Sure, I’ll play Game #2. I’ll even play it repeatedly, with a stopping criterion based on my utility of money.
If my utility of money is approximately linear for at least an order of magnitude or so beyond $100 (which it is), the most likely outcome is that I lose all of my initial $100 stake according to a biased random walk on log(pot). However, the game would be very much net positive in expected utility since an exit via the stopping condition wins so much more. It’s a lottery biased in my favour, where I get to choose the odds of winning to some extent, but the payout increases better than linear in those odds.
I would prefer to repeatedly play Game #1, or better yet a Game #1.5 where I get to choose how much to bet, but if Game #2 was the only option then I’d take it.
Sorry, I wasn’t sure the right way to do a link post without just copying the whole thing (which I don’t have permission to do) but there’s way more in the link. I tried to edit it to make it more obvious that this is an excerpt.
The game you want to play is #5 I think:
Start with $100 and play with the same rules as game #3, but this time, you get to decide what percent of your payout is wagered. I still decide when to quit.
Sure, I’ll play Game #2. I’ll even play it repeatedly, with a stopping criterion based on my utility of money.
If my utility of money is approximately linear for at least an order of magnitude or so beyond $100 (which it is), the most likely outcome is that I lose all of my initial $100 stake according to a biased random walk on log(pot). However, the game would be very much net positive in expected utility since an exit via the stopping condition wins so much more. It’s a lottery biased in my favour, where I get to choose the odds of winning to some extent, but the payout increases better than linear in those odds.
I would prefer to repeatedly play Game #1, or better yet a Game #1.5 where I get to choose how much to bet, but if Game #2 was the only option then I’d take it.
Sorry, I wasn’t sure the right way to do a link post without just copying the whole thing (which I don’t have permission to do) but there’s way more in the link. I tried to edit it to make it more obvious that this is an excerpt.
The game you want to play is #5 I think:
Edit: I decided to remove the whole excerpt.