How about no, because I prefer my stability and I don't want to track random bets on stuff I don't care about?
Apply marginal utility and a 50/50 coin with the opportunity to bet a dollar, and you've got 50% chance to, say, gain 9.9998 points and 50% chance to lose 10 points. Why bother playing?
The only reasons to play are is if an option is discounted (4x payout for heads and 1.5x payout on tails on a fair coin), if you don't care about the winnings but about playing the game itself, or if there's a threshold to reach (e.g. if I had 200 dollars then I could do payoff something else which would avoid the deferred interest from coming into play, saving me 1000 dollars, so I would take a 60% chance to lose 100 dollars because those extra 100 dollars are worth not 100 but 1000 to me).
Plus there's always epsilon - "the coin falls on its side" or other variations.
I'm not suggesting that people actually do this, just that this is a sensible assumption to make when laying the mathematical foundation of rationality.
(Warning: completely obvious reasoning that I'm only posting because I haven't seen it spelled out anywhere.)
Some people say, expanding on an idea of de Finetti, that Bayesian rational agents should offer two-sided bets based on their beliefs. For example, if you think a coin is fair, you should be willing to offer anyone a 50/50 bet on heads (or tails) for a penny. Jack called it the "will-to-wager assumption" here and I don't know a better name.
In its simplest form the assumption is false, even for perfectly rational agents in a perfectly simple world. For example, I can give you my favorite fair coin so you can flip it and take a peek at the result. Then, even though I still believe the coin is fair, I'd be a fool to offer both sides of the wager to you, because you'd just take whichever side benefits you (since you've seen the result and I haven't). That objection is not just academic: using your sincere beliefs to bet money against better informed people is a bad idea in real world markets as well.
Then the question arises, how can we fix the assumption so it still says something sensible about rationality? I think the right fix should go something like this. If you flip a coin and peek at the result, then offer me a bet at 90:10 odds that the coin came up heads, I must either accept the bet or update toward believing that the coin indeed came up heads, with at least these odds. I don't get to keep my 50:50 beliefs about the coin and refuse the bet at the same time. More generally, a Bayesian rational agent offered a bet (by another agent who might have more information) must either accept the bet or update their beliefs so the bet becomes unprofitable. The old obligation about offering two-sided bets on all your beliefs is obsolete, use this one from now on. It should also come in handy in living room Bayesian scuffles, throwing some money on the table and saying "bet or update!" has a nice ring to it.
What do you think?