I'm sure this is something simple - why are there such big gaps in BB between hands that have similar win percentages in the Nash charts? Easily seen in the difference between suited and unsuited - 56s is 20+, and 56o is 2.4

thanks
Dave

What charts are you referring to exactly?

standard nash SB/BB push/fold, like this one

https://www.holdemresources.net/hune

I'm going to guess whatever guy made that up ****ed up somewhere, added flush equity makes nowhere near that much difference in a jam/fold situation

You'd think so, hence my question.

The problem is, it's the same values on plenty of different charts/sites

It's almost as if people steal stuff

It makes a big difference at equilibrium. Hands like suited connectors are semi-bluffs and are in there mostly for balance. Adding in offsuit combos wouldn't add much value to the range. You'd play other weak suited connectors before adding the offsuit ones. Hands like 65s don't block much of the calling range but they do have pretty decent equity when called so they can actually be shoves even at higher stack sizes.

We can actually partially verify the solution without too much work. Take 20BB as an example. The shoving range is:

{22+,A2s+,K4s+,Q5s+,J7s+,T6s+,86s+,75s+,65s,54s,A2 o+,K9o+,Q9o+,J9o+,T9o}

The caller is risking 19BB for a final pot of 20BB, so he needs 19/20 = 47.5% equity. We can use Equilab's hand range calculator to find the range of hands with at least that much equity. This is what it generates:

{33+,A2s+,K9s+,QTs+,A5o+,KTo+}

This happens to be exactly the 20BB range that the chart recommends.

Verifying the shover's range is more tedious because each combo has different blocking effects/fold equity. Let's only do a few examples.

EV of shoving 65s:

274/1225 combos call, 951 fold, and 65s has 36.71% equity

EV = 951/1225*1.5+274/1225*(.3671*40-19.5)
EV = .0872 BB

EV of shoving 65o:

274/1225 combos call, 951 fold, and 65o has 33.26% equity

EV = 951/1225*1.5+274/1225*(.3326*40-19.5)
EV = -.2214BB, as we can see the small equity difference is significant since these hands are so close to breakeven.

To my point earlier that you'd usually end up adding weak suited connectors first, let's look at 53s, which is in the folding range at 20BB.

277/1225 combos call, 948 fold, and 53s has 34.48% equity

EV = 948/1225*1.5+ 277/1225*(.3448*40-19.5)
EV = -.1299BB

K3s is a fold but K4s is a shove:

EV of K4s = 961/1225*1.5+ 264/1225*(.3566*40-19.5)
EV = .0483BB

EV of K3s = 961/1225*1.5+ 264/1225*(.3501*40-19.5)
EV = -0.0077BB

Note that 65s has worse blocking effects, but better equity than K4s

If you wanted to you could do the same thing for each hand to verify that the shoving range is correct.

Thank you for the very detailed examples! I wanted to post the same just for 65s/65o but then decided I was too lazy to even do that. Great work.

You meant final pot of 40BB, 19/40 = 47.5%. No biggie, you used the correct numbers in all following equations.

Wow, thanks for the detail. I'll go through it carefully!

Dave

THANKS! So many points to you for this fantastic breakdown. I'm really digesting this and love what you've done here!

How did you arrive at 36.71% equity? My equity calculator says 43.1% (and most of the starting hand charts appear to have 46%)

thanks
Dave

43.1% is the equity against a random hand. We want the equity against the range of hands that villain calls our shove with which is this according to the push/fold chart: {33+,A2s+,K9s+,QTs+,A5o+,KTo+}

Ah, yes, I had thought that was covered by the 277/1255 but I see now it isn't.

So starting hand percentage against two random cards is not as useful in a real hand as it first appears.

thanks for the help

Well, it’s useful if you know that your opponent has a random hand. Unfortunately, that’s not the case too often.