Thursday, 7 January 2010

Due for a win

"Due" is not a statistical concept. If you've won four hands at cards on a table of five people, what are your chances of continuing to win this hand? What are the odds of any given random coin coming up heads when you toss it? What if that same coin has come up heads sixty-three times in a row beforehand? The answers, in order, are "the same as before", 50-50 and 50-50. Past events do not have an effect on current outcomes. The denial of this tends to manifest as thinking "I'm bound to win sometime". You're not. Your losing streak is not statistically bound to come to an end, ever, because your odds are the same every time you play every game. How likely is the sequence "head-head-head-head" on a coin compared to "head-head-head-tail"? They're equally likely. You are never "due" for a change of outcome.

However, the chances of some tail turning up somewhere in the sequence at some point does rise as the length increases, compared to all heads, but that doesn't affect the individual chances of each run. To illustrate, picture the same coin tossed four times in a row. The chances of "HHHH" (head-head-head-head) are 1:16, but the chances of "HHHT" OR "HHTH" OR "HTHH" OR "THHH" are 1:4. And if you're not worried about more than one tail result, the chances of getting at least one tail in the sequence are 15:16.

Mokalus of Borg

PS - It can get tricky to hold the two concepts in tension.
PPS - If you only consider part of the sequence, the probabilities change again.

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