# Compulsory repetition draw

In conventional chess there is a rule that determines a draw when both players repeat their same actions a certain number of times. Because it is understood that the situation has entered a kind of loop, and there will be no progress from there.

These ties usually occur in two different contexts:

1. Both players choose not to alter their rolls.
2. One of the players forces the other to repeat their moves.

The first situation is common when changing the play will put the player at a disadvantage. The second situation usually involves one of the players realizing that his chances of winning are low, it is interesting to force a draw, forcing the opponent to repeat his moves.

But I wondered, would a context in which both players can’t escape the loop be possible? That is, there are no alternatives for either side, even if that would put them at a disadvantage, by interrupting that looping.

For a long time I was analyzing how this scenario could happen thinking about check situations, in which by diverting the king from the threat, such a move puts the other king under threat. At least that was my idea, as I couldn’t imagine another scenario in which an action could be forced without involving a check.

After testing several scenarios and none of them seemed to work, I wanted to say that such a situation is impossible. But this is basically a mathematical problem, and saying there is no solution is tricky. Because it is not enough just to test with a number of cases, we really need to guarantee for no case. I did something similar in the post that explains that it is impossible to have a triple check in chess. In this post I showed that due to the way the pieces move, it was impossible in one move to open more than two foci of threat to the king (Impossible Check!).

Now for compulsory repetition, that is, a situation where both players can’t escape repeating their actions, I really couldn’t think of a way to ensure that this isn’t possible. At least I hadn’t thought of anything until yesterday, when I played a rather peculiar game.

In it I ended up making a pawn barrier, which made it difficult for both parties to advance without losing pieces for that. It was a peculiar game because even though I was at a disadvantage on points, we entered a scenario of resistance and preservation. Nobody was willing to sacrifice themselves to break the barrier, and the possibilities of breaking it without loss were blocked by both sides.

When this game ended, I realized why I couldn’t prove that a mandatory replay situation is impossible!

I couldn’t prove it’s impossible, because it’s actually possible!

Just think that on both sides the pieces are prevented from advancing due to pedestrian barriers. But there is one more precaution, which involves the impossibility of even sacrificing one of these pieces to force one of the opponent’s pawns to move. A very simple scenario to illustrate this complete impediment is presented below:

Both players cannot move their kings on any row except row 1 and 8, also none of the pawns can move. As each player has his 8 initial pawns this is also not a case of “insufficient material” (when there is no possibility to perform a checkmate with the available pieces).

However, there is no way we can make any progress in this match. That is, the kings will be moving through their 8 squares continuously, without this affecting the state of any of the 16 pawns. That way, at some point, the moves of the two opponents will be repeated and this will put them in a tie by repetition, which neither party can prevent 🙂

Cover image credits to http://megapixel.click – betexion – photos for free by Pixabay