6 ms·
The non-transitivity of Rock-Scissors-Paper is easy to understand, partly because it's so simple, but mostly because you're likely never played outside the usua
by dws 9y ago
The non-transitivity of Rock-Scissors-Paper is easy to understand, partly because it's so simple, but mostly because you're likely never played outside the usual rules, even if adding Lizard-Spock.
Non-transitive dice screw with the 'nature' of dice that most of us expect. To get to the mathematical intuition, one may have to get past a deeply-ingrained feeling that something about these dice just isn't right. That's a big part of the fun.
- deleted 9y ago[deleted]
- kybernetikos 9y agoI think the numeric and gambling aspect helps too. If you're used to probability, you probably start thinking about expected value automatically in these situations, but it isn't the case that the die with the highest expected value wins most of the time against a die with lower expected value. (e.g. 2,2,2,2,2,2s vs 1,1,1,1,1,100).
- hammock 9y agoMean EV doesn't work because the dice have different variances? Trying to wrap my head around the rationale here
- hawkice 9y agoVariance isn't the best lens here, better to look at the distributions. It's also a discrete problem, so EV isn't as precise as looking at all the possible combinations.
- hammock 9y agoVariance describes distribution... Discreteness is another layer. What are the exact defining characteristics of this problem though? You could take two dice 1-2-3-4-5-6 and 2-3-4-5-6-7 and the typical mean EV calculation would work fine... 1-2-3-4-5-7 and 2-3-4-5-6-8 have different variances but are probably not intransitive (haven't checked the math) since they are translations of each other I'm just thinking out loud here and trying to narrow it down...maybe someone reading wants to help me :)
- hawkice 9y agoVariance does describe the distribution, but not well enough, in this case. It reduces the vector of possibilities to a scalar, and hides the most important aspect, the non-transitivity. Numbers have transitive comparisons, so there's essentially no way a scalar value _could_ capture that in any straightforward way. Basically, abandon all single-value summaries. They'll do you no good in understanding this phenomenon. But the detailed analysis isn't too complicated, so it's okay.
- ouid 9y agoEV of what? The faces of dice cannot be added together, except in a very formal sense.
- Double_Cast 9y agoSeasoned gamblers count "outs" (winning outcomes), convert to "hand odds" (out:loss ratio), then weigh hand odds against "pot odds" (weigh expected profit vs investment).