Are we sure the memory depth is 5? It's a weird case since you need to know the round number + the last five rounds.

Are we sure the memory depth is 5? It's a weird case since you need to know the round number + the last five rounds.

This is similar to memory one strategies that all have a memory depth of 1 but that act differently on their first move to any other right?

You don't need to know the full round number. If you gave me just the last five moves as a list, I could check if that list is length 5 or not.

You don't need to know the full round number. If you gave me just the last five moves as a list, I could check if that list is length 5 or not.

Even better point 👍

I guess that's what I'm asking -- on the first move there's no history so it's sort of a special case and players must have a separate rule. Here on rounds say 4, 5, 6 you have to know the round number and then decide from one of two behaviors. So we need to know if there are at least 5 rounds of history already, so we need the size of the history and therefore all of the history. Or is the rule that we can ask "Are there at least X rounds of history?" and then take the minimum needed value of X as the memory depth?

Also think about the case where there's X rounds of initial play and then a behavior that depends on the last Y rounds, where X != Y.

Also, if the implementation were setting a bit if_round_greater_than_five then we usually call that kind of situation infinite memory...

Here on rounds say 4, 5, 6 you have to know the round number and then decide from one of two behaviors. So we need to know if there are at least 5 rounds of history already, so we need the size of the history and therefore all of the history. Or is the rule that we can ask "Are there at least X rounds of history?"

It's a good question. I think that my personal preference would be to define memory as "if you give history[-memory:] or history you get the same behaviour". I believe this isn't the first strategy that poses this question so I'd suggest we merge as is (based on the mem 1 behaviour/convention it feels right to me that this has mem depth 5). And perhaps aim to implement a test for memory on all players?

In this sense, Tit-For-Tat has to know the round number, since there's a special rule for when turn=1, so you have to know the turn number. But I think it's clear that TFT is memory=1; by analogy, this is memory=5. And I think it's intuitive; you're allowed to be forgetful.

"if you give history[-memory:] or history you get the same behaviour"

In this particular case if we're on the third turn with opponent.history=[C, C, C] then opponent.history[-5:] would also be [C, C, C], so:

+        if len(opponent.history) < 5:
+            return C

would return C.

And perhaps aim to implement a test for memory on all players?

This would potentially assist with #597 (not in finding an algorithm but at least verifying upper bounds on memory lengths).

In this particular case if we're on the third turn with opponent.history=[C, C, C] then opponent.history[-5:] would also be [C, C, C], so:

If we're on the 150th turn then len(opponent.history[-5:]) is 5 so the rest of the logic kicks in.

I've opened #1156 as a suggestion for a test (to perhaps move the discussion about the way to go over there).

Ok, let's discuss elsewhere. I'll merge as is.