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Ask the Wizard #210
Eric from Bettendorf, Iowa
John Patrick is probably behind that rumor. The basic strategy was first published in the September 1956 issue of the Journal of the American Statistical Association. The article was titled “The Optimum Strategy in Blackjack” by Roger R. Baldwin, Wilbert E. Cantey, Herbert Maisel, and James P. McDermott. Collectively, they are known today as the “Four Horseman of Aberdeen,” because they worked at the Amberdeen Proving Ground in Maryland at the time they did the analysis. I’m proud to have a copy of that article, and to have seen three of the four Horseman, when they were inducted into the 2007 Blackjack Hall of Fame. It has since been derived from scratch by hundreds of people, including me. If done properly, under the same rules, the results always agree. Then again, maybe I’m just in on the conspiracy.
Nick from San Diego
As usual, the person asking the question is right. For the benefit of other readers, I indicate the rules in my March 4, 2008, column. The probability of the jackpot hitting is inversely proportional to the how far the jackpot is from the guaranteed hit point of $100,000. The closer you get to $100,000 there is a smaller range where the jackpot can hit, so the odds of hitting at any given moment go up. If the current jackpot is j, the probability it will hit before the jackpot goes up $1 (for j<=$99,999) is 1/(100,000-j). At a jackpot of $50,000 the probability of hitting before going up $1 is 0.002%. At a jackpot of $99,999, the probability of hittng before going up $1 is 100%. So, you win the bet.
I like playing there and would be happy to flat bet. How likely is it that they would let me play again? If I went back in four months and flat bet would they even recognize me? Alternatively, would I be better off to approach the pit boss, tell him the situation and ask if I could play if I flat bet? Thanks for the great web site!
Bob from Burlingame
Thank you for the compliment. The Sienna is a classy casino, my favorite in Reno. They are also one of the few places with a liberal single-deck game in Reno, in which you may double on any first two cards. You should not ask permission to play, because they would be unlikely to reverse themselves. Your odds are much better waiting before coming back. Four months is pushing it on the delay, I would skip them a trip, and wait eight months.
My friend was down about $300 and I was up around $150 when all this happened. Since we are both ’full comp’ at the property, I did not raise a stink about this. The dealer seemed very worried about her job and we did not joke around at all. The supervisors and floor person did not say anything to us or offer any compensation. More or less, after a while, they replaced the deck and continued the game.
Personally, I figured that the odds say the missing card was a low card and it probably helped our odds of winning. My friend (who was down) thinks differently, that he should have been compensated. In the end, we did not raise the issue with the floor person. Was that correct? Should we have been aggressive given the situation? And, I am curious, assuming it was a random card, likely a low card, wouldn’t that actually have helped out odds during the time it was gone missing? Regards!
Kevin from Dallas
If you take a single card out of the deck randomly, the odds of Let it Ride do not change. This would be true of any casino game I can think of, where the cards are shuffled between hands. Without knowing the missing card, the effects of removal of bad cards and good cards exactly cancel one another out. So, complaining is not mathematically justified. Even if they found that it was a high card that got lost, it was still accidental. It could have just as easily been a low card that got lost. If it happened to me, I would have let it slide. I think an apology from somebody would be called for, but they probably didn’t want to, lest it give you more bargaining power if you did make a big scene over it.
Matthew from Fort Wayne, IN
The answer will appear in the next column.