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Other Casino Games  FAQ
Tibby from St. Catharines, Canada
Thanks for pointing out this variation to me. They use different semantics to explain casino war at the Casino Niagara. What they fail to mention is that the original wager always loses if in the event of a tie.
What is really going on is they pay two times the Ante for a win after a tie, and three times the ante for a tie after a tie. The usual rules still pay two times the ante for a tie after a tie. This rule change decreases the house edge from 2.88% to 2.33%.
Bob P. from Lake Charles, Louisiana
I could talk about this all day. Part of my income is derived from analyzing games such as these. The gaming authorities require such analysis before a game can be licensed to play. Usually, these games are invented by an individual. Here in Nevada, after the game owner receives a license, then it must go through a 30day trial period. If the trial period went well, then the owner can then apply for a permanent license. The entire process is very slow and it is difficult to get a casino to be the guinea pig for the trial period. Casinos are actually quite risk averse in their business decisions. Yes, the game owner will usually seek a copyright to protect others from stealing the idea.
You can find much more information about the business of marketing casino table games at my Gaming Math site.
Ken L. from Boston, USA
Ask and ye shall receive. Please see my page on Catch a Wave.
Pattie from Arlington, USA
I have never seen solitaire played for money in Vegas. I understand in the early days of Vegas people wagered on the standard Klondike variation of solitaire but I don't anything else about it.
Billy O. from Vancouver, USA
I saw this at the World Gaming Expo, but have never studied it. After I move to Las Vegas in February I will be better at covering new games such as this.
Mark from Vancouver, Canada
Let's let d be the number of decks. The probability of a tie on the first round is (4*d1)/(52*d1)= 0.073955. The probability of a tie in the second round is 12*4*d/(52*d2)*(4*d1)/(52*d3)+(4*d2)/(52*d2)*(4*d3)/(52*d3) = 0.073974. Lets call p_{1} the probability of a tie in the first round and p_{2} the probability of a tie in the second round. Then the player return is p_{1}*(2*p_{2} +(1p_{2})/2*(12))= 0.023301. Multiply by 1 and you have the house edge of 2.33%. I hope I didn't go over this too quickly.
Moe from Philadelphia, USA
I’ve seen it at the Regent, New York New York, and Palace Station. I hear it is also at the Sunset Station and Santa Fe Station.
Bradford Wiley from Winthrop Harbor, U.S.
Thanks for the compliment. I just saw the game at the California casino here in Las Vegas, but it wasn’t open yet. I got the rule card and will work on when I have the chance. At this time I have no information about it at all.
Kara from Castaic, California
I’ve seen it there too, and fortunately took some notes. It is similar to Three Way Action as used to be found at the Las Vegas Club. In Triple Shot the player may make any combination of three bets. The first is a regular blackjack wager. The second is a poker hand. The third is a war bet. I don’t remember if the poker bet is based on the player’s or dealer’s hand but the best five out of six cards are used. If the blackjack hand doesn’t contain six cards then more are added to make six. The following odds table for the poker bet shows the house edge is 3.20%.
Triple Shot
Hand  Combinations  Probability  Pays  Return 
Royal flush  376  0.000018  100 to 1  0.001847 
Straight flush  1468  0.000072  30 to 1  0.002163 
Four of a kind  14664  0.000720  15 to 1  0.010804 
Full house  165984  0.008153  7 to 1  0.057071 
Flush  205792  0.010108  5 to 1  0.050542 
Straight  361620  0.017763  4 to 1  0.071050 
Three of a kind  732160  0.035963  3 to 1  0.107890 
Two pair  2532816  0.124411  2 to 1  0.248821 
Pair  2252472  0.110640  1 to 1  0.110640 
Nothing  14091168  0.692151  1 to 1  0.692151 
Total  20358520  1  0.031321 
Finally there is a war game, the player’s first card against the dealer’s up card, highest card win. In the event of a tie the player loses half. The house edge in the war game is 2.94%. I don’t know of any other casinos that have the game. It is probably in trial period and only at the Treasure Island.
"Anonymous" .
I don’t know. If you find out please tell me. I’m particularly interested because Cryptologic casinos just introduced two versions of Klondike solitaire.
"Anonymous" .
Fortunately I am a big James Bond fan and have all the Bond movies on DVD. I checked Dr. No and it seems he is playing Chemin De Fer. The scene was spoken in French, which doesn’t help me. There is a similar scene in For Your Eyes Only. In that movie it looks like Bond is playing baccarat, acting as the banker, but after the player acts he pauses and another character tells Bond, "The odds favor standing pat". This would imply that Bond had free will in whether to take a third card, an option you don’t have in baccarat. As I understand my gambling history, the American version of baccarat is a simplified version of Chemin De Fer, in which the drawing rules are predetermined. Incidentally, according to www.casinoinfo.com American baccarat originated at the Capri Casino in Havana, Cuba.
Tommy from Houston, Texas
Please see my faro page for the answer to that question.
Carlos from Lisbon
From my Sic Bo appendix we see the probability of a total of 5 or 16 is 6/216, a 6 or 15 is 10/216, a 7 or 14 is 15/216, and a 3 is 1/216. So on any one throw the probability of "big" winning is 31/216, "small" is 31/216, and "aces" is 1/216. The number of ways any of these could win is 2*31+1=63. So given that one of these events did occur, the probability that it was big is 31/63, small is 31/63, and aces is 1/63. The house edge on all three bets is 1.59%.
Annie from Prior Lake
Following is the median high hand according to the number of players. This is based on an assumption of independence between hands, which is not the case, but the table should still be a very close estimate.
Median Hand in Guts
Players  Median Hand 
1  K,10,2 
2  A,Q,8 
3  5,5,K 
4  9,9,7 
5  J,J,Q 
6  K,K,5 
7  A,A,7 
8  8,5,3 flush 
9  10,8,6 flush 
10  J,10,6 flush 
Fred from Buffalo
The standard deviation in Pick ‘em Poker is 3.87. The standard deviation in conventional video poker tends to run from about 4.4 to 6.4. I don’t have any risk of ruin tables for Pick ‘em Poker. So the best advice I can offer is to use the jacks or better table in my video poker appendix 1. Jacks or Better has the lowest standard deviation in that appendix at 4.42, so you can be a little more aggressive than that table calls for.
Mike H. from New Jersey
Generally speaking, you want to put it on a long shot. This is because you don’t get to keep the coupon on a win, which lowers the value by the probability of winning. The less the probability of winning the less the value is reduced. Following are three tables for the three games listed. You’ll see the best bet is a tie between the 12, 30, 60, triple, and any triple in sic bo.
Free Bet Coupon Value in Baccarat
Bet  Pays  Probability  Return 
Banker wins  0.95  0.458597  0.481484 
Player wins  1  0.446247  0.493175 
Tie  8  0.095156  0.761248 
Free Bet Coupon Value in Big Six
Bet  Pays  Probability  Return 
1  1  0.444444  0.444444 
2  2  0.277778  0.555556 
5  5  0.12963  0.648148 
10  10  0.074074  0.740741 
20  20  0.037037  0.740741 
Joker  40  0.018519  0.740741 
Logo  40  0.018519  0.740741 
Free Bet Coupon Value in Sic Bo
Bet  Pays  Probability  Return 
Small, Big  1  0.486111  0.486111 
4, 17  60  0.013889  0.833333 
5, 16  30  0.027778  0.833333 
6, 15  17  0.046296  0.787037 
7, 14  12  0.069444  0.833333 
8, 13  8  0.097222  0.777778 
9, 12  6  0.115741  0.694444 
10, 11  6  0.125  0.75 
Triple  180  0.00463  0.833333 
Any triple  30  0.027778  0.833333 
Double  10  0.074074  0.740741 
Ben B.
I must confess that my 0.17% figure was an error. I discovered the flaw in my analysis when I recently updated it for the Microgaming rules. To all those who played it because of my 0.17% figure, I apologize.
Costa from Ottowa, Canada
The probability that any given player will have a dragon is 4^{13}/combin(52,13) = 0.000106. The probability that exactly one player is dealt a Dragon could be closely approximated as 4*0.000106*(10.000106)^{3} = 0.000424, or 1 in 2,359.
Stephen from Lake Grove, NY
Usually these free bet coupons are limited to even money bets, so this is an interesting case. My advice is to use the free bet on a longshot, to minimize the effect of the rule that you lose the free bet, even if you win. The biggest longshot in Big Six is the joker/logo, with a probability of winning of 1/54. I’m not sure whether the Mohegan Sun pays 40 or 45 on the joker, but assuming 45 the value of the free bet is (1/54)×45 = 83.33% of face value. In Sic Bo the biggest longshots are on the six triples. I’m also not sure what they pay for a specific triple, but I would guess 180. In that case the value of any one of the six triple bets would be (1/216)×180 = 83.33% of expected value. So, we have a tie in terms of expected value. In that case I would go for the bet with the greater probability of winning, the joker/logo in Big Six, but that is up to you.
Paul from London
You're right, you can lower the element of risk by deviating from my strategy, and raising on hands with expected values of slightly less than 1. In your example, 5/2 has an expected value of 1.019987, under the Las Vegas rules. That means if you raise on that bet on average, then you can expected to lose about 1.02 times your original bet by the time the hand is over. After the initial raise, and possible additional raises after the flop and turn, the average wager on that hand will be 3.627374 units. The way I would look at it, making the raise bet is worth 0.0109987 units to the player, over 2.627374 additional units bet. The ratio of marginal additional win to marginal additional bets, by raising, is 0.0109987/2.627374 = 0.00761. That is less than the overall expected value of the game of 2.04%. So, if your goal is to minimize money lost to total money bet, including raises, then, yes, you should deviate from my basic strategy and raise on that hand. Other examples could be made in lots of games that involve raising.
To summarize, if you are trying to minimize money lost per hand, then you should follow the house edge minimizing strategies on this site. If you are trying to minimize money lost per total amount wagered, then you should opt to bet more on very borderline plays.
Kevin from Perth, Western Australia
The expected number of times any number will appear exactly n times in 12 games is combin (12,n)×(6/45)^{n}×(39/45)^{n12}. The following table shows the expected number of occurrences from 0 to 12.
Expected number of repeat numbers
Repeats  Expected 

0  8.0804888027 
1  14.9178254818 
2  12.6227754077 
3  6.4732181578 
4  2.2407293623 
5  0.5515641507 
6  0.0989986937 
7  0.0130547728 
8  0.0012552666 
9  0.0000858302 
10  0.0000039614 
11  0.0000001108 
12  0.0000000014 
Total  45 
So, to answer your question, you will see the same number exactly six times about 0.099 times per set of cards, or about once every 10.1 times. The same number appearing exactly seven times will happen 0.0131 times per set of cards, or once every 76.6 times.
Matthew from Fort Wayne, IN
I hope you're happy; I watched this scene over and over for at least an hour, trying to make sense of the rules. I’ve played guts lots of times, over many years and locations, and have never seen it played as was done in that movie. Let’s call the first player to act Player 1, and the second player to act (the dealer) Player 2. Here is my understanding of how they played.
 Both players ante (or reante).
 Each player gets two cards.
 Player 1 must declare “in” or “check.” If he checks, go to rule 4. If he goes in, go to rule 7.
 Player 2 must declare in or check. If he checks, go to rule 5. If he goes in, go to rule 6.
 Although two checks never happened in the movie, I assume both players would start over from step 1.
 The action goes back to player 1, who must declare in or fold. If he goes in go to rule 8. If he folds, go to rule 9.
 Player 2 must declare “in” or “fold.” If he goes in go to rule 8. If he folds, go to rule 9.
 The two hands are compared; and the higher hand wins. The winner collects the pot, and the loser must match it, creating a new pot. This is equivalent to the loser just paying the winner the amount of the pot. Although there was never a tie in the movie, I assume no money would move. Next, go to rule 10.
 When a player folds, the other player collects the pot. Then repeat with a new hand from step 1.
 An additional card is given to each player, to add to his existing 2card hand, making a 3card hand. The third card is dealt face down, on top of the faceup two card hand. I do not know whether straights or flushes counted at the 3card stage. I prefer to play where they do count (but not at the 2card stage).
 Steps 3 to 9 repeat. If both playes go "in," then go to rule 12.
 An additional two cards are given to each player, to add to his existing 3card hand, making a 5card hand. The fourth and fifth cards are dealt face down, on top of the faceup three card hand.
 Steps 3 to 9 repeat. Then start over at step 1.
If you watch the movie carefully, Huck should have lost $11,000 in total, when he had $10,000 to begin with. I watched the scene lots of times to try to find this missing $1,000. My best guess is that when he went in on the last twocard hand, he should have matched the $4,000 pot, but had only $3,000 left. I assume that, much as in regular poker, he could only stand to win what he was risking. In the last hand, Huck folded. I’m not sure if this was because his threecard hand couldn’t beat his father’s twocard hand on the table, or if he was forced to fold, because he didn't have the money to match the pot if he lost.
If my understanding of the rules or analysis of the scene is in error, I welcome correction.
Pete Braff from Long Beach
The house edge under that pay table is a comparatively low 1.85%. Kudos to the Borgata, assuming your information is correct.
Based on viewer feedback, the Borgata lowered the win on a three of a kind to 30 to 1 sometime during 2008.
Lon from Brooks, CA
My Super Pan 9 page shows the probability of a tie is 11.3314%. So if a tie paid 8 to 1, the expected return would be 9×0.113314 − 1 = 0.019826. Although a 1.98% player advantage is less than your figure, it is still a great bet. Where can I play it?
Vince from North Collins, NY
I'm told that game had to be pulled out of the U.S. casinos, because the game of patent infringement. According to the Fourth Quarter 2008 Statistical Report of the Nevada Gaming Control Board, the following are the table game counts in Clark County.
Clark County Table Game Count
Game  Tables 

21  2537 
Roulette  405 
Craps  334 
Other  243 
Baccarat  233 
Three Card Poker  208 
Pai Gow Poker  194 
Mini baccarat  143 
Let It Ride  98 
Pai Gow  80 
Wheel of Fortune (Big Six)  37 
Caribbean Stud Poker  22 
Sic Bo  1 
ChuckaLuck  1 
Unfortunately, they don't say what the 243 "other" games are, so this isn't of much help to answer your question, but it is still worth mentioning.
Albert from Uncasville
Not that you asked, but you have a 43.4% advantage if your first card is a jack. It is the dealer’s fault for flashing the card. Contrary to what some members of the casino staff, especially in security, incorrectly believe, you are legally allowed to make use of whatever information made available to you under normal playing conditions.
Morally, you should follow your own conscience. You have to live your own life. That said, I think most players, including me, would be okay with increasing the bet in that situation. For one thing, game security is not the player’s job. For another, the casinos take advantage of, if not rely on, player mistakes. For example, consider the big 6/8 bet in craps. The casinos have no compunction about accepting a bet on that, when the place bet on 6 or 8 pays on exactly the same thing, but has better odds. See if you are offered forgiveness if you foul your hand in pai gow poker, even if the correct setting is totally obvious.
If it happens again, don’t get too greedy, and act nonchalant. If you suddenly go from a $10 to a $500 bet, it will set off all kinds of red flags. A good dealer would realize why, and ultimately the bet would not be accepted, or a card would be burned.
Martin from Tallinn
I’m getting asked about this more and more frequently. Unfortunately, the number of combinations in this game would be an unholy gigantic figure. A bruteforce looping program might take thousands of years to finish. However, a good programmer can find short cuts. Weighing the costs and benefits, I don’t find this project to be a good use of my time. If I lived in Russia or the Baltics, I would likely feel differently.
For the benefit of other readers, Royal Poker is like Caribbean Stud Poker, with the following added options. It is my understanding that the player may invoke any or all of these options, except he may not invoke options 2 and 3 both.
 If the player can make two paying hands, which both beat the dealer, and neither hand is entirely within the other, then both are paid. I am not sure whether the ante and/or raise are paid twice. For example, if the player had six cards and could make a straight and a flush, then the player could be paid for both hands.
 The player may switch one to five cards for the price of the Ante.
 The player may buy a sixth card for the price of the Ante.
 The player may buy "insurance" before the dealer turns over his four facedown cards. The insurance bet pays even money if the dealer does not qualify.
 The player may force the dealer to switch his highest card for the next one in the deck for the price of the Ante wager.
 There is an "AA Bonus" side bet, which pays 7 to 1 if the player’s first five cards are a pair of aces or higher.
I can say that the AA Bonus side bet and Insurance Option should never be taken, and thus are not worth anything. The house edge on the AA Bonus is 12.99%. The following table shows the house edge on insurance to range from 8.57% to 33.57%, depending on the dealer’s up card.
Insurance in Russian Poker
Dealer’s Up Card  Combinations  Probability  Exp. Value 
A  132804  0.335714  0.328571 
K  132804  0.335714  0.328571 
Q  108528  0.457143  0.085714 
J  108732  0.456122  0.087755 
10  108936  0.455102  0.089796 
9  109140  0.454082  0.091837 
8  109140  0.454082  0.091837 
7  109140  0.454082  0.091837 
6  109140  0.454082  0.091837 
5  109140  0.454082  0.091837 
4  108936  0.455102  0.089796 
3  108732  0.456122  0.087755 
2  108528  0.457143  0.085714 
I also know from my page on Oasis Poker that just the option to switch cards lowers the house edge from 5.22% to 1.04%. I tend to think the rule about being doublepaid, getting to keep the sixth card (as opposed to switching), and forcing the dealer to switch a card will get the game to a worthwhile player advantage, if you knew the proper strategy. Sorry to pull a Fermat on you, but that is that best I can do at this time.
P.S. I have heard some casinos add a rule that if the player wins, then the ante bet only pushes. This would work significantly in the casino’s favor, I think wiping out any advantage.
Dave from Overland Park, KS
For those unfamiliar with the rules, in Pick ’Em Poker the player is dealt two cards, plus the choice of one of two more. The game then gives the player two more cards to complete a fivecard poker hand. The question at hand is what is the probability of having at least a pair of nines on the deal. Let’s call the players initial two cards that he must keep the "pocket," and the other two cards the "field." This could be accomplished the following ways:
 Four of a kind: 13 combinations
 High (9A) three of a kind: 1,152 combinations
 Low (28) three of a kind with the singleton in the field: 672 combinations
 Two high pairs: 540 combinations
 One high pair, one low pair, with at least one high card in the pocket: 1,260 combinations
 High pair, with at least one in the pocket: 31,680 combinations
Johnny from Cambodia
Assuming eight decks, the probability of winning is 52*combin(8,2)/combin(52*8,2) = 1,456/86,320 = 1.69%. The house edge is 13.98%.
At the Sky City casino in Auckland, New Zealand, both the player and dealer must make use of both his hole cards in Ultimate Texas Hold 'Em. How does this effect the odds compared to the usual rules where any five cards can be used?
"Anonymous" .
That rule increases the house edge from 2.19% to 7.97% and the Element of Risk from 0.53% to 1.90%. This is because the dealer won't qualify more often and it will be harder to win on the Blind bet, which requires a straight or better.
For more details of my analysis, please see my new page on the Auckland variant of Ultimate Texas Hold 'Em.
For discussion about this question, please see the thread ULTIMATE IN NEW ZEALAND in my forum at Wizard of Vegas.
That game Flip It at the Rio looks countable. Do you have any advice on which bet is the most vulnerable?
"Anonymous" .
The red and black bets seem the most vulnerable. I would do a simple red/black count, as follows:
 Let C = count (where red cards are +1 and black cards are 1)
 J = count of jokers left in the shoe
 if JC < 0 then bet on black
 If J+C < 0 then bet on red
For example, if after some play cards played are:
red = 100black = 75
jokers = 10
The remaining cards would be:
red = 108black =133
jokers = 14
The count would be +25. Jokers remaining  C = 1425 = 9. Because that is less than zero, bet on black, because there are more good cards left (133) than bad cards (122) on the black bet.