I find the results of the Kelly criterion extremely counterintuitive, but it does answer my question. Thanks. I note that, presumably, we are discussing a lifetime strategy rather than a one-off, so the bankroll should not be my current cash reserves but the net present value of my expected lifetime income stream; but the Kelly fraction is so small that the optimal bet still works out to less than a dollar. Fascinating!
Note that if your thinking is something like “I should probably forgo buying a latte this morning and buy a lottery tickets instead”, then the Kelly criterion does not apply (it does not affect your lifetime income). Instead you should consider how much of your revenue-neutral funds you can spare and weigh the emotional downside of forgoing one expense (a drink: mmm, feels good) against the actual and potential emotional upside of another (a lottery ticket: what if I win, what if I win! + potentially winning—bummer, I lost!).
Well, actually, I find that I cannot bring myself to alieve this counterintuitive result, even after watching a toy Monte Carlo simulation confirm it. So I guess I’ll put in a dollar, and say “Kelly Criterion, obviously” if anyone asks me why not 100 dollars. :D
I did go a bit further towards alief by putting into my toy MC study, with the simple coin-toss game in your link, a bettor who puts in 50% of his bankroll every time—way, way beyond the Kelly fraction, and then having a think about how he managed to lose all his money. (Not literally, but enough that the remaining bankroll was 0 to my printout accuracy.)In ten thousand iterations my longest win and loss streaks are both of ten games. A loss streak of ten games will reduce this bettor’s bankroll by a factor of 1024. But ten winning games will only increase it by about a factor 80. On the other hand, with the Kelly fraction of 4.5%, ten losses reduce your bankroll by about 40%, while ten wins increase it by 62%. The asymmetry in these specific examples is somehow more convincing than the final numbers from the toy MC run.
I mean pretty much exactly that: I plugged in the payoff numbers into the equation, thought hard about my past record of trades & predictions and how calibrated I was in each certainty range to determine my edge, looked at the result of the Kelly Criterion, and felt terror at the idea of committing that much of my Intrade bankroll to one trade. I discuss the KC in http://www.gwern.net/Prediction%20markets#how-much-to-bet
Beyond your fear, was Kelly Bet sizing too aggressive? That is, were you so poorly calibrated that full Kelly would have led to wiping out your bankroll, with the sequence of bets you made?
No, I did fine and ultimately came out of Intrade with a decent profit. But my trades were few enough that I don’t know whether it could show me well calibrated or whether I got lucky.
I find the results of the Kelly criterion extremely counterintuitive, but it does answer my question. Thanks. I note that, presumably, we are discussing a lifetime strategy rather than a one-off, so the bankroll should not be my current cash reserves but the net present value of my expected lifetime income stream; but the Kelly fraction is so small that the optimal bet still works out to less than a dollar. Fascinating!
Note that if your thinking is something like “I should probably forgo buying a latte this morning and buy a lottery tickets instead”, then the Kelly criterion does not apply (it does not affect your lifetime income). Instead you should consider how much of your revenue-neutral funds you can spare and weigh the emotional downside of forgoing one expense (a drink: mmm, feels good) against the actual and potential emotional upside of another (a lottery ticket: what if I win, what if I win! + potentially winning—bummer, I lost!).
Well, actually, I find that I cannot bring myself to alieve this counterintuitive result, even after watching a toy Monte Carlo simulation confirm it. So I guess I’ll put in a dollar, and say “Kelly Criterion, obviously” if anyone asks me why not 100 dollars. :D
I don’t blame you for not alieving. When I was doing Kelly on my prediction market trades, it was terrifying.
I did go a bit further towards alief by putting into my toy MC study, with the simple coin-toss game in your link, a bettor who puts in 50% of his bankroll every time—way, way beyond the Kelly fraction, and then having a think about how he managed to lose all his money. (Not literally, but enough that the remaining bankroll was 0 to my printout accuracy.)In ten thousand iterations my longest win and loss streaks are both of ten games. A loss streak of ten games will reduce this bettor’s bankroll by a factor of 1024. But ten winning games will only increase it by about a factor 80. On the other hand, with the Kelly fraction of 4.5%, ten losses reduce your bankroll by about 40%, while ten wins increase it by 62%. The asymmetry in these specific examples is somehow more convincing than the final numbers from the toy MC run.
“It was terrifying” is evocative, but not informative.
Can you explain, preferably by including your evidence?
I mean pretty much exactly that: I plugged in the payoff numbers into the equation, thought hard about my past record of trades & predictions and how calibrated I was in each certainty range to determine my edge, looked at the result of the Kelly Criterion, and felt terror at the idea of committing that much of my Intrade bankroll to one trade. I discuss the KC in http://www.gwern.net/Prediction%20markets#how-much-to-bet
Beyond your fear, was Kelly Bet sizing too aggressive? That is, were you so poorly calibrated that full Kelly would have led to wiping out your bankroll, with the sequence of bets you made?
No, I did fine and ultimately came out of Intrade with a decent profit. But my trades were few enough that I don’t know whether it could show me well calibrated or whether I got lucky.