For extra credit: a die game

Find a winning strategy for one of the players (player 1 or player 2) of the following game.

We have a regular die. (It has 6 faces with numbers 1-6 on them, so that the numbers on the opposite faces add up to 7. That is, 1 and 6 are on opposite faces; 2 and 5 are on opposite faces; 3 and 4 are on opposite faces.)

The first player puts the die on the table, and the number on the top is recorded.

The second player rotates the die by 90 degrees in any direction and adds the number on the top to the previously recorded number.

Then the first player goes again, then the second, and so on, with each player rotating the die by 90 degrees in any direction and adding the number on the top to the last recorded number. So, leaving the die in the current position is not allowed, and flipping it over (by 180 degrees) is not allowed either, but it can be turned sideways in any direction.

The game stops when the recorded sum becomes above 31. The player who made the sum larger than 31 loses, that is, the player who had the last sum not exceeding 31 wins.

For example, the first player could put the die with 5 on the top. Then 5 is recorded. The second player cannot make 2 or 5 on top, but can make any other number on top. Say, the second player chose to make 3 on top. Then 5+3=8 is computed and recorded. Say, the first player chose to make 1 on top. Then 8+1=9 is computed and recorded. Say, the second player chose to make 5 on top again. Then 9+5=14 is computed and recorded. And so on, until the number becomes larger than 31. Then the player who got larger than 31 lost.