Solve this game

[gdsdiscgolfer]

It's a variation of a simple take-away game I've solved before. Have ideas, but want to see what the right answer is. Fun little problem:

From a deck of cards,
take the Ace, 2, 3, 4, 5, and 6 of each suit. These 24 cards are laid out face up on a table.
The players alternate turning over cards and the sum of the turned over cards is computed
as play progresses. Each Ace counts as one. The player who first makes the sum go above
31 loses. It would seem that this is equivalent to the game of the previous exercise played
on a pile of 31 chips. But there is a catch. No integer may be chosen more than four times.
(a) If you are the first to move, and if you use the strategy found in the previous exercise,
what happens if the opponent keeps choosing 4?
(b) Nevertheless, the first player can win with optimal play. How?

[Darryl_P]

Answer in white:

<font color="white"> I think the correct play is to take a 5. This way if your opponent tries to make it come out to a multiple of 7, he'll have to take another 5 which leaves him with too few 5's. In other words, you just take a 2 next time. If he takes less than 5, you take 5 minus whatever he took. If he takes a 6, then you also take a 6 and you win. </font>

[MadTiger]

Like the game with matchsticks, Nim I believe it's called.
Classic Game Theory simple game illustrating a situation where you can't lose if you know the strategy and go first.

[gdsdiscgolfer]

What is that move?