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# Farkle Heuristic II

by firebus

07/24/2013 - 12:11

I've been playing solitaire farkle on an app, and my goal is to get on the high score list, which means that I'm starting to aim for higher and higher scores. This has altered my heuristic a little bit. Here's the new one:

- Maximize the number of times you can roll for three of a kind each turn - this means scoring as few dice as possible on each roll as long as you'll still have at least 3 dice to roll on the next roll
- Get hot dice as much as possible - this means that once there's fewer than 3 dice to roll, score as many 1s and 5s as you can. This assumes that you're more likely to get hot dice if you roll a single die (1/3) than if you roll 2 dice (1/36 chance of getting hot dice, 11/12 chance of getting another roll.) I'm just being really lazy here and not doing the math, sorry. Maybe tomorrow.)
- If you're under par (i.e., if you're shooting for 6000, then you need 600 points per turn) and you have fewer than 5 turns remaining, then keep rolling until you hit your adjusted par.

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## Comments

## Probability of getting hot dice with one or two dice left

What I was too lazy to do in the OP.

You rolled 3 dice and you got 1, 5, 3. If you don't want to bank, you can choose between scoring one die and rolling two, or scoring two dice and rolling one.

If you score two dice, you have a 1/3 chance of getting hot dice on the last die.

If you score one die, you have a 1/36 chance of getting hot dice on the next roll, and an 11/36 chance of scoring one die and rolling one die. Then you have a 1/3 chance of getting hot dice on the last roll.

So the overall probability of getting hot dice if there are two dice remaining is 1/36 + (11/36 * 1/3) = 14/108 ~ 13%.