Comment Re:100% paper (Score 1) 167
The opponent is forced to pick 50% rock, but he has no limitations other than that. If you went 100% paper, you'd not beat me playing 50% rock by more than a tiny sliver of a percent it takes me to realize you are going 50% paper.
And the problem has nothing to do with the someone not just picking rock, but doing so in a very predictable manner. Otherwise, we'd not be talking about someone picking rock 50% of the time, but playing against someone that plays randomly, but tells you what he is picking half the time, never lying. That's a very, very boring brainteaser.
The first naive approach that doesn't assume idiocy on the other side's part is to assume he'll try to guess our play. If we play in a non deterministic fashion, his best options is probably random, but instead of
If he is forced to get at least 50% rock after a certain number of plays, then we can change our probabilities depending on how far from the standard distribution our opponent is: For instance, if we were playing to 10 throws, and he never picked rock in the first 5, we'd get him in the last 5, because his moves are forced. To avoid this, someone that has to reach that 50% will probably also change their probabilities after every throw, just to avoid such a 'free' run. One might even consider starting with an over 50% rock probability, because under that set of rules, having overplayed rock lets us play more optimally later, while underplaying rock leads to major losses.
Either way, a more detailed problem specification is required.