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Ask the Wizard #217, and apparently other sites, now have a "Deal or No Deal" gambling game. The site says it has a house edge of 4.54%. The 26 cases range from 2% to 1000% of your bet. The $100 game uses these figures 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 50, 60, 70, 80, 90, 100, 110, 120, 130, 140, 150, 200, 1000. That makes a total of 2482, the 118 shortfall is the 4.54% edge (2482/2600 = 95.46%). Unlike the TV shows, the banker’s offer is always the true average of the remaining cases in every round. There is no mathematical advantage to wait for a better offer. Is there an optimal strategy that can be employed?

Andy B. from Embrun, ON

I agree with your math. The average of those cases is 95.46, for a house edge of 4.54% over the $100 bet. There is absolutely no strategy that will either help you or hurt you. You may as well fly by the seat of your pants.

I was just reading Dave Matthews column, where he wrote, "I went to play a little bit of video poker and was playing 26 lines at $1 each. The frequent video poker players out there will know why I was playing 26 lines." This was on a hundred line machine. Why play 26 lines?

Steven H. from Hilo, HI

I also play 26 lines at the $1 denomination frequently. The reason is if you get a win of $1,200 or more it necessitates a hand pay, which slows down your game, and obligates you to tip. At 26 lines, a dealt full house in 9/6 jacks, which I happen to know is what he was playing, will pay $5 × 9 × 26 = $1,170. One more line and you would have a hand pay at $1,200. If 26 lines, or $130 a bet, is too small, I’ll go up to 39 lines, where a dealt flush will pay $5 × 6 × 39 = $1,170. The next bend-point is at 59 hands, where a deal straight would be $5 × 4 × 59 = $1,180. However, I feel with 59 hands a three of a kind on the deal turns into a hand pay too often.

What is the average number of winning pass line bets a shooter will make?

Robert M from Summit, NJ

Here you go:

Average winning pass line bets = 1.244898
Average total pass line bets = 2.52510
Expected points made = 0.683673
Expected rolls = 6.841837

What casinos in Las Vegas have a small table, called a tub, for craps?

Dave P.

According to the the Bone Man at, here is where and when you can find the tubs:

One Tub at Wild, Wild West (probably open only evenings, weekdays, and on weekends).
One Tub at Ellis Island (probably open only evenings, weekdays, and on weekends).
One Tub at Circus Circus in West Casino section, hardly ever open unless on busy holiday.

2010 update: I hear the Ellis Island replaced the tub with a full craps table.

Recently, I was in a casino in Oklahoma, playing craps. There are a few rule changes to the "normal" craps rules. Instead of dice, the casino uses a deck of 54 cards (Aces through 6). The stickman will ask you for a number between 1-3. He’ll then burn that number of cards and then put the next two face up. That becomes the dice roll. After approximately half to 3/4 of the deck has been used, a new deck is brought in and the old deck is shuffled.

Also, if you want to make a bet on the table, you’ll have to pay a dollar ante to the casino. You pay only $1 per come out roll. Once the point is established you can bet as much/little as you’d like without another payment of ante. The table limits are from 5 dollars to 300 dollars.

If the dealer went through 39 cards (out of 54) before re-shuffling the deck, you can count/see 26 of those cards. Previously, you’ve said that if there are a lot of 5s and 6s left in the deck, you would bet the "yo 11" bet. Can you develop a more effective strategy and way for betting in this casino? I truly feel that this game is beatable. Would a count of high/low, like counting cards in blackjack, work? Thanks.

Chuck from New York

I still say hop bets, like the yo-11, are the way to go. Using chips, you could keep track of how many cards of each face are left in the decks.

With 26 unseen cards, if any one face had 6 left in the deck, you would have a 43.1% advantage on a hard hop bet (two of the same face), assuming it paid 30 to 1. With only 5 left, the house would have a 4.6% advantage.

The easy hops are even more exploitable. If the two dice sides in majority have at least 10 left combined, both with a minimum of 3 left, out of 26 unseen cards, then make an easy hop bet on those two numbers. If two numbers have 5 left, you will have a 23.1% advantage. If one has 4 and one has 6, you will have an 18.2% advantage. If one has 3 and one has 7, you will have a 3.4% advantage. All this assumes easy hop bets pay 15 to 1.

None of the above takes into consideration the $1 fee. As long as you are making large bets, it won’t make much difference.