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Originally Posted by thorns
One thing I was a bit sceptical of, or maybe I have misinterpreted it, but when he was showing how the Kelly criterion works on the coin toss. He was betting 25% per toss, ie a run of 4 wipes him out, yet in his samples it was the best method. That doesn't quite add up to me.
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In an experiment, a mathematician and an engineer enter a room that contains a beautiful woman, leaning against the opposite wall, and are told that every 2 minutes they may move half the remaining distance towards her. The mathematician decries the experiment a waste of time, as he knows that he will never reach the other side of the room if he always halves the remaining distance. The engineer keeps quiet and moves halfway across the room once the first 2 minutes is up. The mathematician can't believe it! Thinking the engineer is a fool, he shouts: "Don't you know you'll never get there!?" The engineer replies: "That may be so, but I'll be close enough for practical purposes..."
(Mathematicians and engineers can be female, of course, the joke works better though if it's a female on the other side of the room. And that everyone's heterosexual and up for it. Jokes are hard nowadays....)
Technically, the bank doesn't get wiped out using any percentage other than 100%. (In a practical application, you have to bet whole units - not percentages of a cent - and there will be a minimum stake. In the example in the lecture though, it's a non-terminating game).
Bet 1 is 25% of bank. If it loses, Bet 2 is 25% of (75% of the original bank) = 3/16 of the original bank, i.e. less than another 25% of the original bank.
The 25% is the optimal figure to use - according to the Kelly formula - given the situation he set up. The presenter could have used a different discrepancy between odds on offer and actual chance, he just chose "2 to 1" to easily explain it to the audience. The 25% is guaranteed to eventually give the greatest rate of growth of capital (under the circumstances of this game) than any other constant percentage of bank.
Kelly doesn't seem to say much of anything about if you were to vary the percentage of bank that is bet throughout the series (e.g. progressive staking, level stakes, etc). I'm not sure whether there have been other papers which investigate this and - if so - how applicable it would be in a general case, rather than under a specific instance.