. . . Three can get to 75% chance of marriage/silver easily:. . .

This is a WONDERFUL puzzle which should appeal to fans of combinatorics and information theory. Even very smart people usually give up and think 50% is the best that can be achieved.

In that puzzle, 50% chance of success is the best any (non-abstaining) guesser can hope for. And. like the 100 Prisoner's Puzzle, ALL guessers must succeed to win. Yet a 75% chance is attainable, as shown by Bomb#20!

As an approximation I'd say the probability is close to zero of the prisoners surviving.

The first guesser has exactly a 50% chance no matter how he plays. Perhaps they agree in advance that he will pick Boxes #1 - #50. If he succeeds, the 2nd prisoner picks #51 - #100 and wins 50/99 of the time. We're down to 25.25% and still have 98 prisoners to go.

With this brutish approach, the chance that 100 prisoners succeed is 0.00000000000000000000000000099%, worse than 1 in 2

^{96}

Is there some clever idea that will let the prisoners do better than this pathetic chance of 1 in 100 trillion quadrillion?

Yes, they can actually achieve a bit better than 31% !!!