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Texas Hold'em Hand Strength, Visualized

chrisbeaumont.org

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Re: Texas Hold'em Hand Strength, Visualized

#3
post #2

I thougt that a 2 and a 7 were the worst, but here a 2 and 3 has -35.4% win%-lose% while 2 and 7 has a slightly better -30.8% win%-lose% (second diagram). Any idea what the difference is?

Not a poker expert by far, but this could be because 2/3 can only participate in three straight draws (A2345,23456,34567) whereas 2/7 can be in seven straight hands. (A2345, 23456, 34567, 45678, 56789, 6789T, 789TJ)

Re: Texas Hold'em Hand Strength, Visualized

#5
post #2

I thougt that a 2 and a 7 were the worst, but here a 2 and 3 has -35.4% win%-lose% while 2 and 7 has a slightly better -30.8% win%-lose% (second diagram). Any idea what the difference is?

72 offsuit is the worst hand against a table of opponents because it is the lowest hand that has no straight or flush opportunities (using both hole cards)

23 offsuit is the worst hand against a single opponent because the likelihood of needing a straight or flush to win the hand decreases and the penalty for having a lower highcard is higher.

Re: Texas Hold'em Hand Strength, Visualized

#6

Fascinating. I've seen a few remarkable showdowns between AQ and KK, I never would have guessed the odds were quite so tilted in KK's favour.

AQ vs KK is no different than A10 or AJ vs KK. Even middling Aces like A7 or A8 aren't much worse off because of the lost straight possibilities due to two K's being taken.

I haven't looked at the numbers but I would bet that A2-A5 are better off against KK than AQ.

Re: Texas Hold'em Hand Strength, Visualized

#8
post #2

I thougt that a 2 and a 7 were the worst, but here a 2 and 3 has -35.4% win%-lose% while 2 and 7 has a slightly better -30.8% win%-lose% (second diagram). Any idea what the difference is?

27 has high card value compared to 23 vs all other hands. Vs a hand someone would actually play, like JT, you don't have any high card value.

Re: Texas Hold'em Hand Strength, Visualized

#9
post #3
post #2

I thougt that a 2 and a 7 were the worst, but here a 2 and 3 has -35.4% win%-lose% while 2 and 7 has a slightly better -30.8% win%-lose% (second diagram). Any idea what the difference is?

Not a poker expert by far, but this could be because 2/3 can only participate in three straight draws (A2345,23456,34567) whereas 2/7 can be in seven straight hands. (A2345, 23456, 34567, 45678, 56789, 6789T, 789TJ)

But you need 4 cards on the board vs using both in your hand for all those 2-7 "straights"

Re: Texas Hold'em Hand Strength, Visualized

#10
post #2

I thougt that a 2 and a 7 were the worst, but here a 2 and 3 has -35.4% win%-lose% while 2 and 7 has a slightly better -30.8% win%-lose% (second diagram). Any idea what the difference is?

I'm going to guess that, after you enumerate all possible opposing hands along with all possible table cards, that the 7 gets paired up for a win more often than the straight lines up for a win. Also, due to their low card value, a 2-3 will pretty much automatically lose with no pairings, straights, or flushes. (And even then, it's a weak flush.)

If you look at the final diagram, they are almost equal in average expected payout, with the 2-7 dropping value much more than the 2-3. I would expect this is due to the paired 7 not being very strong against more commonly played hands with higher average card value. (In other words, 7 doesn't mean as much when the average opponent has cards higher than a 7.)

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