Counting outs

[Aisthesis]

Well, I don't know whether others still have this problem or not, but particularly on twotone boards, I'm often not really counting my outs exactly but just thinking more along the lines of "I have plenty of them." So, I thought I'd explore some simplifying ways of actually counting them. I'll just look at actual nut outs.

Here's my shortcut on straight boards with no flush draw:

First I take the number of cards in my hand where hitting will make the nuts, multiply that by 3, and then add 4 if a card not in my hand will make the nuts (sometimes 8).

Examples on board of 982r:

QJT3: 3 cards in my hand make the nuts, so that's 9 outs, plus another 4 for the 7, so 13 altogether.
QJT7: all 4 cards in my hand make the nuts (12), plus the 6 for another 4 for 16 altogether.

Trickier are:
JT76: Here, only the 7 and the 6 make the nuts for 6, plus another 8 for the Q and the 5, so that's 14.
JT97: Here, only the 7 actually makes the nuts (3) plus the 6 and the Q for another 8, so that's just 11 outs. But, as explored elsewhere, this is still a very strong hand on this board--even though with pure counting of outs, it looks a lot weaker than JT76. In actuality JT76 is dominated due to the pair.

Now, here's the idea that I just had for counting outs when there's also a flush draw. I'll take the board now as 9h8h2d.

Here's what you do to get nut outs: First, count your straight outs as if the board were rainbow. Then subtract one for each straight out in your hand that is not a heart (unless it would make a straight flush). Finally, subtract one on the end(s) unless that would make you a straight flush. Hence:

QJT3 all hearts: We got 13 for the straight on this one. And we don't need to subtract anything because the cards in your hand are all hearts, and the 7h would make you a straight flush. So, it's still 13.

QhJsTh3s: 13 for the straight again if the board were rainbow. But there's one non-heart in your hand. However, that would make a straight flush, so you can still count it. You do have to subtract one, though, because 7h isn't a nut out. So, 12 nut outs here.

QhJhTs7s: 16 outs for the straight, less 2 for the spades. But Th makes the straight flush, so you can still count it. 6h, however, doesn't make you the nuts. So, 14 nut outs.

QhJhTh7s: 15 outs. The 7h makes a straight flush, but the 6h doesn't. So, you only need to subtract one.

JhTh7s6s: We had 14 outs ignoring the flushes. 7h makes a straight flush, but 6h doesn't. So, subtract 1. Also 5h is no longer a nut out, but Qh is. So, subtract another one for 12 true nut outs.

JhTh9s7s: We had only 11 outs for the straight on a rainbow board. 7h is still good. 6h isn't, but Qh is. So, we subtract only 1 for 10 actual nut outs. Again, this is a very strong hand, though. I think it shows that just raw counting of outs isn't really enough to figure what shape you're actually in.

[teknipper]

[Aisthesis]

[Ojingo]