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"If you want a sufficient response to optimism, consider: is the probability that you will persist forever 1? If not, it is 0."

You're only correct if the probability is constant with respect to time. Consider, however, that some uncertain events have a non-zero probability even if infinite time passes. For example, random walks in three dimensions (or more) are not guaranteed to meet their origin again, even over infinite time:

I said "it's not rational for them not to be always rational": I meant to say: "it's not rational for them to be always rational".

The utility here is not just the value of the money received. It's also the peace of mind knowing that money was not lost.

As other comments have pointed out, it's very important that the game is played in a once-off way, rather than repeatedly. If it's played repeatedly, then it does become a "money pump", but the game's dynamics are different for once-off, and in once-off games the "money pump" does not apply.

If someone needs to choose once-off between 1A and 1B, they'll usually choose the 100% certain option not because they're being irrational, or being inconsistent compared to the choice between 2A and 2B, but because the inherent emotional feeling of loss from having missed out on a substantial gain that was a sure thing is very unpleasant. So, people will rationally pay to avoid that emotional response.

This has to do with the make up of humans. Humans aren't always rational - what's more, it's not rational for them not to be always rational. You should be well aware of this from evolutionary studies.