charliepatrick
Joined: Jun 17, 2011
• Posts: 2329
October 31st, 2020 at 7:21:22 PM permalink
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
Last edited by: charliepatrick on Oct 31, 2020
charliepatrick
Joined: Jun 17, 2011
• Posts: 2329
November 1st, 2020 at 5:17:02 AM permalink
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
Wizard

Joined: Oct 14, 2009
• Posts: 22748
November 1st, 2020 at 9:28:32 PM permalink
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.
It's not whether you win or lose; it's whether or not you had a good bet.
rsactuary
Joined: Sep 6, 2014
• Posts: 1797
November 1st, 2020 at 9:55:40 PM permalink
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.
Wizard

Joined: Oct 14, 2009
• Posts: 22748
November 2nd, 2020 at 5:25:50 AM permalink
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.
It's not whether you win or lose; it's whether or not you had a good bet.
rsactuary
Joined: Sep 6, 2014
• Posts: 1797
Thanks for this post from:
November 2nd, 2020 at 6:35:57 AM permalink
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
gordonm888
Joined: Feb 18, 2015
• Posts: 2823
November 2nd, 2020 at 10:46:55 AM permalink
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.
Last edited by: gordonm888 on Nov 2, 2020
So many better men, a few of them friends, are dead. And a thousand thousand slimy things live on, and so do I.
terapined
Joined: Dec 1, 2012
• Posts: 5783
November 2nd, 2020 at 11:22:46 AM permalink
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
"Everybody's bragging and drinking that wine, I can tell the Queen of Diamonds by the way she shines, Come to Daddy on an inside straight, I got no chance of losing this time" -Grateful Dead- "Loser"
Wizard

Joined: Oct 14, 2009
• Posts: 22748
November 17th, 2020 at 7:23:27 AM permalink
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?
It's not whether you win or lose; it's whether or not you had a good bet.
rsactuary
Joined: Sep 6, 2014