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Ask the Wizard #65

While at Treasure Island in Las Vegas last week I noticed a game called Triple Shot which consisted of hands of War, Blackjack, and Poker (6 card stud). It looked pretty interesting but I would like to know all the rules and payout schedules. Can you help? Also can you tell me what other Vegas Strip casinos have the game?

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.

Do the five ten and twenty-five dollar machines pay off just a little better i seem to have a little better luck on them rather than the quarter machines which seem to swallow up a twenty fast?

Mario from Troy, New York

In general the higher the coinage the better the rate of return is. However in my own research I have seen plenty of exceptions, notably dollar machines that paid less than quarters.

I just received the e-mail bonus offer for Casino Grand Bay and downloaded their software. I was not able to locate their bonus requirement information but according to they require a player to bet 1x deposit to receive the bonus and then the player must bet 7x bonus before withdrawing the bonus. Assuming this is correct it sounds like a decent offer. However, it was also stated that Blackjack play does not qualify for the bonus requirement. Therefore, what game, if any, should be played to limit the risk of losing the bonus/deposit?

Joe from Ramona, USA

If only blackjack were excluded I would say craps. However many Internet casinos exclude craps to prevent players from betting on the pass and don’t pass at the same time, thus earning the bonus without risking much. Next I would consider video poker. Casino Grand Bay is a Microgaming casino which offers Jacks or Better video poker. Following the optimal strategy the return is 99.54%. If you use my intermediate strategy, which has a return of 99.54%. So I would go with that. Had this been another casino with stingy video poker I would have played baccarat, always betting on the banker.

After the first five cards are drawn on a video poker machine, are the remaining possible five cards you could draw predetermined? Or is it just a matter of when you hit the draw button that the cards are determined?

Joe from Las Vegas, USA

They are predetermined. Once you hit "deal" the first time both the deal and the draw cards are chosen.

What advantage does a 6-5 payoff on a blackjack add to the house?

Barabbas from Las Vegas, USA

It depends on the number of decks. I have only seen this rule in single decks games, so we’ll assume one deck. The probability of a blackjack in a single deck game is 2*(4/52)*(16/51)=0.0483. The probability of the dealer not having a blackjack, give that the player does have one, is 1-2*(3/50)*(15/49) = 0.963265. So the probability the player has a blackjack and the dealer doesn’t is 0.046492. The casinos keeps an extra 0.3 units every time this happens to the increase in the house edge is 0.3*0.046492 = 0.013948, or about 1.39%. This is a huge increase, making this game the worst blackjack game in Vegas.

Hi Wizard, you’ve got a great site. In double 0 roulette, I realize all the bets have the same high house edge, but I’m just finishing a stats course and it seems to me that not all the bets are quite the same due to their standard deviations. A $1 bet on Red, for instance, has an S.D. of 1.012019 while a $1 bet on a single number has an S.D. of 5.839971, according to my calculations. Thus, the expected probability of coming out ahead over 1, 100, and 10000 trials, respectively is 0.4793, 0.3015, and 0.0000 for an even-money bet, and 0.4964, 0.4641, and 0.1837 for a single number bet. Is my analysis correct? (I assumed normality) Thanks!

Mike from Toronto, Canada

Thanks for the compliment. First of all the standard deviation on any even money bet is 0.998614 and on a single number is 5.762617. The probability of coming out ahead by flat betting even money bets over 1, 100, and 10000 spins is 0.473684, 0.265023, and 0.00000007 respectively. The probability of coming out ahead by flat betting single number bets over 1, 100, and 10000 spins is 0.0263158, 0.491567, and 0.18053280 respectively. It seems you are trying to argue that single number bets are better because of the higher probability of finishing ahead over multiple bets. This is true, however the probability of a substantial loss is also much greater. Over a session the expected results always fall somewhere on a bell curve. With low volatility bets like red or black that bell curve is sharp and doesn’t stray far from a small loss. With high volatility bets like single numbers the bell curve is wide, allowing for a much wider range of net results, both good and bad.