Welcome to the "Be a smart gambler" series! Even if you haven't entered a casino before, you must have some sort of gambling experience, which can perhaps be playing poker with your friends or buying lottery tickets. Gambling is not always pure luck --- some games are indeed a combination of skills and fortune. Is it possible to predict lotto? Are there any optimal strategies for roulette? Can machine learning be used to win horse racing? I know there are lots of questions about gambling to be addressed. In this series of articles, let me show you the way of betting wisely by understanding more about the science of various gambling games to the best of my knowledge : )

Gambler's fallacy

Let me start by talking about gambler's fallacy. Imagine that you are tossing a fair coin, i.e. it is expected to get a tail or head equally likely. Now it comes to the 11th round. You got a head for each of the previous 10 rounds. If you are to bet on whether a head or tail will show up in the coming round, what will you bet?

Some gamblers will start thinking in this way: it is very unlikely to have 11 consecutive heads. Let's bet on "tail" this round. What do you think? Let's simply consider the following 2 events:

A tail followed by 10 consecutive heads
A head followed by 10 consecutive heads

Note that the probability of getting a head is 0.5. So the likelihood of getting 10 consecutive heads is 0.5 x 0.5 x ... x 0.5 = 0.5^10. Therefore the probability of event 1 to happen is (0.5^10) x 0.5 = 0.5^11. Similarly, the probability of event 2 to happen is also 0.5^11. So event 1 and event 2 are indeed equally likely to happen! What's more, given 10 consecutive heads, it is equally likely to get a tail or a head in the coming round.

The simple analysis above is a classical illustration of gambler's fallacy. In a more formal statement, gambler's fallacy refers to the wrong belief that if some events happen more frequently than as usual, those events should happen less frequently in the future. Gambler's fallacy does not only apply to coin toss, but also to any game where each round of the game is independent of any other rounds. Examples include roulette, sic bo and lotto. Indeed, researches (Chen et al. 2016, Suetens et al. 2016) show that asylum judges, loan officers, baseball umpires and lotto players are consistently affected by gambler's fallacy when making decisions. As a smart bettor, don't be trapped by the gambler's fallacy.

Coming Soon...

In the next post, I will share some interesting mathematical properties of lotto. I will show some examples of the approaches that people take to try gaining edges in lotto and analyze if they really work. See you!

References

Chen, D. L., Moskowitz, T. J., & Shue, K. (2016). Decision Making Under the Gambler’s Fallacy: Evidence from Asylum Judges, Loan Officers, and Baseball Umpires. The Quarterly Journal of Economics, 131(3), 1181-1242.
Suetens, S., Galbo-Jørgensen, C. B., & Tyran, J. R. (2016). Predicting Lotto Numbers: A Natural Experiment on the Gambler's Fallacy and the Hot-Hand Fallacy. Journal of the European Economic Association, 14(3), 584-607.
Wikipedia at https://en.wikipedia.org/wiki/Gambler%27s_fallacy#Observations_of_the_gambler.27s_fallacy

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I write articles on machine learning, applied statistics and economics to the best of my knowledge : ) If you like my posts, please upvote, resteem and follow me @manfredcml.

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