Some answers
I made the call because I had heard people talking about Poki calling down with jack-high, and I studied this ahead of time. I think many experienced poker players don't have much intuition about how strong jack-high is. Sometimes it is decent. Sometimes it is hopeless. <a href="www.pokerstove.com" target="_blank">PokerStove</a> is good for this type of question.
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What's the most favorable board for calling on the river with J8 unimproved, where both cards play? Where only the jack plays?
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J8 unimproved can actually be a favorite over a random hand when only the jack plays. J8 has an equity of 0.617 against a random hand when the board is AAKKx, with no flush possible.
When both cards play, boards like AAK64 and AKQ64 both give J8 an equity of 0.368, enough to call when getting 2:1 odds.
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What's the worst possible board?
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96543, with 4 of a suit, gives J8 0.008 equity. Out of 990 hands, J8 only ties 4 other J8 combinations and beats 6 T8 combinations. J8 can't call getting 100:1 odds.
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What are some borderline situations, assuming I'm getting 6:1 on the river?
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I'll leave that for others to work on.
In the actual situation, the board was AKxxx, and J8 had an equity of about 0.26, which would allow me to call with 3:1 odds against a random hand.
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