Powerball

For members who are not located in the United States, the big national news item is neither ISIS nor the impending presidential election. Nobody won the Powerball jackpot Saturday night, so on Wednesday there will be a new drawing for an estimated \$1.3 billion dollar prize. For all practical matters, the prize ends up being about twenty-five to thirty percent of that, as the raw face value is depreciated once to account for a lump sum payment (rather then thirty annual payments of \$43 million) and a second time for taxes. No matter; the pot is so big that most everyone is buying tickets.

When I took Stellar Interiors in graduate school, my professor, Bob Rood, spent the first two days of class giving us random estimation problems so we would refine our sense of what sorts of answers to expect, and be able to make quantitative analogies with large numbers. In that spirit, I find it interesting that the odds of winning the Powerball jackpot, stated as 292 million to one, are pretty close to the odds of being dealt a twelve-card suit in bridge, which is a little north of 313 million to one. Now I've been playing bridge a while, but I have never been dealt an eleven-card suit, much less a twelve-card one. I have twice been dealt ten card suits. The first was in a sectional pairs, and I held AKQTxxxxxx of spades, a small doubleton and a small singelton. There were two passes to me in third seat, so I shrugged my shoulders and opened 4. The opponents bid, but when it came back around to me I successfully bought the hand in 5, and made six when dummy unexpectedly hit with an A opposite my singleton and a KQ opposite my doubleton. The hand was pretty flat, except for a friend who had tried to walk the dog and got abandoned in 3. He got a lot of abuse for that, but insisted there were layouts where a trump promotion would beat 4. Well, I suppose ...

The second ten-card suit was even less interesting, as it was clubs, and missed the A, Q, and J. Moreover, we were at unfavorable, and I heard a major suit opened to my left and a GF 2/1 to my right. I chose never to bid on this monstrosity, and the opponents reached their par 4M game, making five.

It seems as if I have been quite lucky to have been dealt two ten-card suits. The odds on any given hand are over 60,000 to one, and that's a good estimate for how many hands I have played in my life. At my most active, I probably played seventy days per year which would give an annual rate of roughly 3,500 hands. However, there were long stretches where I did not play much, if any, so my annual average is probably closer to half that. Since I joined the ACBL in 1982, that comes to about 60,000 hands in my bridge career. This is consistent with averaging about two masterpoints per session played, times 2,400 lifetime sessions.

Is it likely that any one player has been dealt an eleven-card suit? Jeff Meckstroth has 80,000 masterpoints, and certainly wins them at a higher rate per session than I do. Let's guess he averages six per session, but since he plays a great deal on six-man teams, we will reduce his hand count by one-sixth. This gives an estimate that he has played about 400,000 hands in his lifetime. The average number of deals to get an eleven-card suit is almost seven times that number, and the median is only reduced from that by a factor of the square root of two. Even if my various estimates for him are off, they are not off by a factor of seven! So, while I wouldn't be shocked if he had picked up an eleven-card suit, neither would I bet on it. On the other hand, that number is small enough that I think it likely that someone reading this post has done so. Perhaps you could comment below.

As for twelve-card suits, well, we would typically expect over 5,100 ten-card suits for each twelve-carder. Seems I have many lifetimes to go to get to that. So, if you want to dream, go ahead and play Powerball, but don't say I didn't put your odds in perspective.