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Ask the Wizard #90

I enjoy your site a great deal. This morning I was reading your reviews of online casinos and your experiences with them and it seemed you inevitably lost everything on your deposits. I found this discouraging. Then I saw that you requested donations and now understand why you do so!


Since I started gambling on the Internet four years ago I am up about $20,000, about half of which is thanks to the Golden Palace. What you’re seeing in my reviews is just my most recent experiences, and like everyone else sometimes I lose for a month or two. However I just won $786 at Casino.Net and $2317 at Casino Kingdom. So I don't ask for donations to subsidize a losing gambling habit. Donations simply help me to keep offering this site to the public for free. Although in fact the donations come in through PayPal which I then usually use to buy things on eBay.

Betting all 38 numbers on roulette would make it impossible to beat the odds even for a short time, and with a $1 bet per number there would be a loss of $2 per roll of the wheel.(0, 00 wheel, without advantageous rules for even money bets) Would it seem reasonable that there should be an optimum range of numbers to bet based on statistics?


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.

At the new Seneca/Niagara Casino in Niagara Falls NY they refuse to give me a copy of their house way for pai gow poker. I would like to know the house way before I play. Do they have to provide that info?


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.

I was wondering what happens to the house advantage if you could view all 7 player’s hands. Would this result in a negative house advantage?


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.

What are the odds of passing out 13 cards each to four players using a 52 card deck and all four player have a straight from Ace to two? The cards don’t have to be in the same suit.


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

The index number of 16 against a 10 in most blackjack counting systems is zero. So if the deck were completely neutral you should stand, because you stand if the count is equal or exceeds the index number. Yet the basic strategy tables tell us to hit. This seems to be a contradiction.


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.