balancing asymmetrical rock paper scissors

[deleted]

What I understand of game design says that to balance a multiplayer game all you have to do is make sure that no one thing is completely superseded by any other, people will take care of the rest.

To test this idea I took rock paper scissors and gave
a win by Rock a value of 3
a win by Scissors a value of 2
and a win by Paper a value of 1.

Obviously your choices no longer have an equal utility. But how often would you want to use each available choice?
rock is useful when your opponent uses scissors more than 1/3 of the time that the use paper because you lose 1 point when your opponent throws paper and gain 3 every time they throw scissors
this can be restated as (with '>' standing in for '>=')
R = S>3P
for the rest

S = 3P>2R

P = 2R>S

if you notice the point that all these are true at is when for every 1 scissors you have 2 rocks and 3 paper. This is the balance the game will end up at because this is the balance that you can't gain an advantage against. (Obviously if your opponent is using a different strategy then you can gain an advantage by using the symbol they are weak against)

..|Three P]Two R] S
P | 0| 0| 0]-1|-1] 2 sums to 0
R | 1| 1| 1] 0| 0]-3 sums to 0
S |-2|-2|-2] 3| 3] 0 sums to 0

you can clearly see that no matter how often they use any given sign there is no advantage they can gain on you (though in this case you can win by choosing only rock).

[Dubber]

Theory makes my brain melt... but this makes an odd sort of sense to my melted brain

[deleted]

thank you, I thought this might be useful because you can forecast the final balance of similar games if you know how well each choice does against the others. I'm going to try to solve an asymmetrical rock paper scissors like game where your choice this turn is constrained by past turns. So that I gradually move up towards warlocks.

[Slartucker]

Here's the problem. Your 'solution' to the weighted RSP game is valid -- however, it doesn't actually give you any advantage over the other player. Given enough rounds of play, ANY strategy used by your opponent will result in an average gain of zero for BOTH players.

Using a 'deviant' strategy rather than the solution does not increase, or decrease, your odds of coming out ahead of your opponent. It does, however, increase the likelihood that one player will win by a larger margin.

[deleted]

Nov 14, 2009 10:44:35 GMT -5 Slartucker said:

Here's the problem. Your 'solution' to the weighted RSP game is valid -- however, it doesn't actually give you any advantage over the other player. Given enough rounds of play, ANY strategy used by your opponent will result in an average gain of zero for BOTH players.

Using a 'deviant' strategy rather than the solution does not increase, or decrease, your odds of coming out ahead of your opponent. It does, however, increase the likelihood that one player will win by a larger margin.

you are absolutely right. The solution wasn't for any individual player (unless they know nothing about their opponent and want to play it safe). It is for the game designer. It lets the game designer know the most entropic state of their game before the play testers get to it.

[taliesin]

Nov 11, 2009 20:56:18 GMT -5 deleted said:

What I understand of game design says that to balance a multiplayer game all you have to do is make sure that no one thing is completely superseded by any other, people will take care of the rest.

While this keeps games balanced, it drastically reduces strategic depth. Rock, paper, scissors itself is a balanced game. It isn't, however, a particularly interesting one. That it isn't a particularly interesting one can be disguised to some degree if there is a changing metagame; suppose the weightings you suggest are in effect, and people meet up to play. At first perhaps they overvalue rock, and so paper becomes increasingly popular, then scissors to counter paper, and then the game settles into a balance. The game designers perhaps now announce that the scores for winning with each option have changed. The metagame changes to accommodate this, and having to plan round what other people are likely to do makes it feel like a proper game.

However, if the designers stopped changing the game and allowed it to remain static, it would settle into a single metagame and its poverty of strategy would soon become apparent. In the end, it would degenerate rapidly into relying on luck and wild guesses about psychology.

The really rich strategic games do not rely on this kind of thing; their balance comes after much tinkering and testing. Games like chess, go, arimaa and others do not simplify down to rock, paper, scissors, but instead have extreme complexity and many paths to victory. Creating a game of similar depth does not, unfortunately, allow you to use such shortcuts; you instead have to provide a very large statespace with no initially obvious unbreakable routes to victory (i.e. victory must not be assured and quick or achievable through a simple repetition of actions, and the statespace must not be straightforwardly constrainable by either party). From there, the testing happens.

To tie this back into Warlocks, somehow: Warlocks, with its complex board state of health, monsters and upcoming spell options, for the most part more greatly resembles the chess school of game than the rock, paper, scissors type. It has undergone much testing in its lifespan, and things have been changed from the initial Waving Hands blueprint. SPF became SPFP. cWSSW was added, as were DFWFd and SPPFD, giving some marginal spells slightly greater utility. DSF was altered from Confusion to Maladroit. ParaFF has been tinkered with to create ParaFC (I wonder now if Firetop Mountain's solution to paralysis was not after all a better one.) In its latest incarnation it has taken some years for strategy to substantially converge, but largely converged it has and Warlocks needs a substantial shake-up if it's to recover the damage done to its statespace by the para chains.

[Dubber]

Which brings us back to asking for the FM-style paralysis? (again)

[mikeEB]

Actually, the interesting case is the one where the players value the same state differently; Two mid-level warlocks with different experiences might open D/P and S/W and each think they have a slight advantage. They may even be correct; for example, I'm a less likely to win from FFF/WWP vs. PS/SW on the FF side than a dedicated paramancer of the same general skill.

[Dubber]

I've been thinking about this (but not theorizing as that is not a strength of mine, as my descending ELO demonstrates) Compare the main casts of Warlocks and assign them rankings/ratings similar to:

Rock Paper Scissors Spock Lizard

Which strategy(ies) win(s) more effectively and how once these additional two variables are tossed in?

[succat]

I think I'm in the wrong thread again You want Rock-Paper-Scissors, here you go... www.celtruler.com/games/bards/ That takes about as much skill as rolling dice, but if you find a pattern to consistently beat the 'Computer' I'd be interested in seeing that.