces and suited matching Ten value cards are of the same suit.

12. A method of playing a computerized or live card game with a dealer, at least one player, and two or more standard decks of cards comprising the steps of:

13. A method of playing a computerized or live card game as in claim 12 where the Aces are of the same suit.

14. A method of playing a computerized or live card game as in claim 12 where the Ten value cards are of the same suit.

15. A method of playing a computerized or live card game as in claim 12 where the suited Aces and suited Ten value cards are of the same suit.

16. A method of playing a computerized or live card game with a dealer, at least one player, and four or more standard decks of cards comprising the steps of:

17. A method of playing a computerized or live card game as in claim 16 where the Aces are of the same suit.

18. A method of playing a computerized or live card game as in claim 16 where the Ten value cards are of the same suit.

19. A method of playing a computerized or live card game as in claim 16 where the suited Aces and suited Ten value cards are of the same suit.

20. A method of playing a computerized or live card game with a dealer, at least one player, and one or more standard decks of cards comprising the steps of:

21. A method of playing a computerized or live card game as in claim 20 where the Aces are of the same color.

22. A method of playing a computerized or live card game as in claim 20 where the Aces are of the same suit.

23. A method of playing a computerized or live card game as in claim 20 where the Ten value cards are of the same color.

24. A method of playing a computerized or live card game as in claim 20 where the Ten value cards are of the same suit.

25. A method of playing a computerized or live card game as in claim 20 where the same color Aces and same color Ten value cards are of the same color.

26. A method of playing a computerized or live card game as in claim 20 where the same suited Aces and same suited Ten value cards are of the same suit.

27. A method of playing a computerized or live card game with a dealer, at least one player, and two or more standard decks of cards comprising the steps of:

28. A method of playing a computerized or live card game as in claim 27 where the Aces are of the same color.

29. A method of playing a computerized or live card game as in claim 27 where the Ten value cards are of the same color.

30. A method of playing a computerized or live card game as in claim 27 where the colored Aces and colored Ten value cards are of the same color.