[UtzChips]

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Very standard river bet here, He'll call you on the river with any pair. If he's got you beat, well unfortunately thats poker.

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I agree he'll call with any pair the vast majority of the time.

I'm wondering if his ck/raise on the River is profitable for him when he has the best hand?

As an exercise for myself, I'll put him on a range of hands and see how I stand going into the River.

If he'll play: 66+, A6s+,K7s+,Q9s+,J9s+,T9s,98s, A8o+,KJo+,QJo from the HJ, I think we would need to assume he'd muck (on the Turn at least):
A9o,KJo, and suited A9s/K9s/Q9s, not in hearts. I'll assume that he'll keep QJs/o since he has two overs and a Gutshot and praying I'm betting my AK.

I also don't think he'd play any AT/KT this way, so you have to remove those from his range.

If we say he'll hold onto his 66/77/99 because he thinks I'm on overs, that's 18 hands practically drawing dead, but JJ-AA would not be played this way.

So, going into the River, he may have:
66/77/88/99 = 24 (I am going to say he'll save the ck/raise with 88 until the River, but that's not what he had)

A6-A9s in hearts/diamonds/clubs he may have peeled one on the Flop, so on the Turn he'd still be holding:
A8s = 3
A6/7/9 in hearts = 3
QJs/o = 8 (I have the Q/heart, but I am going to say he'll call with all of them, praying I have AK, since he has a chance at a Straight.)
QTs = 2 (I have Qh)
JTs = 4 (I'm saying he only open/raises with JTo from the CO)

AT/KT he would not play this way.

I'll also say that since he thinks I'm on nothing but overcards and there are 7 bets in the Pot, that he'll peel one on the Flop to 98s clubs,diamonds,hearts.

So he has 3ea of 98s going into the River. One drawing to a Flush.

I'm going to say he mucked A8o/KJo.

I will also say, that he would play AKs/o(16)/AQs/o(8)/AJs/o(16) this way, giving him 40 hands.

So, we have 27 hands where he now has a Pair or will pair his Jack on the River and call:
66/77/99;(18) A8s;(2) QTs;(2) QJs;(2) 98s;(3)

We have x hands that are drawing to a Flush going into the River and will ck/raise the River:

A6s-A9/AJs-AKs = 7 (I assume that he would not slowplay TPTK when his Top Pair is vulnerable to a K/Q/J)
K7s-K9s/KJs/KQs = 5 (again, not slowplaying Top Pair)
JTs =1
98s = 1
Total Flush draws: 14

Then there is 88 (3) and JTs (4) that he'll ck/raise on the River, giving us a total of 21 hands he'll ck/raise with as opposed to 26 paired hands that he'll call with.

We'll also say he'll call with 1/2 of his AK hands, praying that is what we have. That's 8 more, which is more than we should, but I didn't assume he'd play 55 to the River.

So, we have 35 hands that he loses with and 21 that he wins with.

So, we win 1 BB 62.50% of the time and lose 2 BB's 37.50% of the time, if we call his ck/raise.

Multiply 37.50% * 2 and you'll find that we lose money long term calling his ck/raise when he has the best hand.

If we say that he always calls with his 16 AK hands and always calls down with 55, that's another 14 hands that he loses with.

So now its 49/21 in my favor and I win 69.01% of the time, and only have to pay 2 BBs 30.99% of the time, and squeak out a long term profit.

I had to edit the figures, as I counted adding all of the AKs and 55s as 10 more hands when it is actually 14.