First time asking a question here, so apologies if I ask something in the wrong way. I have two problems I got back from an exam and have been struggling to find a reasonable reason for their incorrectness.
The two problems are as follows:
Let's play a game of restricted Nim where a player can only take 2, 3, or 5 stones at a time. Let's start with 1000 stones, and you go first. Whats your move, why, and whats the expected outcome?
Let's play a different but similar game of restricted Nim where a player can only take 1, 4, or 5 stones at a time. Let's start with 1000 stones, and again, you go first. Whats your move, why, and whats the expected outcome?
For both answers I said that I would keep the total stones left at the end of my turn to be a multiple of 5, until my last move, where I take enough to put the stones to 6 or 7. This is so because form here the opponent cannot take all of them, and at a minimum lets me take the rest. I figured since the restrictions all have a sort of 'five-ness' to them that this was the right way to go. In either case I said that I will always win, ie the player that plays first.
Is there some gaping hole I'm missing here?