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Martingale is bogus

On Martingale:
* http://en.wikipedia.org/wiki/Martingale_(betting_system)
* http://wizardofodds.com/gambling/bettingsystems.html

1) In a true random memoryless game, any betting strategy can not improve the odds.  A 50/50 coin flip is still just a 50/50 coin flip, no matter what your bets.  The previous coin flip does not affect the next coin flip.

2) If you flipped a coin 9 times and it was heads all 9 times, what are the odds of the 10th flip being heads?  The only thing going on here with someone who says it’s 0.5^9, is that they misunderstood the question.  (ie, silly language trick gimmick)

3) Okay, I guess the "intuitive" part of why one should expect Martingale to work is…  If you did literally have infinite bank roll, then you would eventually break the streak.

Might be interesting to think through why exactly both "3)" and "1)" are true.

*** wrote this post since friend mentioned it during Vegas trip

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