I tired to evaluate mathematically how likely you are yo win at 2 players when you are playing first.
Playing first is clearly an advantage, but how much of one ?
I don't have the skills to answer the question for the game as it is so I had to simplify as follow:
- both innocent cards are revealed right away at the start of the game
- you don't know what questions the opponent asks nor what answers he gets. (In other words, you cannot make inferences based on the other players answer).
You can however make assumptions about the other player strategy.
I won't give the details (sorry) but I think that with the simplifications above, the mutual "perfect" strategy gives the second player a 38.89% chance to win. But up to 44.44% if the first player plays in a rater intuitive manner and the second player exploits that. 33.3% chance if the second player wrongly believes that the first player does play in the manner (I think...) optimal.
I don't know that the chances are with the real rules nor what the optimal strategy indeed is for the real rules and I cannot be sure that I didn't make a mistake in my maths.
I'm wondering if anyone else tried to quantify this advantage.
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As a side note to all of this, it would be fair for a game like this to have the ELO changes take that advantage into account.
I have no idea how to would work though. One (stupid easy) way to do this would be to treat the game as if the first player had a higher ELO than he really does (or the second player a lower one).
I don't think that even official Chess ELO takes it into account, or does it ? (start player at chess also has an advantage)
Playing first is clearly an advantage, but how much of one ?
I don't have the skills to answer the question for the game as it is so I had to simplify as follow:
- both innocent cards are revealed right away at the start of the game
- you don't know what questions the opponent asks nor what answers he gets. (In other words, you cannot make inferences based on the other players answer).
You can however make assumptions about the other player strategy.
I won't give the details (sorry) but I think that with the simplifications above, the mutual "perfect" strategy gives the second player a 38.89% chance to win. But up to 44.44% if the first player plays in a rater intuitive manner and the second player exploits that. 33.3% chance if the second player wrongly believes that the first player does play in the manner (I think...) optimal.
I don't know that the chances are with the real rules nor what the optimal strategy indeed is for the real rules and I cannot be sure that I didn't make a mistake in my maths.
I'm wondering if anyone else tried to quantify this advantage.
-------------------------
As a side note to all of this, it would be fair for a game like this to have the ELO changes take that advantage into account.
I have no idea how to would work though. One (stupid easy) way to do this would be to treat the game as if the first player had a higher ELO than he really does (or the second player a lower one).
I don't think that even official Chess ELO takes it into account, or does it ? (start player at chess also has an advantage)