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Gambling Winning and Losing Streaks and the Standard Deviation, Part 1

G Chang
2.64K subscribers
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6.8K views 6 years ago
The standard deviation is like an "average distance" away from the single most likely gambling result, an exact match between wins and losses for a fair coin-flip game. You can expect to end up within 1 standard deviation about 2/3 of the time, within 2 standard deviations 95% of the time, and within 3 standard deviations 99.7% of the time. An Excel spreadsheet set up to simulate an even-money coin flip game and graph the change in bankroll for 100 flips. I generated 20 sessions of 100 flips each, or 2000 flips. I expected about 13 sessions to end up within one standard deviation, and about 19 out of 20 sessions within 2 standard deviations, with only about 1 session outside of that range, and none more than 3 standard deviations away. While recording the video, I lost track of the number of key presses, and only generated 16 sessions instead of 20. However, there was one session at the very start and 3 sample sessions shortly after that. If …...more
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Gambling Winning and Losing Streaks and the Standard Deviation, Part 1
68Likes
6,885Views
2018Nov 11
The standard deviation is like an "average distance" away from the single most likely gambling result, an exact match between wins and losses for a fair coin-flip game. You can expect to end up within 1 standard deviation about 2/3 of the time, within 2 standard deviations 95% of the time, and within 3 standard deviations 99.7% of the time. An Excel spreadsheet set up to simulate an even-money coin flip game and graph the change in bankroll for 100 flips. I generated 20 sessions of 100 flips each, or 2000 flips. I expected about 13 sessions to end up within one standard deviation, and about 19 out of 20 sessions within 2 standard deviations, with only about 1 session outside of that range, and none more than 3 standard deviations away. While recording the video, I lost track of the number of key presses, and only generated 16 sessions instead of 20. However, there was one session at the very start and 3 sample sessions shortly after that. If you count those, there are actually 20 sessions in the video in total. Here is a tally of the results: Winning sessions: 11 Losing sessions: 8 Break-even sessions: 1 (I predicted "about equal") Sessions ending within 1 standard deviation: 15 Sessions ending within 2 standard deviation: 19 Sessions not ending within 2 standard deviations: 1 Sessions ending outside of 3 standard deviations: 0 (I predicted 13, 19, 1, and 0) You needn't take my word for it that these results are typical. Set up your own simulation and try it yourself. My Excel setup video shows you how to do it:    • Gambling Simulator Excel Spreadsheet   If you don't trust Excel, you can spend an afternoon flipping a coin and recording the results manually. As the sessions get longer and longer, the standard deviation gets bigger and bigger, but as a fraction of the number of expected wins gets smaller and smaller. For example, for 50 flips, you can expect to win 25 times, with a variation of about 7%. For 2,500 flips, you can expect to win 1,250 times, with a variation of just 1%. The longer you play, the closer you will end up with the expected results, fraction-wise. This becomes really important for UNFAIR games, when you have a statistical disadvantage, as shown in Part 2.    • Gambling Streaks and the Standard Dev...   You might have noticed that the win/loss standard deviation is the square root of the number of flips "n". From your high school Algebra II class, you might remember: standard deviation = one-half[SQRT(n)]. The "one-half" applies to the number of wins, which is one-half the win/loss. For example, for 100 coin flips, the standard deviation in the number of wins is 5, and the standard deviation in the win/loss is 10. The expected number of wins is 50. One standard deviation upward would be 55 wins, which implies 45 losses, for a net gain of 10 bets in the session.

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G Chang

2.64K subscribers