--- Day 21: Dirac Dice ---
There's not much to do as you slowly descend to the bottom of the ocean. The submarine computer challenges you to a nice game of Dirac Dice.
This game consists of a single die, two pawns, and a game board with a circular track containing ten spaces marked 1 through 10 clockwise. Each player's starting space is chosen randomly (your puzzle input). Player 1 goes first.
Players take turns moving. On each player's turn, the player rolls the die three times and adds up the results. Then, the player moves their pawn that many times forward around the track (that is, moving clockwise on spaces in order of increasing value, wrapping back around to 1 after 10). So, if a player is on space 7 and they roll 2, 2, and 1, they would move forward 5 times, to spaces 8, 9, 10, 1, and finally stopping on 2.
After each player moves, they increase their score by the value of the space their pawn stopped on. Players' scores start at 0. So, if the first player starts on space 7 and rolls a total of 5, they would stop on space 2 and add 2 to their score (for a total score of 2). The game immediately ends as a win for any player whose score reaches at least 1000.
Since the first game is a practice game, the submarine opens a compartment labeled deterministic dice and a 100-sided die falls out. This die always rolls 1 first, then 2, then 3, and so on up to 100, after which it starts over at 1 again. Play using this die.
For example, given these starting positions:
Player 1 starting position: 4
Player 2 starting position: 8
This is how the game would go:
- Player 1 rolls
1+2+3and moves to space10for a total score of10. - Player 2 rolls
4+5+6and moves to space3for a total score of3. - Player 1 rolls
7+8+9and moves to space4for a total score of14. - Player 2 rolls
10+11+12and moves to space6for a total score of9. - Player 1 rolls
13+14+15and moves to space6for a total score of20. - Player 2 rolls
16+17+18and moves to space7for a total score of16. - Player 1 rolls
19+20+21and moves to space6for a total score of26. - Player 2 rolls
22+23+24and moves to space6for a total score of22.
...after many turns...
- Player 2 rolls
82+83+84and moves to space6for a total score of742. - Player 1 rolls
85+86+87and moves to space4for a total score of990. - Player 2 rolls
88+89+90and moves to space3for a total score of745. - Player 1 rolls
91+92+93and moves to space10for a final score,1000.
Since player 1 has at least 1000 points, player 1 wins and the game ends. At this point, the losing player had 745 points and the die had been rolled a total of 993 times; 745 * 993 = 739785.
Play a practice game using the deterministic 100-sided die. The moment either player wins, what do you get if you multiply the score of the losing player by the number of times the die was rolled during the game?