One trick I used was to assume that when the perspective of the board flips, the probability of win flips to the probability of loss - ie, that the probability player 1 wins is the same as the probability player 2 loses.
However, that's not really the case. The network returns the probability of win given that it's your turn with the dice - so flipping the perspective does not just flip the perspective, but also hands the dice to the other player!
The starting board is one way to see this, but it is true for any symmetric setup - the probability of a win is forced to be 50%. The most extreme example: both players have only two checkers left to bear in, both on their 1 spot. Then the play with the dice has a 100% chance of winning and the other 0%. In my setup, the network would think both have 50% chance of winning.
So my whole initial assumption about symmetry on board flips is now in question.
But at least it solves one of these issues: the probability of winning the game from the starting position was always 50%. Even adding the bias node didn't change that; the symmetry I enforced always made sure that flipping the perspective was equivalent, when it isn't really.
Have to think about how to tweak the setup. This could require some relatively deep changes.
However, that's not really the case. The network returns the probability of win given that it's your turn with the dice - so flipping the perspective does not just flip the perspective, but also hands the dice to the other player!
The starting board is one way to see this, but it is true for any symmetric setup - the probability of a win is forced to be 50%. The most extreme example: both players have only two checkers left to bear in, both on their 1 spot. Then the play with the dice has a 100% chance of winning and the other 0%. In my setup, the network would think both have 50% chance of winning.
So my whole initial assumption about symmetry on board flips is now in question.
But at least it solves one of these issues: the probability of winning the game from the starting position was always 50%. Even adding the bias node didn't change that; the symmetry I enforced always made sure that flipping the perspective was equivalent, when it isn't really.
Have to think about how to tweak the setup. This could require some relatively deep changes.
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