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Ask the Wizard #56

I’m pretty sure this isn’t possible, but is there any way to count cards when playing blackjack in an online casino? P.S. Your site is great. Being a beginner it has given me lots of good advice.

Dustin from Austin, USA

Thanks for the compliments. Most online casinos shuffle the cards after every hand. At single deck casinos (Boss Media version 1, Microgaming, Unified Gaming) you can use the cards already on the table to alter your play sometimes. See my blackjack appendix3A for all the details. There are some casinos that play into a shoe a little way but not far, and have restrictive betting limits. I have yet to be convinced of any worthwhile opportunity on the Internet to count cards.

I was playing 3 card poker at the Venetian this weekend and a friend of mine drew 3 Queens in the same suit in 2 consecutively dealt hands. Was very curious as to what the odds are of that happening?

Bruce from Williston, Vermont

The probability of getting three queens in one hand is combin(4,3)/combin(52,3) = 0.000181. The probability of doing it twice in a row is 0.0001812, or 1 in 30525625. The probability of them being the same three suits both times is 0.0001812/4, or 1 in 122102500.

You go, wiz. Our local casino hands out promotional coupons, which act as a first-card ace in blackjack. From your BJ appendix, most hands containing an ace have a positive expectation, without counting the BJs you’ll get four out of every thirteen plays. Do you know the overall expectation of having an ace as your first card? Thanks.

Victor from Yakima, Washington

According to Stanford Wong’s ’Basic Blackjack’ he says the player’s edge given the first card is an ace is 50.5% (page 124). Your question however could be rephrased as, "what is the value of the ace, given that the other card is not a ten." Using an infinite deck for the sake of simplicity we can breakdown Wong’s number as follows: 0.505 = (4/13)*1.5 + (9/13)*x, where x is what you want to know. Doing some simple algebra we get x=28.5%.

What is the probability of being dealt a natural seven card straight flush in pai gow poker? I work in a casino and just saw this for the first time in 15 years. The lucky patron won $40,000.

Michael from South Haven, Mississippi

There are 32 possible natural straight flushes (4 ranks times 8 possible spans of 7 cards). There are combin(53,7) = 154143080 possible ways 7 cards can be drawn out of 53. So the answer is 32/154143080, or 1 in 4816971.