you have to play a game with the following rule : white can initially play two moves, then one move each side as usual, and a draw counts as a victory for black. Which side do you choose ? (say differently, do you think this variant favors white or black ?)

Same question with three initial moves for white. Maybe this is already solved?

  • With two moves I would go for black. Three probably too but I am really not sure it's good decision :) – hoacin Jun 24 '18 at 18:43
  • Does black also have initially two moves? – user1583209 Jun 24 '18 at 22:03

Since I'm a 1.d4 player, my first two moves as White would be 1.d4 and 2.c4. After that position, Stockfish gives an evaluation of +0.59 if Black plays ...e6. I would definitely enjoy playing this as White since the threat of playing e4 at any time prevents the Nimzo and Dutch. Black best option is to settle for a QGD one tempo down by playing ...d5 on the next move, but this would be very comfortable for me. So I'd probably choose White, but it's not an easy decision.

That being said, it's not close to winning for White. An extra move just guarantees a pleasant edge.

With three initial moves, I would go for 1.e4, 2.d4, 3.Nf3. Stockfish gives a +0.99 evaluation, and it would be very tough for a human to defend as Black in a practical OTB game. This seems on the verge of winning for White, but still not a definite win.

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  • As a fellow 1.d4 player, I think it's more principled to go for 1.d4 2.e4. IMO the main point of 2.c4 is that it's the next best thing after black has prevented 2.e4 with ...d5 or ...Nf6. – RemcoGerlich Jul 2 '18 at 10:06

It's a common knowledge that White have about 55% probability of winning the game over Black, for the equal strength opponents. Having one extra move at the beginning will give maybe extra 5%, maybe less. And one more move will probably add another 5%, bringing the probability of winning (given everything else being equal) to about 63-65%.

Since most of my games are not drawn, I would definitely go for an extra move(s) at the beginning, but statistically speaking, for the equal opponents with high draw ratio, this would be not advisable, they lose a lot of half-points for the 10% more wins.

So, here it is, if the opponents have more than 20% draw ratio, this new strategy has no advantage. If the percentage of draws is smaller than 20% -- a few extra moves will definitely help.

After some deliberation...

The effect of having a few extra moves will also greatly depend on time control the games are played with. The most impact it will have on the shorter games, with less pronounced effect for 30+ minute games or longer, that tend to end up in draw more often.

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    Notice that the numbers you state, especially the 5%, don't really mean anything (I don't know how you derived those "probabilities", 10%, 20%??). White winning 55% or so in a database (for players of a certain ELO strength) doesn't mean probability of winning the game. – gented Jun 25 '18 at 7:14
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    Because in order for this to be a "true" probability you must repeat the experiment for every opening, every set of initial moves, every middle game position and so on and so forth. At the moment most of the experiments with computers are done by using mainly opening books and not all initial opening positions are played - not to mention that as definition in game theory there is no such a thing as "probability" of winning: White either wins (first move advantage) or it doesn't (no first move advantage) - which still has to be demonstrated. – gented Jun 25 '18 at 7:28
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    1. If you want to derive the P from empirical experiments (as limit of the frequency for N approaching infinity) then yes, you would have to repeat the experiment with all possible initial conditions. 2. However, in the case of a die, the space of events is deterministic and the P measure can be derived therefrom (which is not the case in chess, as we do not have a table book of all possible chess positions and their results). – gented Jun 25 '18 at 8:20
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    @gented ok, let's say, my numbers are rough estimations based on incomplete information, which still might give us some kind of "back of the napkin" approximation for the "real" probability, can we agree on this? =) – lenik Jun 25 '18 at 8:53
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    8% draws is probably some mixture of bullet and Armageddon. That's really not common knowledge that over 90% of games with equal players end in win of one side :D – hoacin Jun 25 '18 at 10:23

2 extra moves for white is not even close enough for white to be winning, I would take black with draw odds any day. Advantage of white is already only around 30 points elo difference. 2 more moves might make it 100 but thats very little chances of a draw is so high.

We have had 3-4 move odds with humans + engines vs engines and it quickly becomes apparently by playing certain openings as black that the advantage quickly disappears, the best the human player can still get is a draw in a worse position.

How many moves white would need to win is an open problem, I think the best lowest proven bound is like 12?

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    If you give four moves to white, can't they just do the scholar's mate? – itub Jul 1 '18 at 11:10
  • no, you are not allowed to make moves above the 4th rank obviously. – Matthew Liu Jul 5 '18 at 0:28
  • Interesting, I didn't know about that restriction when playing with move odds! I see now that it's mentioned in the Wikipedia article about chess handicap. – itub Jul 5 '18 at 0:44

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