Would you take the other side of my bet; having limitless resources, or a FAI, or something, would you be willing to bet losing it in exchange for a value roughly equal to that of a penny right now? In fact, you ought to be willing to risk losing it for no gain - you'd be indifferent on the bet, and you get free signaling from it.

Indeed, I would bet the world (or many worlds) that (A→A) to win a penny, or even to win nothing but reinforced signaling. In fact, refusal to use 1 and 0 as probabilities can lead to being money-pumped (or at least exploited, I may be misusing the term "money-pump"). Let's say you assign a 1/10^100 probability that your mind has a critical logic error of some sort, causing you to bound probabilities to the range of (1/10^100, 1-1/10^100) (should be brackets but formatting won't allow it). You can now be pascal's mugged if the payoff offered is greater than the amount asked for by a factor of at least 10^100. If you claim the probability is less than 10^100 due to a leverage penalty or any other reason, you are admitting that your brain is capable of being more certain than the aforementioned number (and such a scenario can be set up for any such number).