[adhdbrain]

Can someone please explain how the math works out to 89%?

>> let’s imagine two players, Alice and Bob, and a 3-by-3 grid. A referee assigns Alice a row and tells her to enter a 0 or a 1 in each box so that the digits sum to an odd number. Bob gets a column and has to fill it out so that it sums to an even number. They win if they put the same number in the one place her row and his column overlap. They’re not allowed to communicate. Under normal circumstances, the best they can do is win 89% of the time.

[dandanua]

Here the explanation and the picture describes the best strategy https://en.wikipedia.org/wiki/Quantum_pseudo-telepathy#The_M...

[xondono]

Alice and Bob just need to agree before hand on the proper distribution of 1s:

Alice will set the combination 100 if she was assigned either the first or the second rows, and the 010 if she is assigned the last.

Now Bob knows how to win if he gets first column since 110 will always win, and knows how to win if he gets the last column, because 000 always wins.

When assigned the middle column though, he needs to choose between 101 and 011. He will win if Alice got last row no matter what, but the other two are a toss up.

He’ll get it right half of the time, so he will win for sure if row and column meet at 7/9 squares, and the other two he’ll win half of the time, thus 8/9.

[sporkland]

I read the whole wiki page. I don't fully follow how it doesn't count as "communication". Bob may not know exactly what row Alice has or pattern Alice is using, but doesn't he know that she has either a +/- in the first row or a +/- in the second row or a +/- on the third row depending on the measurement he gets back?

I'm sure there is a basic piece I'm missing here.

[Gibbon1]

I'm suspicious of 3X3 = 9 and 1 - 1/9 = 0.88888

[zeroonetwothree]

It's an upper bound, I'm not sure if anyone has constructed an optimal algorithm matching it though.