Depends on how well I can store information in hell. I imagine that hell is a little distracting.

Alternately, how reliably I can generate random numbers when being offered the deal (I'm talking to God here, not Satan, so I can trust the numbers). Then I don't need to store much information. Whenever I lose count, I ask for a large number of dice of N sides where N is the largest number I can specify in time (there we go with bounding the options again - I'm not saying you were wrong). If they all come up 1, I take the deal. Otherwise I reset my count.

The only objections I can think of this are based on hell not providing a constant level of marginal disutility, but that's an implicit requirement of the problem. Once I imagine hell getting more tolerable over time so the disutility only increases linearly, it seems a lot better.