Intuition should be applied at the lowest possible level

Ear­lier to­day I lost a match at Pris­mata, a turn-based strat­egy game with­out RNG. When I an­a­lyzed the game, I dis­cov­ered that chang­ing one par­tic­u­lar de­ci­sion I had made on one turn from A to B caused me to win com­fortably. A and B had seemed very close to me at the time, and even af­ter know­ing for a fact that B was far su­pe­rior, it wasn’t in­tu­itive why.

Then I listed the main re­sults from A and B, val­ued those by in­tu­ition, and im­me­di­ately B looked way bet­ter.

One can model these prob­lems on a bunch of differ­ent lev­els, where go­ing from level n to n+1 means hid­ing the de­tails of level n and ap­prox­i­mat­ing their re­sults in a cruder way. On level 1, one would com­pare the two sub­trees whose roots are de­ci­sions A and B (this should work just like in chess). Level 2 would be look­ing at ex­act re­source and at­tack num­bers in sub­se­quent turns. Level 3 would be cat­e­go­riz­ing the main differ­ences of A and B and giv­ing them in­tu­itive val­ues, and level 4 de­cid­ing be­tween A and B di­rectly. What my mis­take show­cases is that, even in a con­text where I am quite skil­led and which has limited com­plex­ity, ap­ply­ing in­tu­ition at level 4 in­stead of 3 lead to a catas­trophic er­ror.

If you can’t go lower, fine. But there are countless cases of peo­ple us­ing in­tu­ition on a level that’s un­nec­es­sar­ily high. Hence if it’s worth do­ing, it’s worth do­ing with made-up num­bers. That is just one ex­am­ple of where ap­ply­ing in­tu­ition one level fur­ther down: “what quan­tity of dam­age arises from this” rather than “how bad is it” can make a big differ­ence. On ques­tions of medium im­por­tance, briefly ask­ing your­self “is there any point where I ap­ply in­tu­ition on a level that’s higher than nec­es­sary” seems like a wor­thy ex­er­cise.

Meta: I write this in the spirit of valu­ing ob­vi­ous ad­vice, and the sus­pi­cion that this er­ror is still made fairly of­ten.

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