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Ask the Wizard #22

I think your website is one of the best gambling sites on the net, and I have a question that I am hoping you would be able to answer. There is an Indian casino a few hours from my house that has some odd rules and regulations. I was wondering if you would be able to determine the house edge from these rules:

  • There is a 50-cent charge on each hand if your wager is between $5 and $25
  • There is a $1 charge on each hand if your wager is $26 to $500.
  • You can split up to 4 times, not including aces
    -You can double on any first two cards
  • You can double after a split
  • Dealer stands on all 17s
  • Early surrender is available
  • One card on each hand if you split aces
  • $100 bonus on getting 7 cards without busting
  • $100 bonus on getting 3 7's in a row
  • $500 bonus for getting 3 Blackjacks in a row
  • $10,000 bonus for getting 4 Blackjacks in a row

Any help you can give is appreciated.


I'm going to assume that eight decks are used and that the bonuses are not applicable if the dealer has a blackjack. Using the Blackjack Count Analzyer I get a player advantage of 1.4% with a $5 bet. Unfortunately, this advantage is not available at greater bet sizes as the comparable benefit of the bonuses decreases and the additional fee for bets of $25 or over. With a $24 bet the house edge is 1.4%, and with a $25 bet it is 3.3%. This certainly is a very interesting game. If you play it let me know how you do.

Thanks for answering my questions. I want to deposit as much as I can at good casinos to take advantage of the "new player" bonus but how much do you think is too much? I don't like wasting an opportunity to get a large 20% bonus by getting a small 20% bonus, but how much is too much? What's been your experience?

Scott T.

Don't worry about depositing too much money. I almost always deposit the maximum when playing for a bonus. What is much more likely to arouse suspicion is not playing enough.

I like to play the game liars poker with dollar bills. what is the probability of getting any 1,2,3,4, or 5 of the same number on a bill. thank you. If I am playing with 3 people, what is the probability of any 1 number showing up.

John from New York

First let me answer the unasked question on the probability that a specific number will show up n times on a random bill. There are 8 digits on a bill so the probability of n of a specific number is combin(8,n)*0.1n*0.98-n/108. Here is a table showing the probability for 0 to 8 of a specific number.

Specific Number Oddsin Liar's Poker

Number Probability
8 0.00000001
7 0.00000072
6 0.00002268
5 0.00040824
4 0.00459270
3 0.03306744
2 0.14880348
1 0.38263752
0 0.43046721
Total 1.00000000

The next table shows the probability of every possible type of bill, categorized by the number of each n-of-a-kind. For example, the serial number 66847680 would have one three of a kind, one pair, and three singletons, for a probability of 0.1693440.

General Probabilities in Liar's Poker

8 o.a.k. 7 o.a.k. 6 o.a.k. 5 o.a.k. 4 o.a.k. 3 o.a.k. 2 o.a.k. 1 o.a.k. Probability
1 0.0000001
1 1 0.0000072
1 1 0.0000252
1 2 0.0002016
1 1 0.0000504
1 1 1 0.0012096
1 3 0.0028224
2 0.0000315
1 1 1 0.0020160
1 2 0.0015120
1 1 2 0.0211680
1 4 0.0211680
2 1 0.0020160
2 2 0.0141120
1 2 1 0.0423360
1 1 3 0.1693440
1 5 0.0846720
4 0.0052920
3 2 0.1270080
2 4 0.3175200
1 6 0.1693440
8 0.0181440
Total 1.0000000

o.a.k. = "of a kind"

For more information, see my page on liars poker.

What are some of the best online casinos to play blackjack on, with the following criteria in mind - Best player odds, fewest decks, fairness?

Robert from Hamilton, Canada

Assuming you put the greatest priority on player odds I would have to go with a Unified Gaming casino. You'll enjoy a player edge of 0.57% assuming you following the proper strategy.

Is there any mathematical proof you can provide that will prove a player sitting at "third base" on the blackjack table can’t change the outcome of the game by making bad decisions based on "basic strategy" I have had many people argue that poor decisions at third base, or anyplace on the table for that matter, cost them money. I would love to see the actual numbers on this if it is possible. Great site by the way. I love gambling, and your site is one of the best I have seen on the web. Actually has real proven info.

Mike Castelluccio from Lafayette, U.S.

Thanks for your kind words. Unfortunately I do not have any such proof at hand. If I did set about proving it myself I would use a computer simulation. However skeptics would probably claim something ridiculous, like that bad players disrupt the karma of the game, which can’t be replicated in a computer.

I’ve been a dealer in Vancouver, Canada for over six years. Having dealt all casino games (except craps) I’ve decided that a person’s best betting strategy would be to bet all their bankroll on a one-shot bet, preferably in bacarrat, and on Banker. My decision is based on the observation that the longer a player gambles, the more likely that the odds will get the best of them, and the more likely it is that they will lose everything. The one-shot method may not be entertaining, but surely it’d be more profitable (or I should say, "less damaging")

Mel C. from Coquitlam, BC, Canada

You’re absolutely right. The fewer bets actually made the better the odds are of actually winning. The expected loss is also a function of the total amount bet. If the player keeps circulating money back and forth between himself and the dealer the house edge will gradually grind the player down. However maximizing the odds of winning should not be the only objective to gambling. Having fun is also important. Plopping an entire bankroll on the table in one bet may not be as fun as playing it out gradually. It may also may have a greater chance at a large loss depending on how much play is involved in the alternative. If one really wants to cut down the house edge the best thing to do is put your money in the machine marked "change."

I have a few questions regarding blackjack: How often can one expect the dealer to bust and how often can a player expect to win four hands in a row?

John from Westminster, USA

When the dealer stands on a soft 17, the dealer will bust about 29.1% of the time. When the dealer hits on a soft 17, the dealer will bust about 29.6% of the time. According to my blackjack appendix 4, the probability of a net win is 42.42%. However, if we skip ties, the probability is 46.36%. So, the probability of a four wins in a row is 0.46364 = 4.62%.

Could you please tell me what are some of the better paying slot machine to play? Also about the placement of the machines that pay off the best? any help would be appreciated. I like slots but never win!!!!

Denise from Lowell, USA

Based on my research, the placement of the machine doesn't matter. Regarding what type of slot to play, choose something simple, not a game with fancy signage and video. My best advice is to switch to video poker.

Dear Mr. Wizard, thank you for your very informative website. My question is about baccarat. What are the good cards for the Player and what are the good cards for the Banker. Kindly give them in their order of strength. Thank you, and more power to you.

Herman from Manila, Philippines

I have a whole page on the topic of card counting in baccarat. Briefly, the best card for the Player is 4, and for the Banker is 6.