20100107:
I think the expected value is around 260. 63+25=98 on top. 25+25+25+30+40+0+20=165 on bottom. For 263 total. This matches well with my score sheet above. 1610 divided by 6 is 268 1/3. But there is a program called the Optimal Solitaire Yahtzee Player whose expected final score is 254.5896... (here) Looking at the table on that page, it would seem I overestimated the score that comes from four of a kind. Knowing OSYP to have an average of 13 in four of a kind, one would be less greedy...
One of the tables should be of particular interest to Josh. The OSYP plays optimally and obtained the following series of "unlucky" rolls:
Rd Final Rll Sc Category
01 1 4 4 5 5 01 Aces
02 1 2 3 5 5 02 Twos
03 1 1 2 2 6 00 Four of a Kind
04 1 2 2 4 6 00 Yahtzee
05 1 1 2 2 6 00 Threes
06 1 2 2 3 3 00 Fours
07 1 2 2 3 3 00 Fives
08 1 2 2 3 3 00 Full House
09 1 2 2 3 3 00 Sixes
10 1 1 2 3 3 00 Large Straight
11 1 1 2 2 3 09 Chance
12 4 5 5 6 6 00 Three of a Kind
13 5 6 6 6 6 00 Small Straight
-- - - - - - 12 GRAND TOTAL
20100108:
Basically I'm seeing how close I am to making the right choices by playing Yahtzee on this website here. After you're done playing, or even after you make a move, you can press Analyze to see whether or not your move was considered Optimal compared to OSYP. One number is the total delta of all your choices, i.e., the sum of all the mistakes you made. On the other hand, if you're playing a game either online or on pencil and paper, and you want to know your best move, you can enter all the current data at this page here and it'll give you a list of possible moves, ranked by most optimal to least optimal. Prior to playing the above six games, I had gone through three entire games on the second page (the one that lets you know a list of moves) comparing my choices with the optimal choices and always choosing the optimal move to proceed. Essentially OSYP was playing and it got (1:279, 2:278, 3:195).
20110821:
[Where applicable '.' signifies who went first]
200XXXXX Tawnie (253) Tim (244)
200XXXXX Crystal (208) Tawnie (198) Tim (262)
200XXXXX Ann (201) Crystal (253) Tim (370)
200XXXXX Tawnie (184, 132, 232, 151) Tim (270, 261, 263, 196)
???????? Tawnie (141, 310)
???????? Tim (257, 209, 218)
20090717 Josh (1:263, 2:194, 3:193) Daniel (1:154, 2:192, 3:189) Stephanie (1:256, 2:254, 3:268) Me (1:289, 2:198, 3:229). 1:I won, 2:Stephanie won, 3:Stephanie won.
200907XX Josh (4:153) Chris (4:202) Stephanie (4:236) Me (4:259). 4: I won.
20090721 Josh (5:222) Daniel (5:321) Stephanie (5:253) Me (5:126). 5: Daniel won.
20100107 Josh (.1:209, .2:188) Tiffany (1:211) Tiffany/Chris (2: 247) Tim (1:270, 2:255). 1: I won, 2: I won.
20100107 Josh (.3:240, .4:196, 5:208, 6: 203; 6GameTotal:1244) Tim (3:266, 4:236, .5:314, .6:269; 6GameTotal:1610). 3: I won, 4: I won, 5: I won, 6: I won, 6GT: I won.
20100108 Tim (1:320, 2:179, 3:264, 4: 253, 5:267, 6: 198, 258). Delta (1:1.2, 2:6.34, 3:1.78, 4:6.92, 5:10.47, 6:3.88, 13.56).
20110709 Crystal (1:265) Tim (.1:368, 2:237). 1: I won.
20110806 AM Hours Josh (A:260, B:237, .C: 175) Chris (A:161, B: 206, C: 163) Tim (.A:373, .B:196, C:209). A: I won, B: Josh won, C: I won.
20110806 PM Hours Chris (D:251, .E:209, F: 167, G:267, .H:216, .I:237) Josh (.D: 206) Steve (D:245, E:302, .F:293, .G:160, H:244) Tim (D:236, E:225, F:243, G:261, H:320, I:274). D: Chris won, E: Steve won, F: Steve won, G: Chris won, H: I won, I: I won.
Personal Best from Above: Ann (201) Chris (267) Crystal (265) Daniel (321) Josh (263) Stephanie (268) Tawnie (310) Tiffany (211) Tim (373).
Average (All): Chris (11 games, 211.45) Josh (15 games, 209.8) Tim (39 games, 254.92)
Average (Last Five): Chris (224.5) Josh (214.83) Tim (259.83)
20110809 Tim,Delta (185,6.31 238,12.21 249,2.96 201,11.21 201,9.09 316,9.14 304,4.10 238,8.41 249,16.00)
20110820 Tim,Delta (162,1.64 257,1.20 189,5.53)
20110831 Tim,Delta (258,5.47)
Yahtzee
Relevant Links:
Yahtzee (BoardGameGeek.com)
Yahtzee Proficiency Test
I think the expected value is around 260. 63+25=98 on top. 25+25+25+30+40+0+20=165 on bottom. For 263 total. This matches well with my score sheet above. 1610 divided by 6 is 268 1/3. But there is a program called the Optimal Solitaire Yahtzee Player whose expected final score is 254.5896... (here) Looking at the table on that page, it would seem I overestimated the score that comes from four of a kind. Knowing OSYP to have an average of 13 in four of a kind, one would be less greedy...
One of the tables should be of particular interest to Josh. The OSYP plays optimally and obtained the following series of "unlucky" rolls:
Rd Final Rll Sc Category
01 1 4 4 5 5 01 Aces
02 1 2 3 5 5 02 Twos
03 1 1 2 2 6 00 Four of a Kind
04 1 2 2 4 6 00 Yahtzee
05 1 1 2 2 6 00 Threes
06 1 2 2 3 3 00 Fours
07 1 2 2 3 3 00 Fives
08 1 2 2 3 3 00 Full House
09 1 2 2 3 3 00 Sixes
10 1 1 2 3 3 00 Large Straight
11 1 1 2 2 3 09 Chance
12 4 5 5 6 6 00 Three of a Kind
13 5 6 6 6 6 00 Small Straight
-- - - - - - 12 GRAND TOTAL
20100108:
Basically I'm seeing how close I am to making the right choices by playing Yahtzee on this website here. After you're done playing, or even after you make a move, you can press Analyze to see whether or not your move was considered Optimal compared to OSYP. One number is the total delta of all your choices, i.e., the sum of all the mistakes you made. On the other hand, if you're playing a game either online or on pencil and paper, and you want to know your best move, you can enter all the current data at this page here and it'll give you a list of possible moves, ranked by most optimal to least optimal. Prior to playing the above six games, I had gone through three entire games on the second page (the one that lets you know a list of moves) comparing my choices with the optimal choices and always choosing the optimal move to proceed. Essentially OSYP was playing and it got (1:279, 2:278, 3:195).
20110821:
[Where applicable '.' signifies who went first]
200XXXXX Tawnie (253) Tim (244)
200XXXXX Crystal (208) Tawnie (198) Tim (262)
200XXXXX Ann (201) Crystal (253) Tim (370)
200XXXXX Tawnie (184, 132, 232, 151) Tim (270, 261, 263, 196)
???????? Tawnie (141, 310)
???????? Tim (257, 209, 218)
20090717 Josh (1:263, 2:194, 3:193) Daniel (1:154, 2:192, 3:189) Stephanie (1:256, 2:254, 3:268) Me (1:289, 2:198, 3:229). 1:I won, 2:Stephanie won, 3:Stephanie won.
200907XX Josh (4:153) Chris (4:202) Stephanie (4:236) Me (4:259). 4: I won.
20090721 Josh (5:222) Daniel (5:321) Stephanie (5:253) Me (5:126). 5: Daniel won.
20100107 Josh (.1:209, .2:188) Tiffany (1:211) Tiffany/Chris (2: 247) Tim (1:270, 2:255). 1: I won, 2: I won.
20100107 Josh (.3:240, .4:196, 5:208, 6: 203; 6GameTotal:1244) Tim (3:266, 4:236, .5:314, .6:269; 6GameTotal:1610). 3: I won, 4: I won, 5: I won, 6: I won, 6GT: I won.
20100108 Tim (1:320, 2:179, 3:264, 4: 253, 5:267, 6: 198, 258). Delta (1:1.2, 2:6.34, 3:1.78, 4:6.92, 5:10.47, 6:3.88, 13.56).
20110709 Crystal (1:265) Tim (.1:368, 2:237). 1: I won.
20110806 AM Hours Josh (A:260, B:237, .C: 175) Chris (A:161, B: 206, C: 163) Tim (.A:373, .B:196, C:209). A: I won, B: Josh won, C: I won.
20110806 PM Hours Chris (D:251, .E:209, F: 167, G:267, .H:216, .I:237) Josh (.D: 206) Steve (D:245, E:302, .F:293, .G:160, H:244) Tim (D:236, E:225, F:243, G:261, H:320, I:274). D: Chris won, E: Steve won, F: Steve won, G: Chris won, H: I won, I: I won.
Personal Best from Above: Ann (201) Chris (267) Crystal (265) Daniel (321) Josh (263) Stephanie (268) Tawnie (310) Tiffany (211) Tim (373).
Average (All): Chris (11 games, 211.45) Josh (15 games, 209.8) Tim (39 games, 254.92)
Average (Last Five): Chris (224.5) Josh (214.83) Tim (259.83)
20110809 Tim,Delta (185,6.31 238,12.21 249,2.96 201,11.21 201,9.09 316,9.14 304,4.10 238,8.41 249,16.00)
20110820 Tim,Delta (162,1.64 257,1.20 189,5.53)
20110831 Tim,Delta (258,5.47)
Yahtzee
Relevant Links:
Yahtzee (BoardGameGeek.com)
Yahtzee Proficiency Test
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