YAHTZEE strategy

Quote: gordonm888

Here is some statistical information...

I agree with the lower numbers on the assumption that on the last round (of three rolls) a yahtzee can provide a winner in any of the sections (except "chance"). I don't quite get the top numbers (currently getting near 2.08 not 2.106481), assuming an incorrect yahtzee is 0. I'll have another look at my code tomorrow as I possibly have an error when the player should re-roll everything which can't happen in the bottom half.

Aces	2.079 564
Twos	4.159 128
Threes	6.238 692
Fours	8.318 256
Fives	10.397 819
Sixes	12.477 383
3 of a kind	15.194 661
4 of a kind	5.611 263
Full House	9.153 620
Short Straight	18.477 282
Long Straight	10.612 741
Yahtzee	2.301 432
Chance	23.330 717

Now I agree - I guess there are situations where you do re-roll everything in the chance saloon, I'm guessing when you've seen all ten dice (1st round and 2nd round) rolled less than 4! Also a warm feeling that chance is a fraction.

Aces	2.106 481
Twos	4.212 963
Threes	6.319 444
Fours	8.425 926
Fives	10.532 407
Sixes	12.638 889
3 of a kind	15.194 661
4 of a kind	5.611 263
Full House	9.153 620
Short Straight	18.480 750
Long Straight	10.612 742
Yahtzee	2.301 432
Chance	23.333 333

Let's say it's your first turn and after the third roll you have #$%*, like 1-2-2-4-6. Which field should you fill in?

I'd probably fill in 4 for twos.

Quote: Wizard

Let's say it's your first turn and after the third roll you have #$%*, like 1-2-2-4-6. Which field should you fill in?

I'd probably fill in 4 for twos.

Personally, I'd fill in the 1. If you fill in the two 2s, you have to get a fourth 3, 4, 5 or 6 to get the upper bonus. If you fill in the 1, you have the additional benefit of being able to get four 2s to get the bonus.

Quote: rsactuary

Personally, I'd fill in the 1. If you fill in the two 2s, you have to get a fourth 3, 4, 5 or 6 to get the upper bonus. If you fill in the 1, you have the additional benefit of being able to get four 2s to get the bonus.

Good point. It just feels so feeble but write in a "1," but I suspect you're right.

Of course, papers have been written...

http://gunpowder.cs.loyola.edu/~jglenn/research/optimal_yahtzee.pdf

and...

http://www-set.win.tue.nl/~wstomv/misc/yahtzee/slides-2up.pdf

Here is an optimal strategy analyzer which suggests playing the two 2s instead of the one 1. Seems counter-intuitive to me. I guess the advantage of having the ability to get four 2s on a future roll is more than offset by the probability of not getting at least two 2s again?

http://www-set.win.tue.nl/~wstomv/misc/yahtzee/osyp.php

These results are from the Verhoeff paper on Optimal Yahtzee Strategies.

1. First turn, first roll: 1 1 6 6 6
a. Keep: 6 6 6 _____265.12 +/- 61
b. Keep all and score 25 in Full House: 253.91 +/- 57
I suspect the ranking of these options would be flipped if this roll occurred late in the game, because Full House is so hard to get points for when you target it, rather than get it accidently. Although it probably depends upon what is needed on top to get a total of 63 or higher.

2. First turn, second roll: 1 1 3 4 6
a. Keep 3 4: 245.17 +/- 57
b. Keep 1 1: 245.14 +/- 57
c. Keep 4: 244.96
d. Keep 3: 244.74
e. Keep none: 244.55
f. Keep 6: 244.52
The fact that “f: Keep 6” scores the lowest seems to show the importance of targeting the SIXES when your first roll has at least two 6s. Scoring at least 18 with a shot at scoring 24 in SIXES is one of the keys to getting a high score.

3. First turn, third roll: 6 6 6 6 1
a. Score 24 in Sixes: 268.23 +/- 53
b. Score 25 in Four of a Kind: 260.54 +/- 54

I suspect the difference between these two options would be smaller (by 4) if it were 6 6 6 6 5.

Ive been playing lately
cool game
Have it on my switch, part of a 50 game package of games
My strategy is to try to hit the straight and take ones or 2's or 3's when I dont because those dont score much anyway
Overall, seems whoever can hit a straight 1st will win.
You hit it early, you will score high
You hit it late, you will score low

At the end of your first turn you have 6-6-6-6-5. Do you fill in 24 for sixes or 29 for a four of a kind?

Quote: Wizard

At the end of your first turn you have 6-6-6-6-5. Do you fill in 24 for sixes or 29 for a four of a kind?

I'm going for 24 for sixes in a heartbeat as it practically ensures you're going to get the 35 point bonus.