Yesterday morning, millions of Americans woke up and heard the news that they did not win Powerball — a multi-state lottery with a grand prize that had swollen to over $900,000,000. As there was no winner, the next drawing will likely offer around $1.3 billion, more than twice as big as any American lottery prize in history.
Thinking about how nearly a billion dollars might change my life led me down a mental path of pondering what poker lessons can be learned from the lottery. Here’s what I came up with.
1. Irrationality reigns supreme
Clear, sound thinking is a rare commodity among gamblers. I once heard magician Penn Jillettedescribe Las Vegas as “an entire city built on the big, broad shoulders of mathematical illiteracy.” He’s right.
Many people feel that they have lucky lottery numbers that are more likely to be picked than other than other combinations — just as many poker players feel that they have lucky hands that win more than hand-strength charts predict.
In one news story yesterday, USA Today reported, “Patti McFadden of Fort Myers, Fla., a lottery-playing veteran, said before Saturday's drawing that she visited multiple Powerball sellers to improve her chances.”
Of course, it can’t possibly make any difference in your probability of winning if you buy ten tickets at one location or one ticket at each of ten locations. But this woman has apparently come to believe that it does, so she wastes time and energy spreading out her purchases.
I’d love to interview Ms. McFadden and learn the details of her theory, but I suspect the answer would be as silly as the ones I get when I ask poker players why they think that asking for a new deck of cards will make them more likely to win. That is, the answers would not be flattering to the notion that ours is a super-intelligent species.
2. The gambler’s fallacy is front and center
It seems that people just cannot wrap their minds around the idea of random events being truly independent of each other.
In the lottery, this is manifest by one week’s winning numbers being selected by many players for the next drawing, in the belief that there’s something special about them that makes them more likely to occur again. Similarly, when news stories mention where a winning ticket was sold, that store gets flooded with buyers for the next several cycles, because people convince themselves that there’s something “lucky” about that particular outlet, and a ticket bought there will be more likely to win than one purchased elsewhere.
As I’ve discussed here before, the gambler’s fallacy is common among poker players, too. That fallacy whispers to us, falsely, that recent events predict future events — for example, that if flops have been showing a lot of fives recently, your chances of flopping a set of fives are temporarily increased.
I particularly remember one time when I heard a player ask to move to a just-vacated seat, saying that he wasn’t getting any good cards where he was. But he couldn’t move until they finished playing the hand that the dealer had already started. As it happened, the player made quads and won a large pot. When the hand was over, the dealer told him that he could move now. The player was indignant. “Why would I want to move now?” he asked, as if the dealer were the stupidest person on the planet for assuming that the player still wanted what he had asked for a minute earlier.
One moment he believed that if he stayed put, he would continue getting bad cards, because it was an unlucky seat. One hand later, he believed that he should stay there so that he would continue getting good cards, because it was a lucky seat. The gambler’s fallacy causes strong but fickle beliefs!
3. You’ve got to know the rules
Some lottery games have a “second-chance” drawing. You mail in your losing ticket, and at a later date there’s a special drawing for another prize. But most players don’t read the fine print, and thus don’t know that when they throw away their tickets, they’re missing out on a substantial fraction of its expected value.
In the poker context, visitors to Vegas poker rooms often don’t know how high-hand jackpots work. They assume that the hand has to play out to showdown, when actually you’re eligible for the prize as soon as you’ve made your four-of-a-kind or straight flush, regardless of how the betting action subsequently goes.
Because of this misunderstanding, these players miss out on a ton of potential value in their very strongest hands, because they play as passively as possible, not wanting to risk a bet that might make all opponents fold. Even worse, they sometimes fail to realize that there is a minimum pot size to qualify for the jackpot, and thus win nothing.
4. Actions that are usually –EV can sometimes be +EV
The conventional wisdom is basically right: Buying a lottery ticket has an overall negative expected value. However, you can shift the expected value into the positive range, or at least make it significantly less negative, by smart selection of when to play and how you select the numbers. See this article from the Scientific American blog for details.
In his excellent book How Not To Be Wrong: The Power of Mathematical Thinking, Jordan Ellenberg tells the story of how a procedural change in the Massachusetts State Lottery resulted in some of the drawings having a strongly positive expected value. This did not go unnoticed. In fact, at least three large syndicates of investors quickly devised schemes of buying enormous numbers of tickets when the value shifted to the positive side of the ledger. See chapter 11, “What to Expect When You’re Expecting to Win the Lottery,” for the whole fascinating tale.
In poker, placing a traditional straddle under the gun is generally a bad use of your chips. You’re doubling the big blind from bad position before you’ve even looked at your hole cards. Nevertheless, in certain circumstances it can be a good investment.
For example, if the table generally plays too tightly, having to call two big blinds instead of just one may cause your opponents incorrectly to even further reduce the number of hands that they play. If they’re afraid to play big pots, and you’re not, effectively doubling the stakes of the game can work in your favor. If you’re generally better than your opponents at bluffing, hand-reading, not sinking money on second-best hands, and so on, straddling can work out in your favor, too.
Even when any one straddle is not in and of itself a +EV bet, it may be that habitual straddling will give you an image of being looser than you really are, which can pay off as a “metagame” phenomenon.
5. You have to adjust for how others play
One of the biggest drains on the EV of a lottery ticket is having to share the prize with others who pick the same numbers. That Scientific American blog post mentions a 1995 UK National Lottery prize that got split by an amazing 133 people, because all of the winners had selected their numbers the same way: straight down the middle column of the ticket. In another famous incident, Powerball second-prize money was divided among 110 winners, because they had all used the same numbers which they had found in mass-produced fortune cookies.
To maximize your lottery EV, you have to pick numbers less likely to be chosen by other people. The easiest way to do this is to let the computer pick random numbers for you, because any non-random method you use will likely be duplicated by somebody else.
So it is in poker. You can’t just play one default strategy and hope to maximize your winnings. You have to adjust to how other people at your table are playing.
If the two people to your left will only defend their blinds with premium hands, then you should greatly widen the range of hands with which you put out a blind-stealing range from late position. If you’re near the bubble in a tournament with a healthy stack, you should widen your opening-raise range when you recognize that several short stacks at the table are folding everything in an attempt to survive into the money. If your opponents are calling stations, cut out the bluffing and value-bet the heck out of them. Conversely, if they fold too much, crank your bluffing dial up to 11.
There are probably more poker lessons that one could derive from lotteries, but I’m out of space. Besides, I’ve got run out to my three lucky convenience stores and play last week’s numbers, my birthday and special favorite numbers, and make sure I ask the teller to reboot the lottery machine before running my picks.
Photo: sh11play (inset), Upupa4me. Creative Commons Attribution Share-Alike 2.0 Generic.
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