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I still enjoy playing chess at the age of ninety four.Those contemporary opponents I used to play with have all passed away without me even getting even scores with any of them. On my spare time I just play a game or two against myself or the computer. Yesterday, while I'm on the middle of the game in deep thought my wife called to remind me to take the medicines. So I did. But when I returned to the chessboard, I can't remember what is the last move I made for either side and whose move it should be. That gave me an idea. What if I spin a coin to decide whose move is it? Will it be more interesting to play none turn-base chess with balanced skill vs. luck? Let's see. With all regular rules applied, starting with initial position, the first move depends on head or tail result of the coin spin. Next move likewise and so on until white/black wins or draw. While in case a player's King is in check, it is his turn to make a move unless it is a checkmate.

Suppose I want to help win against myself in five or less coin spins, what is the maximum probability that I can make a checkmate?

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    $\begingroup$ What do you mean by maximum probability? Such as consecutive moves to mate? $\endgroup$ – Shinjo Aug 28 at 8:10
  • $\begingroup$ After the coin spin..the 1st turn could be for Black..make a move for black so that the next move either for black or white leads to a checkmate in 5 turns or less (total of both sides) If you make Na6 on first black move then move a Knight again (either side turn) you probably have 0 chance of mate on 5th turn $\endgroup$ – TSLF Aug 28 at 8:47
  • $\begingroup$ Could "maximum probability" be replaced with just "probability"? What is the distinction here? $\endgroup$ – hexomino Aug 28 at 8:53
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    $\begingroup$ Maximum across all strategies, I assume. $\endgroup$ – Gareth McCaughan Aug 28 at 10:10
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I will use White to mean the winner of the first coin flip, all moves can be mirrored, so this should have no impact.

First move should be King's pawn, to free Queen and bishop, let's say e4.

If White wins the next toss

Play Bc4, preparing for a 4 move mate, while leaving the door open for a 3 move after black plays g5 and f6. This section wins 5/8 times.

If Black wins

Play g5.

If White wins the third toss

Play Bc4 as above, white will then win on flips of BW or WW, for 2/4 games.

If Black wins the third toss

Play f6, this results in a win on Wx or BW flips, black being able to make a waiting move of say, a6 if necessary. This is 3/4 games.

This results in a total win% of

62.5%

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I'd say combining

The scholar's mate with the Bong Cloud

looks very promising. Let's see:

  1. e4*
  2. Qf3                    v 2: (black) e5
  3. Bc4  v (black) e5      | 3: Qf3*
    (75%) | 4: Bc4  v Ke7   | 4: Bc4         v 4. Ke7
          |   (50%) | (50%) |    (50%)       |    (50%)
 
(The positions marked with * are symmetrical, so if the coin toss came up black, just mirror all the following moves.)

This gives a

50% mate 75% of the time, and a 75% mate 25% of the time, for a total of 56.25%.

Hmm. Not as good as I thought. Maybe black could do better by playing g5 instead of e5.. Oh, that seems to be what @Sconibulus is already saying.

Oh well, posting anyways :-)

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  • $\begingroup$ If we consider WWWWW or WWWWB for scholar's mate as one posibility and WBBWW or WBBWB for fool's mate..we get 8/14 instead of 10/16. $\endgroup$ – TSLF Aug 29 at 17:10
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To be honest, it's more like a combination of chess and mathematic problem.

For chess normal move at best you can mate in 2 for black and 3 for white:

Mate 2 for black:

1. f3 e5 2. g4 Qh4#

Mate 3 for white:

1. e4 f6 2. d5 g5 3. Qh5#

In this case, we can take the probability as 50% (1/2) because of equal chance with both player moves in order. And assuming for each move taken for either player was count as turn it was exactly 5 moves or less.

For sequential moves:

You would need another piece to support your mate example move for white(doesn't matter actually if it was black just reverse it):
e4 Qf3 Bf4 Qxf7#

You would have 1/(2^4) which is 1/16 chance of it happening.

In this case, I would say the maximum probability was actually:

50% since both players taking a turn to move was the biggest probability.

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  • $\begingroup$ We are looking for optimal set of move lines. After the first move of white or black we don't know if the second move is for white or black. The lines above is WBWB & WBWBW turn sequence..Other possible sequence BBWW 1...f6 2...g5 3. e4 4.Qh4#.. this is not taking turns $\endgroup$ – TSLF Aug 28 at 10:01
  • $\begingroup$ @TSLF Unless maximum wasn't as I stated in spoiler. I would still stand by my answer. Since the probability remains with only move variants differ $\endgroup$ – Shinjo Aug 28 at 10:13

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