How much are high cards, especially AK, hurt by inability to make J-2, K-4 straights? - Gambling and Probability

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How much are high cards, especially AK, hurt by inability to make J-2, K-4 straights?

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05-22-2020 , 02:34 PM

NovaAce

centurion

Join Date: Sep 2019 Posts: 129

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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05-23-2020 , 02:21 AM

ejames209

veteran

Join Date: May 2016 Posts: 2,698

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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05-23-2020 , 10:23 AM

whosnext

Carpal \'Tunnel

Join Date: Mar 2009 Posts: 6,730

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

Category	As Ks	6h 6d	Js Ts	6h 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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