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# Games

## Farkle Heuristic II

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

## Farkle Heuristic I

I've been playing a lot of solitaire Farkle recently, having been introduced to it a few years ago by the Yun family.

I haven't started to grind out the probabilities for ideal play yet, but I'm thinking that I need to calculate the expected outcome for each possible throw (6 dice, 5 dice, etc.), and then determine if it makes sense to bank or roll based on the expected outcome and the probability of farkle for that roll.

Here's a heuristic for playing farkle, with some explanation of the assumptions it makes:

## Backwards compatible casual games

The problem with multiplayer (or massively-multiplayer) casual games is that at some point after release, everyone moves on to the next big thing and they become empty wastelands. Crickets. Tumbleweeds.

I propose that a games publisher release a series of games where the actions in the most recently released games are translated into actions in the previous game.

## What's the dumbest possible life-sized board game with human pieces?

I think it would be connect four.

## No-Repeat Guess Who

Since "Guess Who" is really a mind-numbingly boring game if you are above the age of 6, it's probably natural that adults trapped in a cabin, surrounded by flesh-eating zombies, with nothing on the shelf except Guess Who are going to invent some more difficult variations.

Trapped in the suffrage shack, this version was invented.

## Yahtzee Golf

I'm not sure how I never thought of this before, but I've been having a really bad run of Yahtzee and was wondering what my lowest ever score has been. Probably something a little south of 150. 135 maybe?

The lowest possible Yahtzee score is 5 - you put five 1s in chance and conspire to score 0 in every other box.

But what's the lowest possible score you can get if you are playing in good faith?

If you rolled 1-1-2-2-3 for every roll, then you'd get

1:2

2:4

3:3

4:0

5:0

6:0

Bonus:0

3K:0

4K:0

Full House:0

Small Straight:0

Large Straight:0

Yahtzee:0

Chance:9

## A 4K in the hand is worth 1.88

On the second roll of a play, I had 4 sixes and a five.

4K and Yahtzee were both open.

Obviously, the play would be worth 29 points in 4K, and Yahtzee is only a 1 in 6 chance, with a 2 in 3 chance of getting less than 29 on the next roll.

My heuristic is to *always* roll for Yahtzee on 4K if Yahtzee is open (and sometimes if Yahtzee is closed and Large Straight is open).

Expected outcome in this case is the average of all the possible outcomes: avg(50, 29, 28, 27, 26, 25) = 30.88. Go heuristics.

## General Yahtzee Strategy

Some counter-intuitive, some not. I haven't done the math on many of these. Some of them I gleaned from looking at the logs of the Optimal Solitaire Yahtzee Player, an invaluable resource.

- Early in the game, ditch a bad roll in the ones.
Sure, you'll go negative on the bonus, but it's likely you'll make it up if there are still 4 or 5 number boxes left to fill on the left.

- Don't actively try to fill the 1s and 2s boxes.

## Natural 3 of a kind Yahtzee chances

Typically what happens is that on your first roll you get 3 ones, and maybe a potentially useful singleton.

And you've already used the ones box.

So the question is, should you go for Yahtzee here? Or should you try to build off the singleton or just re-roll all five dice?

I suspect that if the probability is reasonably close to 1 in 6, it's probably your best chance at a Yahtzee in the game, and thus worth risking the Yahtzee box on.

There are 3 ways to get to Yahtzee from here, and we can sum their individual probabilities to get the overall chances.

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