This is fairly well-trodden ground, but I’ll respond regardless.
There is important information missing. I presume these are both once-in-a-lifetime game offers, but it still matters what ELSE one might do with a bankroll and the time spent playing these games. Game 1 is a no-brainer unless you absolutely need that marginal $40 for something immediately. Game 2 is “play until your time is more valuable elsewhere”. Depending on rounding, there may be a lower-bound where it’s no longer positive EV as well, but for most, it’ll be a waste of time to keep playing before that happens.
Game #3 (the opponent decides when to stop, not you) depends on real-world considerations—there’s no such thing as an infinite bankroll, nor infinite time to play. What happens when the amounts get ludicrous? If he can keep playing until everyone’s dead and nobody can collect/pay anyway, then certainly just walk away. If there’s a reasonable maximum value (and timeframe) they’d have to pay out rather than continuing, then play.
The rest are just variations making the same mistake (assumption of infinity). And the attempt to link to investment “strategy” is just silly.
Why do you think the link to investment strategy is silly? I just found this article last night and thought it was really useful, so if it’s giving me bad intuitions that would be good to know.
Isn’t real life somewhat like games #3 and #5 (the game doesn’t go on forever, but the “dealer” decides when you die quit), and applying the trick from game #6 really does help?
It’s silly because real investing doesn’t have consistent, known outcome probabilities, nor independent trials that multiply together that simply. Causal reasons outside the initial payout estimate hold FAR MORE sway than the casino-game-like toy problems would suggest.
No monetary activity in real life works like #3 - sure, you don’t know when you die, but you have MANY choices of what games to play while living, and you can change the games you play at will. In that sense, it’s a little like #5, but in reality there are a whole lot of non-monetary factors that matter, as long as your money is reasonably in range of your perceived peer group.
Game 6 shows the value of independent bets—you would achieve the same thing with one bet, run twice as often. The misleading part here is just how independent each bet (and each iteration of a bet-sequence) is. Sure, diversification of investments reduces variance, but this example is a pretty strange way to demonstrate it.
This is fairly well-trodden ground, but I’ll respond regardless.
There is important information missing. I presume these are both once-in-a-lifetime game offers, but it still matters what ELSE one might do with a bankroll and the time spent playing these games. Game 1 is a no-brainer unless you absolutely need that marginal $40 for something immediately. Game 2 is “play until your time is more valuable elsewhere”. Depending on rounding, there may be a lower-bound where it’s no longer positive EV as well, but for most, it’ll be a waste of time to keep playing before that happens.
Game #3 (the opponent decides when to stop, not you) depends on real-world considerations—there’s no such thing as an infinite bankroll, nor infinite time to play. What happens when the amounts get ludicrous? If he can keep playing until everyone’s dead and nobody can collect/pay anyway, then certainly just walk away. If there’s a reasonable maximum value (and timeframe) they’d have to pay out rather than continuing, then play.
The rest are just variations making the same mistake (assumption of infinity). And the attempt to link to investment “strategy” is just silly.
Why do you think the link to investment strategy is silly? I just found this article last night and thought it was really useful, so if it’s giving me bad intuitions that would be good to know.
Isn’t real life somewhat like games #3 and #5 (the game doesn’t go on forever, but the “dealer” decides when you
diequit), and applying the trick from game #6 really does help?It’s silly because real investing doesn’t have consistent, known outcome probabilities, nor independent trials that multiply together that simply. Causal reasons outside the initial payout estimate hold FAR MORE sway than the casino-game-like toy problems would suggest.
No monetary activity in real life works like #3 - sure, you don’t know when you die, but you have MANY choices of what games to play while living, and you can change the games you play at will. In that sense, it’s a little like #5, but in reality there are a whole lot of non-monetary factors that matter, as long as your money is reasonably in range of your perceived peer group.
Game 6 shows the value of independent bets—you would achieve the same thing with one bet, run twice as often. The misleading part here is just how independent each bet (and each iteration of a bet-sequence) is. Sure, diversification of investments reduces variance, but this example is a pretty strange way to demonstrate it.