Ask the Wizard #90

I measure the value of a bet to be the expected return, not the probability of winning. So betting on all 38 numbers has a house edge of 2/38 = 5.26%, the same as for one number or any number of numbers covered. Although betting all 38 numbers has a 0% chance of showing a net win, the down side is losing only 5.26% of your total bets. If forced to bet and you want to minimize variance then you should bet all 38 numbers. A practical example is if you had promotional chips you had to bet and you don’t want to gamble bet get your exact expected value out of them. So to answer your question there is no optimal range of numbers. All ranges are equal in expected value.

They probably don’t have to. Once at the Tropicana in Atlantic City their pai gow poker rules said the house way was available upon request. So I requested it and they ran out of public copies and couldn’t show me a house copy because it didn’t have the Gambler’s Anonymous disclaimer on it. In my opinion the player should always have the right to know the rules of a game, but unfortunately all gaming authorities seem to think differently.

In "Mastering the Game of Let it Ride" Stanley Ko addresses this topic. Ko says, most of the value in seeing other player’s cards is when you have a borderline hand of 4 to an outside straight with no high cards or JQKA. Viewing a single card should not encourage you to "let it ride" but seeing a card that won’t help you should cause you to "let it ride." Ko doesn’t indicate that this can result in a negative house edge, and I doubt this chips away at the house edge much at all.

The answer is (4¹³/COMBIN(52,13))* (3¹³/COMBIN(39,13))* (2¹³/COMBIN(26,13)) = 1 in 61,204,166,001.

Good question. My educated guess is that if the index numbers were not rounded then it would be greater than 0 but less than one half. So it is getting rounded down to zero. Making the index number 1 would result in more of a rounded error, causing players in slightly positive decks to hit when they should stand.