Board Game Arena

What's the probability of this... another player (lion48) did exactly the same moves as me (Fermax) for an entire game!

Game: https://boardgamearena.com/6/cantstopex ... =237441997#

Sure, we can both have similar strategies, but the chances of matching exactly are quite low!

I tried to calculate, but I didn't played enough to do a proper calculation.
From what I have seen in the first few turns there is usually only 1 to 2 'good' choice, outside maybe of the first turn.
Which mean that most the turns can be similar.

((1/2)^12)=4096. So if you do 12 coin flips, there is one chance of 4096 to have same results. This is what I would be with really approximative probabilities. But like I said, I stopped after ~5 turns.
And it look once you choosed all your numbers your good choices are even more limited.

There is no reason to take the probabilities of making the exact same moves as if you were both playing random. That's not the case, you both try to play the correct move, which will often be very similar.
And there's one thing that can contribute a lot to that. It all comes down to your 5th dice choice in the beginning. If they differ, you won't have the same choices after that. But provided you both "agree" on what's the best start in the game and get the same 5ths, then there is much room for you both to keep playing the same.
I also had a quasi twin game, so to name it, and the only difference was balanced out (5&5, 9&9 vs 5&9, 9&5).