This arose out of a thread in General Questions (Luck and skill in card and board games) discussing luck in games. I’d like to establish just how lucky you have to be to randomly find good moves at chess.
So I play White and anyone can play a Black move. I’ll give my assessment each time of every Black move, so we get an approximation of the above chance.
Hope that makes sense!
e2-e4
Possible replies total 20.
Very good replies (4):
1… e7-e5
1… c7-c5
1… e7-e6
1… c7-c6
… c7-c5
Of course to compile some data you could pit a random-move player against a decent computer program for many hundreds of games. Even playing, say, 3-minute games the random player would have almost no chance in my opinion.
Although what’s going on here is more interesting – what is the probability of making a good move at any particular point in a game? I’d like to see the game at least make it past the opening … my expectation is that as a game progresses, the margin of error gets tighter and tighter. The tolerance in some endgames is very tight, plus there may be more possible bad moves on a more open board.
Oh, and there was a rook move (Rh8-g8) on move 3 I missed. (I’m a chessplayer, not a random move generator!)
It joins the other blunders, but the maths is still OK.
Blunders (12):
5… b7-b5
5… c5-c4
5… Nd5-b4
5… Nd5xc3
5… Nd5-e3
5… Nd5-f4
5… Nd5-f6
5… g7-g5
5… Qd8-f6
5… Qd8-g5
5… Qd8-h4
5… Bf8-d6
Current random chance of good or very good choice: 4/33, say 12%.
Cumulative random chance of good or very good choice:
0.4 (move 1) * 0.23 * 0.05 * 0.15 * 0.12 - say 0.00008 by move 5.
I switched because I’m worried about losing a decimal place. Do you prefer the above, or 0.008%?
Black to move.
(You may like to try a good move, as opposed to a very good move.)
Average number of moves for Black so far:
(20 + 22 + 23 + 27 + 33) / 5, say 25.
Current random chance of good or very good choice: 2/35, say 6%.
Cumulative random chance of good or very good choice:
0.4 (move 1) * 0.23 * 0.05 * 0.15 * 0.12 * 0.05 * 0.03 * 0.06 - say 0.000000007 by move 8 (or 0.00000017%).
The chance of winning the UK lottery 1st prize is 14 million to 1. I make that about 0.0000007.
So by move 8, you’re 100 times more likely to have won the UK lottery than to have reached a good position! (And the random player is facing an experienced player who has analysed the whole opening for several moves further on.)
Black to move.
Average number of moves for Black so far:
(20 + 22 + 23 + 27 + 33 + 37 + 40 + 35) / 8, say 30.
