I like the idea a lot. I’m not nearly as crazy about your analysis, but, then your analysis is maybe 100 x more complicated than the idea itself in terms of Kolgormoioff-who’s-his-face-complexity, so that’s not too too surprising.
I think if we’re going to apply strict Bayesian religious payoffs, we’ll need to give each player more chips to drive the point home. With six chips and three choices, e.g., it’s trivial to learn to bid 3:2:1 or 4:1:1 (the only combinations that don’t leave a zero anywhere), depending on whether you’re “sure” or not that your #1 pick is correct. It’s also suboptimal: if you’re only going to play, say, 3 or 4 games with the same group of people, and each game has 3 rounds, and you are rationally 95% confident that your #1 pick is correct with 3.5% in your #2 pick and 1.5% in your #3 pick, then you could bid 5:1:0 and expect to beat all your friends until they got bored with the game. It teaches the wrong lesson, maybe. Life offers more iterations than one-off Clue.
With six weapons and six characters and, say, 40 chips, there is still a temptation to play zero chips on some weapons, but the dangers of this strategy are likely to become vividly apparent in only a few games...because you don’t need to leave a tile open in order to win (you can win by outguessing others with your distribution, maybe putting 15 chips on a weapon that you are quite sure of, and only 5 on the character you are most sure of, because you are well-calibrated and know what you know), the downsides of leaving a zero open are fairly apparent. Your final score could be the chips you bid on the winning weapon times the chips you bid on the winning character.
I like the idea a lot. I’m not nearly as crazy about your analysis, but, then your analysis is maybe 100 x more complicated than the idea itself in terms of Kolgormoioff-who’s-his-face-complexity, so that’s not too too surprising.
I think if we’re going to apply strict Bayesian religious payoffs, we’ll need to give each player more chips to drive the point home. With six chips and three choices, e.g., it’s trivial to learn to bid 3:2:1 or 4:1:1 (the only combinations that don’t leave a zero anywhere), depending on whether you’re “sure” or not that your #1 pick is correct. It’s also suboptimal: if you’re only going to play, say, 3 or 4 games with the same group of people, and each game has 3 rounds, and you are rationally 95% confident that your #1 pick is correct with 3.5% in your #2 pick and 1.5% in your #3 pick, then you could bid 5:1:0 and expect to beat all your friends until they got bored with the game. It teaches the wrong lesson, maybe. Life offers more iterations than one-off Clue.
With six weapons and six characters and, say, 40 chips, there is still a temptation to play zero chips on some weapons, but the dangers of this strategy are likely to become vividly apparent in only a few games...because you don’t need to leave a tile open in order to win (you can win by outguessing others with your distribution, maybe putting 15 chips on a weapon that you are quite sure of, and only 5 on the character you are most sure of, because you are well-calibrated and know what you know), the downsides of leaving a zero open are fairly apparent. Your final score could be the chips you bid on the winning weapon times the chips you bid on the winning character.