How many times can the same position repeat?

woton

Here's a simplistic, unrealistic example of what I was talking about in Post 75.  The position has been duplicated 10 times, but only eight can be attributed to castling.  Now that it is Black's turn to move, neither side has the castling privilege, so you cannot gain eight more duplications by using the castling maneuver.

 

Yenny-Leon
woton wrote:

Here's the challenge.  So far we have several theories about the number of times that a position can be duplicated.  However, they are just theories.  Can anyone demonstrate on a chessboard that it's possible to have 21 (or whatever) duplicate positions before three-fold repetition occurs?   Without experimental evidence supporting your theory, it's just an interesting idea.

 

Here's an example, and it looks like my initial calculation over-counted the number of distinct castling situations.  I get only 11 different "optically identical" positions, without true repetitions in the sense of the 3-fold repetition rule.  The 2nd diagram below shows the position that will occur optically 11 times, before it starts repeating in the actual sense of the 3-fold repetition rule.  The sentence fragment "B lost O-O" means that black lost the ability castle short.

 

This example indicates that the maximum number of instances of an "optical position" that can appear before 3-fold repetition occurs is 12 (including 1 actual repetition at the end).

 

 

ThrillerFan
woton wrote:

ThrillerFan

You might want to check your example.  I put it into my chess program (Stockfish 8) and got three-fold repetition on move 6 (Note:  it was one of the maneuvering positions rather than the subject position).

 

I may or may not have repeated in the maneuvering positions - don't know, don't care!  There are a million ways to play the maneuvering moves.  Alter them if you must.  All I care about is the specific position that was repeated 21 times to illustrate the point!

ThrillerFan

Post 82, what you are failing on is you can repeat positions 2 thru 11 one more time each and it's not 3-fold.  The first position can only occur once.  But take your second position, why not do it AGAIN with White to move.  Why not do the 3rd position a SECOND TIME with Black to move?

 

That's why 21 is the most without 3-fold repetition.  Your first position once, your second thru 11th twice each makes 21.

 

Then, on the 22nd occurrence (your 12th), it will be 3-fold!

Yenny-Leon
ThrillerFan wrote:

Post 82, what you are failing on is you can repeat positions 2 thru 11 one more time each and it's not 3-fold.  The first position can only occur once.  But take your second position, why not do it AGAIN with White to move.  Why not do the 3rd position a SECOND TIME with Black to move?

 

That's why 21 is the most without 3-fold repetition.  Your first position once, your second thru 11th twice each makes 21.

 

Then, on the 22nd occurrence (your 12th), it will be 3-fold!

 

Yes, now that you mention it, it's obvious that you're correct.  Looks like you nailed it!

BlueKnightShade

The question in the topic headline says "How many times can the same position repeat?". The original post then elaborates on the matter in the headline and makes it clear that it is related to when you can claim a draw by 3-fold repetition.

 

In order to claim a draw by 3-fold repetition the position needs to be the exact same position of course with the exact same possibilities, 100 % exact. The arrangement of the pieces on the board is just an arrangement. A chess position is more than an arrangement, a chess position includes who has the move, castling rights and en passant possibility. If any of those has changed you have a position with different possibilities, so it is a different position.

 

Thus the answer is simple. You can always claim a draw when a (100 % exact) position appears the third time. Arrangements of pieces is a different subject.

woton
ThrillerFan wrote:
woton wrote:

ThrillerFan

You might want to check your example.  I put it into my chess program (Stockfish 8) and got three-fold repetition on move 6 (Note:  it was one of the maneuvering positions rather than the subject position).

 

I may or may not have repeated in the maneuvering positions - don't know, don't care!  There are a million ways to play the maneuvering moves.  Alter them if you must.  All I care about is the specific position that was repeated 21 times to illustrate the point!

The problem is that if you repeat another position three times, it invalidates the remainder of your analysis.  You may be right that there is a way to avoid other repetitions, but you have to show it.  You have shown that it is possible to repeat other positions, now you have to show that it is avoidable.

By the way, I'm looking at your analysis to figure out what's wrong with my logic.  What you have done seems reasonable.

woton

OK.  I found my error.  I didn't think about changing colors after each rook move.  I waited until all rook moves had been made.  

DjVortex
woton wrote:

ThrillerFan

You list five options and multiply by four.  I'm assuming that you're considering positions where White moving first can be transposed to Black moving first.

The problem is that the castling options can only be multiplied by 2.  Once the castling privilege has been lost, it cannot be restored by transposing who moves first.

Four is the correct multiplier. That's because for each castling right we can repeat the piece arrangement four times (without the 3-fold repetition rule kicking in): Twice so that it's white's turn to move, and twice more so that it's black's turn to move.

If the 3-fold repetition rule didn't care about which player's turn it is to move, then it would be indeed only two repetitions per castling right.

DjVortex
woton wrote:

Here's a simplistic, unrealistic example of what I was talking about in Post 75.  The position has been duplicated 10 times, but only eight can be attributed to castling.  Now that it is Black's turn to move, neither side has the castling privilege, so you cannot gain eight more duplications by using the castling maneuver.

 

You have to repeat the visual position four times before moving a rook (to maximize the number of visual repetitions). You can do this by first repeating the position twice with white to move, and then repeating it twice more with black to move, and only then move a rook to get rid of a castling right.

DjVortex
BlueKnightShade wrote:

Thus the answer is simple. You can always claim a draw when a (100 % exact) position appears the third time. Arrangements of pieces is a different subject.

That's a correct answer, but not to the question I asked. I asked what's the upper limit of times that the (visual) position can repeat before the 3-fold repetition rule kicks in. (Ok, technically speaking I asked people to corroborate my math, but still...)

I think that the consensus is that yes, the theoretical upper limit is indeed 22 times.

Yenny-Leon
DjVortex wrote:
BlueKnightShade wrote:

Thus the answer is simple. You can always claim a draw when a (100 % exact) position appears the third time. Arrangements of pieces is a different subject.

That's a correct answer, but not to the question I asked. I asked what's the upper limit of times that the (visual) position can repeat before the 3-fold repetition rule kicks in. (Ok, technically speaking I asked people to corroborate my math, but still...)

I think that the consensus is that yes, the theoretical upper limit is indeed 22 times.

 

This unexpectedly high result explains why even super-GMs make invalid 3-fold repetition claims.