I was wondering if you would like to add in backdoor draws to your 4 and 2 calculations, how would I do it?

Let's say I have a backdoor flush draw, I have 10 outs to hit a flushdraw on turn, so that would be about 20% but then I have 9 outs to hit the flush on the river, about 20% again. Would that be .2*.2 for about 4% extra equity?

You can't add in backdoor draws to the rule of 2, because you can't hit a backdoor draw in one card.

You can add it to the rule of 4, sure. Basically just add the approximate value of hitting a backdoor draw. For a flush, say there is 1 spade on the board and you hold 2. There are 3 known and 10 unknown spades so you need to hit 2 perfect cards, 10/47 for the turn and 9/46 for the river. To hit both is
10/47*9/46 = 4.1%
That's about the same as 1 out so you can either add 4% to the the number you get with rule of 4, or add 1 to your outs and then multiply by 4.

For a backdoor straight draw it's similar. Say you have a T and the board comes 89x. Either a J or 7 will give you 8 outs on the river, a Q or a 6 will give you 4. So the total chance is
8/47*8/46 + 8/47*4/46 = 4.4%

So again I'd count that as one out. Having both doesn't give you 2 added outs, though, because some of them would be counted twice.

I just pulled this out of my ass so it's possible I made a mistake, but it looks right to me.

As you can imagine, this question has been discussed in several threads over the years.

http://forumserver.twoplustwo.com/15...+how+many+outs

I don't use the rule of 4 and 2. I use realizable equity as a fraction of the pot. If my realizable equity > risk/reward, I continue. If the risk/reward > my realizable equity, I fold.

The only way one doesn’t realize his equity is that he mistakenly folds hands he would have won and does so more often than villain mistakenly folds. (my theory)

I assume to estimate realizable equity, you do something like the following. At some early street, you estimate your showdown equity, (using the rule of 2 and 4 is one option). Then to estimate the realizable equity you adjust that based on the particular situation.

If you agree with this, can you provide some insight on how you adjust. If you don’t agree, can you explain why.

I have the outs to odds calculations memorized thanks to years of playing limit holdem.

It's not just about mistakenly folding. Any two cards will have equity vs any rational range. Any time you fold, correctly or incorrectly, you're forfeiting that share of the pot.

I have designated two remaining decks for a particular hand – winners and losers - with relative proportions determining the overall hand equity. Folding a hand that would have lost if it went to showdown does not lose equity. Folding a hand that would have won if it went to showdown does lose equity.

But, the main point of my post was to learn how you adjust the showdown equity to develop a realizable equity, what you recognized to be a better metric for comparing to pot odds.

I would argue that vs decent strategies, any two cards will fall into this latter category.

When I said I use realizable equity, I was speaking mostly about hands that can beat a bluff, which was off topic. My bad.

My approximate calcs are:

• 10c2/11 ≈ 4.1 for a back door flush draw
• 3*4*4/11 ≈ 4.4 for the 3 possible back door str8 draws

Replace 11 with 10.81 (=47c2/100) for exact.

Sorry for the delay as I forgot about this thread:

This depends on a few factors in no particular order:

a) realizable unimproved showdown equity
b) realizable pair equity
c) realizable nutty equity
d) realizable fold equity

What it works out to is that when we're out of position vs a good player, all of these values are smaller than those same values would be if the positions are reversed. For example, realizable fold equity is a much higher value when in position, hence the float.

it's best to think about how much of the pot you capture on later streets. tipton talks extensively about this

a backdoor draw adds about 4% equity so is the naively the equivalent of one clean out.

but it's more valuable than that due to the playabilty on later streets, or more accurately its Capture Factor.

draws captures a significant share of the pot as they do much better than their equity share - the reason for this is they draw to near nutted hands, and do so on turns and rivers where pots are biggest. so, on a significant number of turns you improve to a draw and capture a decent share of the pot. you also improve by hitting pairs / bluff catchers - which also capture some share of the pot. and even when you have air, you also have bluffing opportunities on turns and river, eg when villain checks and gives up. with high card backdoors you also have showdown. all these scenarios allow you to capture some % of the turn and river pots.

having a backdoor is therefore very valuable, more so than its naive or raw equity.

you can see this effect with solvers: gto really values backdoor draws

^ Nice post. I would add that having multiple pieces of equity can allow you to take lines that would be suboptimal with each piece of equity individually. And it's hard to put a number value on that.