Ask The Wizard #187

The Grand Victoria Casino in Elgin, Illinois offers a promotion called "Craps for Cash." A shooter wins a $4,000 cash bonus for making all six points on the same hand. All that's required is a $5 bet on the pass line. How does this affect the house edge on this particular game?

John B. from Riverside, Illinois

We can see from my analysis of the Fire Bet that the probability of a shooter making all six points is 0.000162435. So, the value of the promotion per shooter is $4,000 × 0.000162435 = 0.649739.

The next question to be asked is what is the expected loss per shooter. The house edge on the pass line bet is 7/495 = 1.414141%. The tricky part is how many pass line bets will a shooter make, on average.

There are four possible states the shooter can be in. Let's define each one as the expected number of future pass line bets for that shooter.

  • A = Come out roll
  • B = Point of 4 or 10 made
  • C = Point of 5 or 9 made
  • D = Point of 6 or 8 made

Here are the equations showing the probability of each state leading to the next state.

A = 1 + (12/36)*A + (6/36)*B + (8/36)*C + (10/36)*D
B = (1/3)*A
C = (2/5)*A
D = (5/11)*A

A little algebra results in A = 2.525510, the number of pass line bets made per shooter.

So, the expected loss per $5 shooter is $5*2.525510*0.0141414 = 0.178571.

The expected amount bet by the shooter is $5*2.525510=$12.627551.

Finally, the expected return is the expected win divided by the expected bet: (0.649739-0.178571)/12.627551 = 3.73127%. So the house edge is -3.73%.

I have a very complicated question, which divided a friend and me. In a three-person Texas Hold’em game two players hold K/3 off-suit, and one player has K/2 off-suit. Before the flop, which is the stronger hand the K/2 or either K/3?

Mirza from Uppsala, Sweden

The K/2 is much better, because the K/3 players may have to split the pot. As my three to five player Texas Hold’em calculator shows, the K/2 player can expect to win 42.96% of the pot, and each K/3 player 28.52%.
What agency oversees the Indian Casinos in California? Whom do I complain to? I have seen the automatic shufflers come up with blackjack too many times. When dealing, I have seen the dealers tap the table when I have an ace showing, as to signal the shuffler not to give me a ten, so I would not get 21/blackjack. Is there any truth to my theory? Additionally, I have hit on hard 14, when the dealer has a 4 up card. I know I should stay, but the dealer almost always gets a 5 or 6. This seems to have happened too many times to be coincidence! I know what I’m insinuating, but it just seems to happen too often. Is there a way of checking up on the casinos to make sure they are not cheating the public? Lastly, I was at the BJ table by myself and on a incredible winning streak, the pit boss came over and inserted about 10 cards into the deck. I left the table.

Davis from Carson

All I know of is the NIGC. However, as far as I know, there is no formal process to arbitrate a dispute between player and casino. Even if there were such a dispute process, with this lack of evidence, I think your odds would not look good. A good way to make a case would be to tally blackjacks and hands played, or fives and sixes against all cards played, and then have the results analyzed. Regarding the tapping of the table when you have an ace up, I think the dealers do it as a way of saying "good luck," because players tend to slap the table in that situation.
Great Site! Could pai gow poker be a positive expectation game if the other players bet enough while you are banking?

Michael from Knoxville, TN

Yes! The following table shows the house edge as both player and banker according to the number of other players. The last column shows the ratio of overall action as banker to player to break even. So with seven players, or six opponents, you would need to bet 13 times more as banker than player.

Required Banker Ratio to Break Even in Pai Gow Poker

Players House
2 0.2% 2.73% N/A
3 -0.02% 2.73% 136.5
4 -0.1% 2.73% 27.3
5 -0.15% 2.73% 18.2
6 -0.19% 2.73% 14.4
7 -0.21% 2.73% 13

There are a lot of free online video poker games available. However, I am looking for a version I can run without being connected to the Internet. Do you know of a free downloadable version of Jacks or Better that does not use the Internet while running? I’ve found some free download demos, but they still connect to a site when they run even though the game is loading locally. Just a nice basic, realistic (functionally) version would be great. Thanks.

Mark from Braham

I believe the free Winpoker demo will do that and never expire. The download is available at
I just started playing no limit Texas Hold’Em. My question is, when the small and large blinds have been posted and everyone has either checked or called and then comes the flop, what is the minimum bet that has to be made? Does it have to be at least equal to the large blind, or can it be of any amount (including less then the large blind)? Is it different after the turn and river cards?

Rick from Alpena

In a no limit game the minimum bet is whatever the big blind is. This is true at before and after the flop.
For pai gow poker at Mohegan Sun Casino in CT, the casino allows you to bet your commission (i.e. bet $21 to win $20). I see it as a small advantage because you are not paying commission on the extra 5% you are betting. Is it truly advantageous to do so? How does it change the house odds?

Jay R. from Shelton, CT

From my pai gow poker section, the probability of the banker winning is 29.91%. So instead of paying the usual 5% commission as player you are paying 4.76%. That will lower the house edge by 0.2991*(0.05-0.0476) = 0.07%.
Hi almighty Wizard. My friends and I had a bet about Texas Hold’Em. They said 7/2 always is the worst hand you can have, no matter what your opponent has. But I said 6/2 would have less chance of winning facing 7/2 pre-flop. Who is right?

Yester from Amsterdam

If a 7/2 off-suit faced off against a 6/2 off-suit, the possible outcomes would be as follows, according to my Texas Hold ’Em Calculator.

7/2 wins: 57.07%
6/2 wins: 25.13%
Tie: 17.80%

However that doesn’t prove that 7/2 is the superior hand in general. Considering only your own hand, according to my various power rating tables, 7/2 off-suit is worse than 6/2 off-suit. For four or fewer players, the worst hand is 3/2 off-suit.

So, if the bet was phrased as who would win between 6/2 and 7/2 offsuit, then you win. However that doesn’t prove that 7/2 is the better hand in general, only for that one situation.