I’m not a gambler, though I’m intrigued by people who are, and especially who gamble on tennis (a sport I know well) which is prone to upsets. How would one model event probability there, where there are many, many matches played and upsets (judged by comparative ranking of each player) unlikely but possible? Do you aggregate all the match results, with 1 for expected and -1 for upset (or larger for a bigger disparity: if the No 300 beats the No 7, as happened this week, is that a -293?
I’m just thinking out loud, but there are people who gamble stupid amounts of money on such things, but I doubt they have any model to guide their behaviour.
I agree. I think you could try and model it - if you calculated an Elo rating https://en.wikipedia.org/wiki/Elo_rating_system for each player then in theory it gives you a probability of each outcome for example.
But (and this is not based on any particular players!) I'd have a nagging feeling that there might be people out there who were prepared to take a dive in minor tournaments, or that I might be betting against people who were better informed than me about whose knee just went and so on.
Oh certainly about the “better informed” or dive-taking. The ITIA (tennis integrity authority) is VERY hot on betting patterns around upsets in lower-ranking matches particularly.
Look, I'm just a petty gambler, but it is odd not to mention Kelly.
And the truth for anything financial is that you don't have ever have to have the really funky distributions where you have massive tails against you. You can almost always reasonably limit your loss to a fixed sum - but that's boring to a lot of people because when you do the return profile looks very small.
No, I don't think it's necessary to talk about Kelly here - I tend to think of that stuff as upstream of this. That is, yes, if you are in a situation where (your model of) the underlying probabilities don't match the odds then Kelly can tell you how to exploit that in terms of a strategy. And one result of the strategy would be something like a red or blue payoff curve. But my point is that even a Kelly-optimized strategy needn't be immune to the problems of heavy tails I'm talking about here
Nice! Like I say, I'm very much coming at it from the academic end of things, so very interesting to hear perspectives from people on that sharp end. My perception is that this heavy-tailed problem was an issue in the Long-Term Capital Management mess (with Scholes and Merton on board of course), but I'm not 100% sure if that's accurate or not!
As someone who coincidentally just finished readying When Genius Failed, covering the rise and fall of LTCM - yes it absolutely was. Lowenstein references this concept in the book several times, so was fun to see it covered more comprehensively in your post here as well! The other major problem that bit LTCM is that Black-Scholes assumes continuous pricing in securities; we all know that this isn't true, liquidity dries up in times of crisis and concern, leading to prices gapping downwards (or upwards, if you're holding a short position, which you could conceive of LTCM's core thesis of spread convergence as).
Cool, thanks! Yes, I think the whole "equivalent martingale measure" thing is very pretty, and should hold regardless of any assumptions about the underlying tails, but it's very interesting to hear about that particular slice of history
I’m not a gambler, though I’m intrigued by people who are, and especially who gamble on tennis (a sport I know well) which is prone to upsets. How would one model event probability there, where there are many, many matches played and upsets (judged by comparative ranking of each player) unlikely but possible? Do you aggregate all the match results, with 1 for expected and -1 for upset (or larger for a bigger disparity: if the No 300 beats the No 7, as happened this week, is that a -293?
I’m just thinking out loud, but there are people who gamble stupid amounts of money on such things, but I doubt they have any model to guide their behaviour.
I agree. I think you could try and model it - if you calculated an Elo rating https://en.wikipedia.org/wiki/Elo_rating_system for each player then in theory it gives you a probability of each outcome for example.
But (and this is not based on any particular players!) I'd have a nagging feeling that there might be people out there who were prepared to take a dive in minor tournaments, or that I might be betting against people who were better informed than me about whose knee just went and so on.
Oh certainly about the “better informed” or dive-taking. The ITIA (tennis integrity authority) is VERY hot on betting patterns around upsets in lower-ranking matches particularly.
Look, I'm just a petty gambler, but it is odd not to mention Kelly.
And the truth for anything financial is that you don't have ever have to have the really funky distributions where you have massive tails against you. You can almost always reasonably limit your loss to a fixed sum - but that's boring to a lot of people because when you do the return profile looks very small.
No, I don't think it's necessary to talk about Kelly here - I tend to think of that stuff as upstream of this. That is, yes, if you are in a situation where (your model of) the underlying probabilities don't match the odds then Kelly can tell you how to exploit that in terms of a strategy. And one result of the strategy would be something like a red or blue payoff curve. But my point is that even a Kelly-optimized strategy needn't be immune to the problems of heavy tails I'm talking about here
This is very interesting - thanks!
Gambling where you come out ahead?
Sure. Insurance. The ookies are called actuaries.
Legal. It's socially useful risk transfer.
Ease of entry means competition. But innovation is rewarded.
Nice! Like I say, I'm very much coming at it from the academic end of things, so very interesting to hear perspectives from people on that sharp end. My perception is that this heavy-tailed problem was an issue in the Long-Term Capital Management mess (with Scholes and Merton on board of course), but I'm not 100% sure if that's accurate or not!
As someone who coincidentally just finished readying When Genius Failed, covering the rise and fall of LTCM - yes it absolutely was. Lowenstein references this concept in the book several times, so was fun to see it covered more comprehensively in your post here as well! The other major problem that bit LTCM is that Black-Scholes assumes continuous pricing in securities; we all know that this isn't true, liquidity dries up in times of crisis and concern, leading to prices gapping downwards (or upwards, if you're holding a short position, which you could conceive of LTCM's core thesis of spread convergence as).
Thanks for the great post(s)!
Great, thanks for confirming!
Really interesting, thanks!
Cool, thanks! Yes, I think the whole "equivalent martingale measure" thing is very pretty, and should hold regardless of any assumptions about the underlying tails, but it's very interesting to hear about that particular slice of history