3 card poker hole carding combinatorics
March 16th, 2011 at 8:28:24 AM
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This is kind of a question for the Wizard himself, unless of course someone else has produced this information.
https://wizardofodds.com/games/three-card-poker-flash.html
This page has the combination table used to derive the 3.48% player advantage when the player has perfect knowledge of one of the dealer's cards. It also states that the player advantage when he can determine that one of the dealer's cards is an ace or face card (but not necessarily which face card) is 2.41%, and that the house advantage when he can determine that one of the dealer's cards is a face card or not is 2.43%.
Does there exist the combination table used to derive those last two advantage numbers?
https://wizardofodds.com/games/three-card-poker-flash.html
This page has the combination table used to derive the 3.48% player advantage when the player has perfect knowledge of one of the dealer's cards. It also states that the player advantage when he can determine that one of the dealer's cards is an ace or face card (but not necessarily which face card) is 2.41%, and that the house advantage when he can determine that one of the dealer's cards is a face card or not is 2.43%.
Does there exist the combination table used to derive those last two advantage numbers?
April 1st, 2011 at 5:30:26 PM
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For those that are interested, I've generated them. I also independently generated the perfect hole carding numbers, just to be sure my work was correct.
PERFECT HOLE CARDING
Win Combinations Probability Return Variance
7 1,851,132 0.15% 0.01061 0.07352
6 2,795,916 0.23% 0.01373 0.08145
5 867,312 0.07% 0.00355 0.01750
3 26,929,356 2.20% 0.06614 0.19383
2 272,048,544 22.27% 0.44543 0.86010
1 357,814,224 29.29% 0.29293 0.27288
0 689,736 0.06% 0.00000 0.00000
-1 142,804,152 11.69% -0.11691 0.12519
-2 415,710,828 34.03% -0.68065 1.40913
1,221,511,200 100% 0.03483 3.03360
ACE/FACE/OTHER
Win Combinations Probability Return Variance
7 1,851,132 0.15% 0.01061 0.07375
6 2,795,916 0.23% 0.01373 0.08174
5 867,312 0.07% 0.00355 0.01758
3 26,929,356 2.20% 0.06614 0.19524
2 271,222,128 22.20% 0.44408 0.86690
1 342,422,604 28.03% 0.28033 0.26699
0 689,736 0.06% 0.00000 0.00000
-1 179,148,312 14.67% -0.14666 0.15381
-2 395,584,704 32.38% -0.64770 1.32677
1,221,511,200 100% 0.02407 2.98278
FACE/OTHER
Win Combinations Probability Return Variance
7 1,851,132 0.15% 0.01061 0.07477
6 2,795,916 0.23% 0.01373 0.08307
5 867,312 0.07% 0.00355 0.01792
3 26,929,356 2.20% 0.06614 0.20164
2 271,671,288 22.24% 0.44481 0.91135
1 342,422,604 28.03% 0.28033 0.29410
0 720,216 0.06% 0.00000 0.00000
-1 118,236,312 9.68% -0.09680 0.09215
-2 456,017,064 37.33% -0.74664 1.45726
1,221,511,200 100% -0.02427 3.13227
Apologies for the formatting.
PERFECT HOLE CARDING
Win Combinations Probability Return Variance
7 1,851,132 0.15% 0.01061 0.07352
6 2,795,916 0.23% 0.01373 0.08145
5 867,312 0.07% 0.00355 0.01750
3 26,929,356 2.20% 0.06614 0.19383
2 272,048,544 22.27% 0.44543 0.86010
1 357,814,224 29.29% 0.29293 0.27288
0 689,736 0.06% 0.00000 0.00000
-1 142,804,152 11.69% -0.11691 0.12519
-2 415,710,828 34.03% -0.68065 1.40913
1,221,511,200 100% 0.03483 3.03360
ACE/FACE/OTHER
Win Combinations Probability Return Variance
7 1,851,132 0.15% 0.01061 0.07375
6 2,795,916 0.23% 0.01373 0.08174
5 867,312 0.07% 0.00355 0.01758
3 26,929,356 2.20% 0.06614 0.19524
2 271,222,128 22.20% 0.44408 0.86690
1 342,422,604 28.03% 0.28033 0.26699
0 689,736 0.06% 0.00000 0.00000
-1 179,148,312 14.67% -0.14666 0.15381
-2 395,584,704 32.38% -0.64770 1.32677
1,221,511,200 100% 0.02407 2.98278
FACE/OTHER
Win Combinations Probability Return Variance
7 1,851,132 0.15% 0.01061 0.07477
6 2,795,916 0.23% 0.01373 0.08307
5 867,312 0.07% 0.00355 0.01792
3 26,929,356 2.20% 0.06614 0.20164
2 271,671,288 22.24% 0.44481 0.91135
1 342,422,604 28.03% 0.28033 0.29410
0 720,216 0.06% 0.00000 0.00000
-1 118,236,312 9.68% -0.09680 0.09215
-2 456,017,064 37.33% -0.74664 1.45726
1,221,511,200 100% -0.02427 3.13227
Apologies for the formatting.
