Wizard
Joined: Oct 14, 2009
• Posts: 23626
Thanks for this post from:
July 23rd, 2020 at 5:24:16 PM permalink
I think I have found my error. It was how the program handled a dealt straight on the first roll. It did not properly weight it, so the player was throwing it away.

It takes my program about two hours to cycle. Hope to have good news soon. My EV's on some sample hands agrees with those of MattUK.

Thanks again everybody for your help!
It's not whether you win or lose; it's whether or not you had a good bet.
ThatDonGuy
Joined: Jun 22, 2011
• Posts: 5072
July 23rd, 2020 at 6:35:50 PM permalink
Quote: DJTeddyBear

Nice job, but I wish there was also a chart showing the possibility of each hand at the end of 3 rolls. Kind of important when figuring the house edge.

Here's the complete breakdown:

362,797,096 Nice Dice
18,570,954,200 Five of a Kind (except Nice)
86,360,256,000 Four of a Kind
94,383,221,760 Full House
39,907,676,160 Straight
86,556,211,200 Three of a Kind
70,073,579,520 Two Pair
63,892,592,640 One Pair
10,077,696,000 No Pair/Straight (12346, 12356, 12456, 13456)
Wizard
Joined: Oct 14, 2009
• Posts: 23626
July 23rd, 2020 at 7:10:36 PM permalink
I found the bug in my program. It effectively didn't let the player keep a pat hand, except a five of a kind, on the first roll. Here are my new numbers.

Event Pays Combinations Probability Return
Five of a kind on first roll 9 362,797,056 0.000772 0.006944
Five of a kind 3 18,570,954,240 0.039497 0.118491
Four of a kind 1.5 86,360,256,000 0.183673 0.275509
Straight 1 39,907,676,160 0.084877 0.084877
Full house 0 94,383,221,760 0.200736 0.000000
Loser -1 230,600,079,360 0.490445 -0.490445
Total 470,184,984,576 1.000000 -0.004624

They could have had a much more attractive pay table if a straight paid more than four of a kind. In the game of Yahtzee, a large straight pays 40, while a four of a kind pays only the "sum of the dice," which would average 17.5 assuming no strategy to go for the higher four-of-a-kinds.
It's not whether you win or lose; it's whether or not you had a good bet.
MattUK
Joined: Jul 25, 2017
• Posts: 138
July 23rd, 2020 at 7:51:31 PM permalink
Personally, I like to think that the chance to get Nice Dice is 1/1296 and the return is 9/1296 = 1/144. On your table, it's extended by as much as 6^7. Still true, but devoid of much of elegance. For the same reason, the total number is 6^15 and all values can be divided by at least 6^7 to get more manageable figures.
Wizard
Joined: Oct 14, 2009
• Posts: 23626
July 23rd, 2020 at 8:32:31 PM permalink
Quote: MattUK

Personally, I like to think that the chance to get Nice Dice is 1/1296 and the return is 9/1296 = 1/144. On your table, it's extended by as much as 6^7. Still true, but devoid of much of elegance. For the same reason, the total number is 6^15 and all values can be divided by at least 6^7 to get more manageable figures.

The reason the total is 6^15, is that you have six dice that can be rolled three times. Much like in video poker many of my return tables total to 5*combin(52,5)*combin(47,5), although there is usually a common denominator to each line item.

After all the work I put into my program, I prefer to leave the raw results as they are.
It's not whether you win or lose; it's whether or not you had a good bet.
rsactuary
Joined: Sep 6, 2014
• Posts: 1881
July 23rd, 2020 at 8:46:19 PM permalink
Your answers differ than Don Guy's by 40 in the 5 of a kind (not nice) and loser categories.

Not sure who is wrong, but someone is!
Torghatten
Joined: Feb 3, 2012
• Posts: 85
July 23rd, 2020 at 8:49:20 PM permalink
Quote: rsactuary

Your answers differ than Don Guy's by 40 in the 5 of a kind (not nice) and loser categories.

Not sure who is wrong, but someone is!

470,184,984,576 / 1296 shows that Wizard is right.
charliepatrick
Joined: Jun 17, 2011
• Posts: 2495
July 24th, 2020 at 3:16:20 AM permalink
I agree with the wizazrd's numbers. You can confirm the Nice Dice as it's 7776*7776*6 (six ways to get the five of a kind, no dice rerolled so all 6^5 combinations, repeat). btw I classified the One Pair events as the strategy was different for them.
EventCombinationsPaysContribution
Nice Dice
362 797 056
10
3 627 970 560
Fiver
18 570 954 240
4
74 283 816 960
86 360 256 000
3
215 900 640 000
FH
94 383 221 760
1
94 383 221 760
Straight
39 907 676 160
2
79 815 352 320
Trips
86 556 211 200
Two Pair
70 073 579 520
Pair/EasyStr
14 511 882 240
Pair/InStr
40 310 784 000
Pair/NoStr
9 069 926 400
Inside Str
10 077 696 000
TOTAL
470 184 984 576
468 011 001 600
Any Pair
63 892 592 640
RTP:
99.537 632 411%
ThatDonGuy
Joined: Jun 22, 2011
• Posts: 5072
July 24th, 2020 at 7:03:15 AM permalink
Quote: rsactuary

Your answers differ than Don Guy's by 40 in the 5 of a kind (not nice) and loser categories.

Not sure who is wrong, but someone is!

My "loser numbers" add up to the Wizard's.

You're right about the "not nice 5 of a Kind" number; I calculated the total 5 of a Kind count and then subtracted the wrong number of Nice Dice rolls. Notice that my Nice Dice number is off by 40 as well.
Wizard