Powerball Nears Best EV (Updated)

This is a quick post that is the exact same as the Mega Millions post I did. I break down the Powerball odds, use some sales data, and look at the EV over various jackpots.

The quick takeaway, as the Powerball is up to $450 million for Wednesday, is that either this drawing (or the next if no one wins) is as near to the possible expected value for this lottery. The other takeaway? Don’t buy lottery tickets!

UPDATE: Going back I found an error in my code. I’ll update it at some point, but for now, take it with a grain of salt (except the historical data part, that part was fine).

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Mega Millions, Multiple Winners, and Expectations

The Mega Millions lottery is a popular number-picking lottery game in the US. It exists in 45 states (including D.C.), and is played by millions of people every week. Lotteries are well known for having negative expected values, meaning that players lose (on average) more than they win. This should be expected, given that lotteries (and gambling in general) are profit-seeking enterprises.

The potentially large jackpots of Mega Millions (the jackpot is pari-mutuel) can push the game into a region of positive EV, though. This is counter-balanced by the fact that duplicate tickets will result in splitting the winnings equally among the winners, driving down the available EV. This post explores what kind of impact that has on the game. Continue reading →

Progressive Betting Strategies Analysis with Markov Chains

If you are a fan of statistics and probability, then you might have a certain affinity for various games of chance. It can be quite fun to, for example, figure out card counting strategies in Blackjack with simulation. It might also be interesting to try to use some machine learning on the basic strategy tables to figure out smaller, easier to learn sub-sets (something that I want to try at some point).

Hopefully you are also aware of the Gambler’s Fallacy. If you have (or think you have) a problem with gambling, don’t be afraid to seek help! Also, never EVER gamble with money that you can’t afford to lose. Always set aside a given amount of money that you are 100% fine with losing all of (because that will happen).

There are excellent sites out there (like Wizard Of Odds) that give excellent information on probabilities and house edges (notice how none are in our favor!). There are also plenty of discussion of strategies (usually about how bad they are). What I was curious about was whether or not some betting strategies were able to increase the probability of making a set profit (and then stopping). Most people don’t go to the casino very often (if at all), so I wanted to find out about short-term behaviors of these strategies, rather than the obvious long-term failure.

Using Markov Chain analysis and Monte Carlo simulation (in the next post), I’m going to examine some betting strategies. The obvious conclusion is “you will still lose everything in the long run”, but there are some interesting twists along the way. I’ve included some code so you can set up your own analyses, too!

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