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Say you won a contest where at halftime of an NBA game you got to shoot a free throw and if you make it you win \$1 million. Further, you can keep shooting free throws, double or nothing, till you miss or choose to stop. If you’re a 75% free throw shooter, when would you stop? Can you ever? At some point the money starts to mean less and less. What would you do?

Pete from New York

At some point you should refuse a good bet because the stakes are too high. Personally I think a good measure of the enjoyment one gets from money is the log of the amount. The base of the log does not matter so let’s use 10. However we can’t take a log less than 10, so let’s say the enjoyment is 0 for any amount less than ten. So in your example let’s assume you have \$0 before winning the \$1,000,000 with your first throw. Now you have log(1,000,000) = 6 units of happiness. The expected value of your happiness taking another free throw is 0.75*log(2,000,000) + 0.25*0 = 4.975772. This is less than 6 so in this case you should take the million and walk. However it might be different if you already had some money. Let’s say you already have \$200,000. Then your happiness by walking is log(1,200,000) = 6.07918. Your happiness by risking the million and taking another shot is 0.75*log(2,200,000) + 0.25*log(200,000) = 6.082075, so you marginally take the second shot. If you were to win that one your choice would be between log(2,200,000) = 6.34242 and 0.75*log(4,200,000)+0.25*log(200,000) = 6.29269. In this case you should not take a third shot and instead walk with the \$2,000,000 win. The breakeven point for accepting the first double is an existing wealth of \$191,487. To accept two doubles you should have \$382,975 in other money.

A friend of mine told me that the casinos also have video blackjack. Are the odds or randomness the same for both methods? I mean do the video programmers give the casinos a better house edge with the video version of blackjack vs. the table version, or is the video version programmed exactly to mirror the table game?

Rich from Marietta

It is a law in Nevada that video representations of card games must be truly random. Thus the odds would be same as in live blackjack with the same rules. Most other jurisdictions more or less accept Nevada regulations. You should be warned that the vast majority of video blackjack games pay even money on a blackjack, which is a terrible rule whether on a video or live game.

Casino "comps" are supposed to be based on average bet x hours played x house edge (or something close to this). Why do they record your buy-in, your re-buys and the amount you color out? None of these should affect your comps. Is it truly theoretical loss or does actual loss(or win) come into play?

P.S. Your site is terrific and thanks for restarting the "Ask the Wizard" feature.

Dr. Tom from Youngstown

Thanks for the kind words. I asked a pit boss this question and he first agreed that comps are generally based on the product of average bet, hours played, and the house edge. The reason that buy-ins are recorded are to adhere to government regulations. There is different paperwork that must be filled out when buy-ins reach the \$3,000 and \$10,000 levels.

How much wood WOULD a woodchuck chuck, if a woodchuck could chuck wood?

A woodchuck would chuck as much as he could chuck if a woodchuck could chuck wood. Now say the question and answer ten times really fast.

Since most online casinos deal each hand out of a "fresh shoe," is there an opportunity to create a special basic strategy card for the "first hand out of a shoe," or do your various basic strategy cards work as well?

Bill W. from Summit, New Jersey

The traditional way to create a basic strategy chart is based on the odds the first hand after a shuffle. So the existing basic charts, including mine, are already perfectly suited for most online games where the cards are shuffled after every hand.

Have you ever evaluated Spin Poker and does it pay off comparable to regular multi-hand video poker? What is unique about spin poker is that while it is a multi-hand game, is that on the draw, once a card is drawn it is gone and can not come up on another line. While I have done well at this game, I’ve been very uneasy about this aspect of it.

Jeff from San Diego, California

The same can be said about standard video poker, once a card is discarded it can not come back on the draw. Thus the expected return in Spin Poker is the same as conventional video poker with the same pay table.

I'm assuming you're aware, but if not, in the Italian lottery, there is a twice-weekly drawing of 50 out of number 1 through 90 (five numbers from each of 10 cities). For roughly 2 years, the number 53 has not shown up, leading up to a "number 53 frenzy", to the point where people have committed suicide after betting everything they have on what they were sure would be a corrective! So I got to thinking - what are the probabilities that the 53 would not come up for two years? ()

Andrew from Hollywood

I did some research and six numbers are chosen each drawing. In any given drawing the probability of the number 53 not making an appearance is combin(89,6)/combin(90,6) = 93.333%. In two years there would be 208 drawings. So the probability of 53 not occurring in a specific two year period would be 0.93333208 = 0.000000585665, or 1 in 1,707,460.

What are the odds in Faro?

Tommy from Houston, Texas