Topics on the Powerball Lottery
I am torn between discussing:
(1) how the odds are calculated;
(2) how not to choose numbers;
(3) how the lottery is a very regressive tax on poor people;
(4) How its funding of education is only a small sliver of state educational funding;
(5) how the lottery encourages people to think of all the things that they desire, but can’t afford;
(6) How that can make people depressed after losing again;
(7) How the selective reinforcement by random, small winnings can make you addictive;
(8) How social reinforcement makes you not want to be different or left out;
(9) How thinking that God cannot reward you if you don’t try by buying tickets (which is sacrilegious);
(10) How you can think that gambling is not a sin or addictive, since it is legal and everyone is doing it;
(11) How you are going to be jealous when someone else wins the lottery;
(12) How getting some of the drawn numbers is again selective reinforcement.
(3) and (4) are discussed in articles that I have seen, and I think more freely available up-to-date research is needed on this, as well as on the bad psychological consequences: (5) to (12). The one very disturbing number that sticks in my mind under the regressive tax is that people under the poverty level income of $13,000 a year spend 9% of their income on the lottery.
I will content myself in this article to only discussing the odds, and how choice of numbers matters. The odds are found by calculating all possible combinations, taking account that order of the first five doesn’t matter, and then taking the reciprocal of the results.
The possible ways of drawing the first five numbers are 69 for the first, times 68 remaining for the next, then times 67, 66, and 65, giving 1,348,621,560.. But the results for the lottery don’t care which order they are drawn. So we have to divide by the number of different arrangements of the five drawn numbers, which is 5 for the first, times 4 for the next, times 3, times 2, times 1. The number of rearrangements is then 120. We divide the first number by 120, giving 11,238,513 combinations for the first five numbers drawn. We then multiply by the 26 possibilities for the sixth number, giving the widely known, 292,201,338 possibilities. The odds of winning for one ticket are one in 292,201,338. Oddly, this is close to the US population.
Each possible set of numbers has an equal probability of showing up. Those who look at a list of numbers that have come up, or have most often come up, are just kidding themselves. Avoiding numbers that haven’t come up, is also just kidding yourself. Playing the same numbers each time, is also just kidding yourself. Normally, any choice of numbers would do.
But if you want to win a larger amount, and not just a share with many people, giving the biggest payoff, you should avoid commonly chosen numbers. Some people choose “lucky” numbers. These numbers are too common choices, and if they win, the prize will be shared by many. A worldwide survey of lucky numbers turned up 7, 3, 8, 5, 6, 2, 11, and others. People picking numbers probably pick smaller ones, not the larger ones among 1 to 69. Since we and some others are betting contrarian to common choices, maybe 13 is also bet on by others.
Others play a given date. This limits one number choice to 1 to 12 for the month, out of a possible 69 numbers. That is limiting one choice to only about one sixth or 0.174 of the range, as well as sharing that choice with many other bettors, to split an award. The day of the month as 1 to 31, is also restricting to about one half of numbers, or 0.45 of the range, as well as sharing those numbers. Betting the current year of say 2016 as 20 and 16 again shares with a vast number of people. Betting any 20.. year is also bad, as is any 19.. year.
If the lottery odds were such that each week’s lottery has a winner, so you could bet over and over again for the same amount, you should pick your own numbers, avoiding the commonly played numbers, to get the largest payoff per bet.
About 70% of lottery tickets sold are just by random numbers. For only single run dates with the biggest payoffs, that is actually the best bet, since the results may contain some of the most commonly bet numbers, and sharing a very large jackpot is not so bad.
However, random numbers are often not random, but part of a sequence generated from a given starting number. If each machine starts from the same number, the sequence would be the same for all machines. We assume that this is not the case, and that the numbers are generated from a common source, that may be truly randomized.
It is odd that with some people’s belief in lucky numbers, or in their own birth date being special, as in astrology, or in looking at numbers that have or have not come up, they are actually lowering their payoffs or increasing their odds against maximum winnings, with their beliefs.
The other thing is that the psychological effects are fairly common, yet people may not be considering their effects, which are enhanced by addictive or serial betting.
Should you buy more tickets when the jackpot increases? That would involve having data on tickets sold per jackpot level, to see if your odds per dollar of winnings increase. I don’t have that data to figure it out.
Leave it to say that I am not interested in standing in line in cold 60 degree days in the winter here to buy tickets, as well as inducing all of the psychological effects in my dull brain.
