Ask the Wizard #72
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.
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.
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.
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.
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.
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.
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.
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.
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.