A stranger comes up to you and says he’s going to offer you the chance to wager with him on the outcome of a single coinflip. If you accept the wager, he’s going to offer you a 10% vigorish – that is, when you win, you collect 10% more than you will have to surrender if you lose. You know with certaintly that the man will pay if he loses (and that you will have to pay if you lose), and that the coinflip will be fair. He will make one offer, and you cannot negotiate it.
What is the largest proposed wager that you would accept? Remember, you’re not choosing the wager you prefer, you’re choosing the maximum amount you’d be willing to tolerate in order to get the vigorish.
A) $10 (to win $11)
B) $100 (to win $110)
C) $500 (to win $550)
D) $2,500 (to win $2750)
E) $10,000 (to win $11,000)
F) $50,000 (to win $55,000)
G) $200,000 (to win $220,000)
Does you answer change if you’re only offered 5% vigorish, instead of 10%? Also, are you refusing the next highest offer because it would be fiscally bothersome to lose it, or because you just hate the idea of risking so much money?
Assuming it’s an honest coin, and an honest coinflip, your stranger would seem to me to be an idiot. He’s offering you better-than-even odds on an even-odds proposition. In the long run, he will lose more than he wins, under those conditions. I’d keep betting for as long as he wanted to go for; I’d probably make a profit doing so.
But you said a single coin flip against a stranger. In that case, and not knowing the stranger or his coin or his flipping method, I’d have to say I’d bet $10. I can afford that on an even money prop. Assuming his game was honest, of course–but if he was really putting himself at a disadvantage as your conditions would indicate, I would question both him and the game’s honesty first.
Of course, which is why I said you had absolutely certainty that the bet would be paid and that it was a true 50/50 proposition.
The question isn’t about the real world implications of the offer, it’s about how much variance (risk) you’re willing to accept in exchange for a certain amount of equity.
ETA: given that the OP’s assumptions are definitely true, would you still only bet $10? If so, why so little?
I think Varloz is correct that the OP is just asking about variance.
I’d wager $50. Not catastrophic if I lose, but enough to add some suspense to the risk (and the odds ARE in my favor). Honestly, the 10% vig isn’t a big deal and I would not raise or lower my wager if it were anywhere between 0 & 10%.
I wouldn’t bet anything, I work too damn hard for my money. (even with the slightly improved payout for a win you’ve still got a 50/50 chance you’re going to lose your bet)
If there was a 50/50 chance the stock was going under? Yeah, of course. It’s all about risk vs. return. Now you said in the OP that it was a single flip, but if the person was offering unlimited flips I would just keep betting until I was a millionaire.
To you, it may seem little. To me, it is what I feel I can afford in your scenario. Ten bucks was one of your choices, after all.
To try to answer your “why so little?” question though, maybe I’ve seen (and played) far too many informal gambling games in my life. A stranger offering to play a game at which he is at a disadvantage odds-wise raises a red flag in my mind. I know, I know, you’ve put forth a hypothetical where the honesty of the game is not at issue. But having seen enough strangers propose bets with great-sounding odds for the [del]mark[/del] player in bars and whatnot, I’m just automatically careful in such situations, and therefore prudent with my money.
I’d bet $100 right now, because I’m momentarily unemployed and may need the money. If I had a job I could see betting $500. Not because the +$25 expected value is so great, but I just really love the idea of making such a good bet. It gives me the same warm feeling I get when they put out the college football point spreads and there’s a great line on the board.
I am a keen gambler but for a one off offer I don’t think I would bet at all. However I will happily bet on a horse or sports result paying $2.10 if I consider it good value.
I was about to explain that because the bet is not part of a continuum of bets I wouldn’t be interested but I realized that a bet, is a bet, is a bet. So I have changed my mind and will have $100 on it. That is the same bet I would have on any other event at the moment.
On a single flip, a 10% bonus isn’t really enough to give me an incentive; it doesn’t affect how much I’d be willing to bet. Maybe I’m a scaredy-cat but I don’t think I’d take the bet at all at 50-50 odds; any sum of money worth winning would be too much to risk losing.