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Ask the Wizard #72

At bingogala.com they offer a $500 prize for a coverall within 54 calls. You told me earlier that the probability of that at least 1 card in 600 will get a coverall in 54 calls is 3.21%. So in 380 days (to date) at 8 sessions per day they should have 97.58 $500 winners, right? However I counted only 76 winners on their home page. When I brought up my question about this in chat my husband and I were both banned from the site which really sent my antenna up? Sorry to be a pest but if they are running an unscrupulous site I want to know how to figure it out so that I can shout it far and wide with facts. Thank you for any help you can give me in this matter.

Anonymous

First let me explain that this is a rather old question that I put on the back burner, bingogala has now been in operation for two years according to their home page. The probability of a coverall within 54 calls for a single card is combin(74-24,54-24)/combin(54,54) = 0.000054. The probability at least one card in 600 will get a coverall in 54 call is 1-(1-.000054)600 = 0.032121. The expected number of winners over 380 days at 8 sessions per day is 97.65. The standard deviation is (380*8*0.032121*(1-0.032121))1/2 = 9.72. So this is (97.58-76)/9.72 = 2.23 standard deviations south of expectations. The probability of 76 or fewer winners in a fair game is 1.30%. So this could either be explained by bad luck on the part of the players, or fewer than 600 players on average. Perhaps they didn’t get as many in the early days. So the evidence doesn’t warrant an accusation of foul play in my opinion.

I recently witnessed a strange event. I was watching five card draw poker, where you could only draw a maximum of 2 cards. One player drew 1 card and completed a heart flush. The dealer drew one card, and drew a spade flush. Naturally, the dealer’s flush was higher. There were 3 other players in the game. What are the odds of having two flushes in the same hand?

Ted from Mandeville, USA

Let’s define the probability of a flush of either getting one on the deal, or drawing to a 4-card flush. For the sake of simplicity we’ll assume a player will draw to a pat pair or straight with 4 to a flush. The probability of getting a flush on the deal (not including a straight/royal flush) is 4*(combin(13,5)-10)/combin(52,5) = 5108/2598960 = 0.0019654. The probability of being dealt a 4-card flush is 4*3*combin(13,4)*13/combin(52,5) = 111540/2598960 = 0.0429172. The probability of completing the flush on the draw is 9/47. So the overall probability of getting a 4-card flush and then completing it is 0.0429172*(9/47) = 0.0082182. So the total probability for a flush is 0.0019654 + 0.0082182 = 0.0101836. The probability that exactly 2 out 5 players receiving a flush is combin(5,2)* 0.01018362*(1-00.0101836)3 = 0.001006, or about 1 in 994.

Why is a straight a higher hand than a flush in the new casino game 3 card poker?

Joe from Sloatsburg, USA

The probability of a straight is less than a flush with 3 cards. The number of ways to form a flush is 4*(combin(13,3)-12) = 1096. The number of ways to form a straight is 12*(43-4) = 720.

As I have little experience of casinos and do not think I can memorize all the finer points of the information your site offers, what would you recommend I play on my forthcoming trip to Las Vegas?

Alastair from London, UK

I’d recommend craps or baccarat. In craps stick to the line bets and the odds. In baccarat bet on the banker every time.

Does shorter play, the number of hands not time increase my odds over the house edge? Playing 750 or under hands as opposed to playing over 2000 on a single visit.

Shuck from Las Vegas, USA

No, the number of hands does not affect the house edge. The amount you can expect to lose is the product of the house edge, average bet size, and number of bets.

Your internet newspaper column has not been updated since June. Are you OK? I hope so. I have a Black Jack basic strategy card and it is very beneficial. Are there basic strategy cards for electronic poker games? Thanks for your time.

Charlie from Shaumburg, Illinois

I'm not sure what Internet newspaper column you are referring to. However I'm okay. As a matter of fact you can get my own video poker strategies in a handy dandy strategy card at Custom Strategy Cards. The video poker cards may not be listed yet but I know the proprietor has them so just ask.

Update: The Custom Strategy Cards business no longer exists.

If I hold just the queen of clubs what are the odds (ten million to one etc.) of drawing to a royal flush?

Bradford from Houston, USA

There are combin(47,4) = 178365 ways to choose 4 cards out of the 47 remaining. Only one way will result in the three cards you need. So the probability is 1 in 178365.

I have two friends that have a bet on which game (craps or baccarat) have the best odds for the player. Could you help me settle this. They are both casino workers and are sure they are right.

Charline from Las Vegas

It depends on how the games are played. If optimal strategy is compared to optimal strategy then craps is better. By betting only the line bets and taking maximum odds the combined house edge in craps is well under 1%. The best you can do is baccarat is bet on the banker at a house edge of 1.06%. However it wouldn’t surprise me if the actual house edge in craps is higher, due to all the sucker bets players make.

LOVE the site! Question on Caribbean Stud. You suggest that a player should stay with any pair. On a low pair, you’re basically hoping the dealer does not qualify. If the dealer matches any card, other than a "2", you lose. The risk then, assuming a $10 bet, is $30 to win $10. While you just lose $10 if you fold. Is this a good move? I know you have the math to prove it, but on your simulator, I lose more often than not when I stay on a very low pair.

Dave from Cincinnati, Ohio

Thanks for the compliment. Trust me, you should raise on any pair, even a pair of deuces. It isn’t just that you hope the dealer won’t qualify, but you also win the ante and raise if the dealer gets an ace/king. You will still have a negative expectation on a low pair, but the expected loss by folding is even more.