How does RPS probability impact game flow?

Question

I've recently started playing By Night Studios' version of Vampire: the Masquerade, and I have a couple of questions concerning the RPS resolution system, and how it affects the flow of play. These questions assume that players will not be telegraphing their moves, or predicting the moves of others; I want to examine RPS resolution purely by its statistical merits.

1. You have a 33% chance of success if you do not have a test pool high enough to let you win a tie. If you do have a test pool that is high enough, you only have a 66% chance of success. A 66% chance of success seems far too low to me. Would a 66% chance of success prevent skilled characters from actually being skilled in-game?
2. Conversely, you always have a 33% chance of failure, regardless of how high your test pool is. Would a 33% chance of failure consistently impede the characters, and slow the game to a crawl?
3. Willpower, though costly, allows you to call for a retest. By how much does Willpower increase your chances of success? Is spending a Willpower really worth a retest?
4. Finally, how valid is a purely statistical analysis of RPS? In other words, Do the statistics of RPS resolution really matter, if we now assume that players will predict and telegraph moves?

Thanks! This is my first post to Stack Exchange. If there's anything that I should add, change, or remove, please let me know!

Answer 1

Taking each point in order:

1. Yes. 66% is perfectly reasonable, and does not prevent skilled characters from being skilled.

   There are a lot of reasons for this, but the most important is also the simplest: players (and GMs) shouldn't bother to test when the outcome isn't in doubt.

   The rules of a roleplaying game, especially a LARP, do not exist to resolve routine problems that the characters can handle without trying. They handle dramatic problems - where the task is unusually difficult, or another character is supplying opposition.

   The Willpower pool is an additional alleviating factor, here - see below.

2. No, 33% failure chance doesn't impede gameplay. Or at least, it shouldn't.

   This is not a Vampire-specific concept, but a general principle of GMing: Never allow the plot to depend on a specific test being passed or failed. (If the game is going to stall if a roll is failed, even a 1% chance of failure is too high.)

   Again, if the action was not dramatic and difficult, why are you bothering to test at all?

   Note that if the test is really important a player will spend Willpower, so the odds of a failure by a skilled character in a critical situation are closer to 1 in 9.

3. Yes. Willpower is absolutely worth spending.

   By basic maths, a skilled character who decides to spend willpower if they fail has improved their chances from 66% to nearly 89% - since they now have to lose twice to fail. And even an unskilled character (33% chance to win) increases their odds to 56% - better than 50/50.

   (Of course, that assumes the opposition isn't doing the same.)

4. Mostly valid.

   In game-theory terms, RPS is absolutely neutral - you can't do better than the even Win/Draw/Lose equilibrium. Assuming all players are playing perfectly, and randomly.

   In the real world, the human brain is a truly terrible random number generator, which is why some people do better than chance at RPS. They're just good at reading other people. The mathematics and psychology of RPS have been studied at length, and there are meaningful strategies, taking advantage of those limits in the human brain.

   The thing is - those strategies cancel out. Quite rapidly. And while they can do better than 50/50, none of them are massively better.

   So it is extremely difficult to be game-breakingly better than chance at RPS. (And players whose moves are easy to predict have a good motivation to learn to be more random... which there are simple techniques for.)

This sort of thing is why some players don't like RPS resolution, but if your game is working at all in the first place, it can probably take this kind of variation in stride.