Gambling and Statistics

Preface

I remember being about 16 years old and spending a few weeks each summer at Devil’s Lake with my grandparents. One of the fun things we would do at night is play “casino.” My grandpa would get out a green felt cover for the table. It had a Blackjack table on one side and Craps on the other. Grandpa would be the house, calling out our bets, informing us of bad bets, and paying out the winner.

It was during one of those summers when I first put advanced mathematics to use trying to calculate probabilities for games of chance. I had just learned about calculating sums for inifinite series in school the previous year. I remember trying to work out the odds on craps and realizing it was an infinite series that could be summed just like we had learned in class. I was amazed and excited. While it was widely believed we would never actually use the math we were learning in class, here was a great example of how it could be put to practice use in real life. After calculating the return on different craps bets, I realized Grandpa was paying out incorrectly on one of the bets. I told him that, and he didn’t believe me. I placed that bet over and over until I won so much that he pulled out the rules and realized he had it wrong. Math is not just fun. It can be profitable too!

That example of using math to calculate the expected returns in craps stands out in my mind as something that really drove my interest in gambling and applying statistics to different games. It wasn’t too long afterwards that I started building computer simulations for games like Blackjack and Poker, trying to re-create basic strategy and the different statistical tables I had seen for Texas Hold ’Em.

Now I’ll be the first to admit this is well-trodden ground that doesn’t require any new work or discovery by me. The Wizard of Odds has already calculated statistics and expected returns for pretty much any game you can imagine. There really isn’t any value in me going through and calculating them all myself… except that I like it. I think it’s fun, and I’ve decided that is reason enough.

I intend to put my notes here as I accumulate them, adding a chapter for each game or subject. There’s even a chance that this could turn into a good reference for statistics applied to gambling games. I intend to start with the most basic games and build up to the more complex. So maybe there is some value in arranging the content in this way and emphasizing the math that gets you to the answer rather than just the result. But really, when it comes down to it, I just find this a fun way to spend time, and that is all that matters.