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[TheCaviarKid]

This is a nice read.

[esoito]

Before anyone gets too excited I noticed this towards the end:

"However the point of this article is not to make you a better gambler (in spite of the title), but to uncover some beautiful mathematics. "

That should excite the 'mathz-boyz'

[TheCaviarKid]

For anybody who does not like maths or can't be bothered reading to the end!

The Summary

With timid play, the gambler makes a small constant bet on each game until
she is ruined or reaches the target. This turns out to be a very bad strategy in
unfair games, but does have the advantage of a relatively large expected number
of games. If you play this strategy, you will almost certainly be ruined, but at
least you get to gamble for a while.
With bold play, the gambler bets her entire fortune or what she needs to
reach the target, whichever is smaller. This is an optimal strategy in the unfair
case; no strategy can do better. But it's very quick! If you play this strategy,
there's a good chance that your gambling will be over after just a few games
(often just one!).
Amazingly, bold play is not uniquely optimal in the unfair case. Bold play
can be rescaled to produce an in¯nite sequence of optimal strategies. These
higher order bold strategies can have large expected numbers of games, depend-
ing on the initial fortune (and assuming that the casino is nice enough to allow
you to make the weird fractional bets that will be required for the strategy).
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A lot of gamblers on forums mistakenly think flat betting is the way to go because progressions 'don't work'. Well that's not true when playing a negative expectation game. That doesn't mean you have to go out and do an 'ashley revell'. You can learn plenty from maths articles related to gambling even if you don't understand everything what's written.