Your turn — roll or hold
The old push-your-luck dice game. Roll as long as you dare to build a turn total, hold to bank it, and pray you don't roll a 1. First to 100 beats the rival — then the rival gets smarter.
Tap Roll to throw the die; every 2 to 6 is added to your turn total. Tap Hold to bank the turn total and pass the die. Roll a 1 and the whole turn total is lost. The first player to reach 100 points wins the match.
Banked points are safe forever — only the points you are still risking in the current turn can be lost. You may roll as many times as you like, and you win the moment your bank plus your turn total reaches 100, without needing to hold. Each player's bar shows the banked points in colour and the points at risk this turn as a pale extension.
You play a run of matches against one AI rival. You roll first in the first match, and after that the opening roll alternates, so the rival opens matches two, four, six and so on. Win and your streak grows; lose once and the run is over.
The rival climbs a ladder as your streak grows. At streaks 0 and 1 it holds as soon as it has 15 points in a turn. At streaks 2 and 3 it holds at 20. From streak 4 to 6 it races: it holds at 21 plus about one point for every 8 points it trails by (minus one for every 8 it leads by), and once either player has 71 or more it keeps rolling until it wins or busts. From streak 7 on it plays the mathematically optimal strategy for every score.
Your Hall of Fame score is your streak times 10,000 plus the sum of your winning margins (the 100 points you reached minus the rival's banked total), capped at 9,999. Two runs with the same streak are separated by how convincingly you won.
The famous rule of thumb is to hold at 20. Each roll gains 4 points on average when it is not a 1, which happens five times in six, but costs your whole turn total when it is a 1, one time in six. The expected change of one more roll is (20 − turn total) ÷ 6, so below 20 another roll gains points on average and above 20 it loses them. That is exactly why the rival's second rung holds at 20.
Holding at 20 only maximises points per turn, not the chance of winning, and the difference shows near the end. When the rival is close to 100, every turn you give it is a real chance for it to finish, so you should keep rolling well past 20 — at the extreme, if it sits on 95 you should simply roll until you win or bust. When you are far ahead, take smaller safe bites instead. The race-aware rival from streak 4 does both: it pushes harder when behind and goes all-in once anyone reaches 71.
Rolling first is an advantage. With perfect play on both sides the player who opens wins about 53 percent of the time, which is why the opening roll alternates between matches. Expect your best streaks to come from strings of opening matches and lucky rolls; against the optimal rival even perfect play only breaks even over many matches.
Think in chances, not hopes. The chance of getting through five rolls without a 1 is (5/6)⁵, about 40 percent, and through ten rolls it is only about 16 percent. When you need 30 more points from a turn, you will usually need seven or eight safe rolls, so decide in advance how far you are willing to push.