I’m studying odds on improvement of poker hands, but I’m stymied by two items on the table of this reference
and
Now I’m just trying to establish a probability for taking a pr to two pair on the river, and I can’t see a difference in these two hand to merit any difference in probability. You might want to check the cite for the relevant suits, but if you can explain it to me , I’d appreciate it. I might be just losing my mind.
I haven’t checked the calculations myself, but I believe it’s just based on the fact that it’s much more likely you’ll get a straight in the first hand.
In other words, both hands will have the same percent chance of having two pairs after seven cards (whether it’s called that way or not), it’s just that J J Q K 10 will actually have a straight as well some of those times, which is the better hand.
**Cabbage ** has it. In more detail, if the next two cards are both 9’s or A’s in the first example, you have a straight (as well as two pair). In the second example this cannot happen (running pair making a hand better than two pair).
You guys aren’t helping. 
The table also expresses odds against and what it says is that the odds against hitting two pair off an existing pair by the time the river turns is different in the two cases. Whether I might get a better hand through a straight shouldn’t affect the odds on pairing up again should it ? I understand that one hand has better possibilities, but not for hitting two pair.
The table lists the odds of a particular hand being your best hand. In short, it’s not counting the hands where you make two pair and a straight as two pair, but rather as the straight only. A simplified example. You have AAKK and draw one card. 4/48 times, you pull another A or K and make a full house. 44/48 times, you don’t and make two pair. Most charts would list this as follows:
Full house: 8.3%
Two pair: 91.7%
Not as:
Full house: 8.3%
Three of a kind: 8.3%
Two pair: 100%
One pair: 100%
What game are you playing?
Texas
Using their numbers, they conclude there are 82 possible hands that count as two pair for the second situation but not the first. As indicated above, they only count the hand as two pair if you haven’t made a straight or higher (as is done in real poker). Flushes are equally likely in the two scenarios, so only straights and straight flushes are “different”.
Those 82 hands are:
40 hands where you make a A-high straight and two pair (not including flush hands)
40 hands where you make a K-high straight and two pair (not including flush hands)
2 hands where you make a straight flush and two pair
I can enumerate these hands for you if you like.
Is that a relevant question? Not trying to be snarky (though I’m aware that’s exactly how it sounds!), genuine question. In other words, in the absence of any other information about exposed cards, the odds are the same whatever game you’re playing. Except maybe 5-card draw, but the question mentions seven cards.
Thankyou. Now I get it !
Probably not (hindsight being 20/20).