themikep82/matthand-dice

dice rollling game simulator and analysis

After a night out with some friends, they taught me a simple dice rolling game. The rules are as follows.

The goal is to roll the highest cumulative score with 5 dice. However, you must keep a 4 and a 1 in your rolls to make your score count. Failing to roll and keep a 4 and a 1 means you score 0 points, similar to going bust in Blackjack.

This means you'll finish, ideally, with 2 'qualifying' dice and 3 scoring dice. Since 6 is the max roll, the highest possible score is 18 (3 scoring dice x 6), meaning your final dice roll would be [6, 6, 6, 4, 1].

Each round you roll all unkept dice and are required to keep a minumum of 1 die, which can be a score die or a qualifying die. You can keep more than 1 if you choose. That's the strategy of the game. Do you go for big scores? Or do you try to qualify ASAP to secure a score. It's risk/reward, cost/benefit.

The veterans of the game kept their 4s and 1s early in order to qualify. I surmised that keeping qualifiers early robbed you of additional die rolls which eventually robbed you of high score potential, so I kept my 6s and rerolled my qualifiers. There was much hullabaloo. I won a bunch. Then I lost a bunch. We only played maybe two dozen games, a sample size far to small to tell if I'm a genius or an idiot, but I was inspired to find the answer, so I did this analysis to find out.