I have always heard a rumor that casinos invented basic strategy. Where did the basic strategy come from?

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.

Hiya Wizard, I’m hoping you can settle a bet between me and my wife. Do the odds of hitting the Station Casinos Jumbo Jackpot get better as the jackpot increases? My wife believes that it doesn’t matter when you play, because it’s equally likely to hit at any time. I believe that this means it’s better to play later, because it’s an equal distribution over all the numbers but you’re playing against a subset so it’s an increased likelihood of hitting. Who is correct?

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 was backed off while playing for low stakes at Sienna in Reno. I was being careless, obviously varying my bet from \$5 to \$20. They were very nice about it, and just asked me to stop playing blackjack. I play there about one weekend every four months.

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.

I had an interesting occurrence at a major high-end strip property and I was wondering how I should have handled the situation. A friend and I were the only players at a Let It Ride table. After playing for a while, the blue deck started getting stuck in the shuffler. After a while, the dealer asked the floor manager to replace the deck. Before replacing the deck, the dealer counted the cards, only 51 cards! Several recounts, looking all around, calling in another supervisor etc failed to produce the missing card.

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.

Three logicians are playing a game. Each must secretly write down a positive integer. The logician with the lowest unique integer will win \$3. If all three have the same number, each will win \$1. The logicians are selfish, and each wishes to maximize his own winnings. Communication is not allowed. What strategy will each logician follow?

Matthew from Fort Wayne, IN

The answer will appear in the next column.