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Science and Gambling
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great video,brilliant!
thanks for sharing... |
Good watch, actually watched the whole thing.
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. |
it is my understanding that he is offering double odds for a winning toss, compared to normal. He concedes it is a stupid bet on his part.
If you look up a Kelly calculator the odds are an important part of the equation so I guess by doubling the odds on offer he is ensuring the 25% option doesnt get wiped out. I am not a Kelly expert - maybe others know more about this?? |
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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. |
Gotta admit I get totally bamboozed by these things but I presume that (to make it simple) that we are doubling the bet after a loser when in fact 1 out 3 (approx) favs win! @ odds of about 2-1 (average) i.e level stakes would result in a loss of about 10% on T/O, cos I see it IF youve got a few Billion to play with, you have to win at least a $ or am I way off the thinking here? nothing would surprise me!
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It's arguable whether Kelly staking is a good method for horse betting. It was only intended for a system where: it's a non-terminating game and both the odds on offer and the odds of the event actually occuring are explicit. Non-terminating means you won't ever go bust. You could be down to a bank of 1c and betting 0.25c and you will still eventually make your fortune (under the terms of the game he used). With a bookie, once your bet slips below the minimum allowable stake - unless you have a lucky run of wins with your remaining pennies that bumps you back above the minimum - that's it; game over. In his coin flip game we know that - unless the coin is flawed or the procedure of flipping compromised - there is a 50-50 chance of the event occuring. In horse racing we know that the favourite has a 30% chance of winning BUT this is the average of all favourites over time. Each individual favourite actually has a totally different chance of winning - only some of which is reflected in the market pricing. Unfortunately no-one knows what the actual chance of a horse winning is before the race, and little more of an idea after it. The market is totally wrong as often as it is far too conservative. Altogether though, it averages out to just about right (fave-longshot bias and other human betting biases notwithstanding). So the important figure is not just what the long-time strike rate of a selection is, it's also the standard deviation. If you were to use a Kelly calculator online, you'd find that they all urge you to be conservative with your estimate of the odds. Most users arbitrarily knock off a percentage point or two, but essentially they're asking you to look at your mean (e.g. 30% of favourites) and standard deviation. That is, 95% chance that the actual chance is within 30 - (1.96 * stdev) and 30 + (1.96 * stdev). Instead of plugging 30% in the calculator you would pop in the conservative 30 - (1.96 * stdev) 'cause your estimate is wrong and will always be wrong, so at least be cautious about how wrong and in which way wrong it is. You likely wouldn't bet very often, but you also likely won't go broke. |
Walkermac, thanks for the reply, I was on the wrong staking plan altogether, I was thinking it was the Martingale......... (the Chardonay does it again)
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