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Ask the Wizard #138
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.
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.
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.
Jim from Bradley, Illinois
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.
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.
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.
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.
Tommy from Houston, Texas
Please see my faro page for the answer to that question.