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Old 05-22-2020, 02:34 PM   #1
NovaAce
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How much are high cards, especially AK, hurt by inability to make J-2, K-4 straights?

One of the classic examples of relative hand strength being different than overall card strength is the following all in probabilities:

AKs vs. 22: 49.70% to win
J10s vs. 22: 53.70% to win

I was wondering, is almost all of this 4% disparity due to the lack of ability for AK to make J-2 to K-4 straights?

To avoid blockers to the straight, how about

AKs vs. 77: 47.88% to win
J10s vs. 77: 50.82% to win

If AK could make all straights, would they certainly be better than J10 against the underpairs?

Last edited by NovaAce; 05-22-2020 at 02:40 PM.
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Old 05-23-2020, 02:21 AM   #2
ejames209
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Re: How much are high cards, especially AK, hurt by inability to make J-2, K-4 straights?

Yes I do believe that is a driving factor.

As another example, QJs is a statistical favorite vs every pocket pair below 88, since 88 blocks two cards necessary to make one of the straights.
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Old 05-23-2020, 10:23 AM   #3
whosnext
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Re: How much are high cards, especially AK, hurt by inability to make J-2, K-4 straights?

Here are the tallies of win categories for AsKs vs 6h6d and for JsTs vs 6h6d.

CategoryAs Ks6h 6dJs Ts6h 6d
Royal Flush
990
0
990
0
Straight Flush
43
430
2,838
430
Four of a Kind
2,390
15,177
2,282
15,174
Full House
39,066
134,949
38,994
134,868
Flush
106,446
36,328
103,737
36,328
Straight
44,111
36,005
150,905
21,603
Three of a Kind
44,030
179,224
42,920
170,316
Two Pair
303,359
305,640
292,052
283,560
One Pair
276,408
181,425
254,072
151,335
High Card
0
0
0
0
All Ties
6,283
6,283
9,900
9,900
TOTAL WINS
816,843
889,178
888,790
813,614
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