Would first like to express gratitude, as your contribution is much appreciated. It has enlightened the importance of Combos and the fundamental flaw of not considering them. Have always been alert to unlikelihood of draws in relation to calling ranges but was unable to express that understanding mathematically until now.

What websites would you recommend for analyzing combos?

I think I need to buy a deck of cards and actually do it visually cos I have difficulty wrapping my head around this.

I recommend Flopzilla, which produced the graphics in Split's OP.

I'll check it out, thanks.

here is a video i did on how to use flopzilla if that helps you

imo, everything that isn't a pair is very easy. For instance:

Say the flop is K94 and we have 55. If we want to figure out how many combos of KQ our opponent has, we take the 4 remaining Qs in the deck and times it by the the 3 remaining Ks in the deck (4*3 = 12).

If we want to figure out how many combos of K9 he has, then we take the 3 reamining Ks in the deck and times it by the 3 remaining 9s in the deck (3*3 = 9)

If the board is Jc8c4s and we think our opponent would only have flush draws that are AQs or better, there is one combo of AcQc, and one combo of AcKc. Making for 2 FD combos. If we had Ac7s in our hand, then there are no logical flush draws in our opponent's range

Say we have AK and the board comes AT5. We think our opponent would call PF with AT+ (suited and off), then do this:

AK = 2*3 = 6 combos
AQ = 2*4 = 8 combos
AJ = 2*4 = 8 combos
AT = 2*3 = 6 combos

hopefully this gets you in the right direction...

Cheers Split, I'll bookmark this COTW and work on my combotency.

The key is not just how many combos beat you, but how many combos you beat. Against this person, I don't see a lot of combos he plays this way that beat you. So you're not getting the odds to call because you don't beat much of his range.

a new way for me to look at it, thank you much.

I will now look out for hero calls for the next entire week cuz of this damn COTW

Great post, ty.

Just started analyzing my own key hands after every session, and along with assigning ranges and determining my EQ, this will help my understand how big every part of his range is, combinatorically speaking.

this just made my life so much easier. you're a beast, split.

glad i could help =)

Great stuff Split. Well done.

thanks to those with the kind words =)

I hope Split does not mind me putting this in here and hope it is educational.

Hand Combination Exercise

So I searched thru my DB and I found this for you guys.

Villian 23/16 3bet% 7 400 hands
Note: Villian has 3bet 99 in the past vs Hero

Below is a classic hand combination and Expected Value problem you will be confronted at the table.
Ignore whether Hero played the hand well or not.

Work out how many combos of splits & bluffs vs Full houses.

Can Hero call or not?

You should be able to work this thing out at the table.


Poker Stars $0.05/$0.10 No Limit Hold'em - 8 players
The Official 2+2 Hand Converter Powered By DeucesCracked.com

Hero (UTG+1): $10.00
MP1: $8.50
MP2: $10.85
CO: $10.71
BTN: $9.52
SB: $10.05
BB: $10.02
UTG: $10.88

Pre Flop: ($0.15) Hero is UTG+1 with K K
1 fold, Hero raises to $0.30, 5 folds, BB raises to $0.90, Hero calls $0.60

Flop: ($1.85) T A Q (2 players)
BB bets $1, Hero calls $1

Turn: ($3.85) T (2 players)
BB checks, Hero checks

River: ($3.85) J (2 players)
BB bets $8.12 all in, Hero ?

p.s. I am not gonna help ya with this........

10 boats/quads, 6 AK 1 KK, 16 99s if they are in his range.

16 99s? don't you mean 6?

yeah that's right 6 obv.

So that's 10 hands that beat you, 7 splits and 6 bluffs.

That's if we give him the range of AK+ 99+.

It's a fold i think.

One problem I see, AK, 99+ is only 4%, this villain's 3bet percentage is 7%. If we start adding the AQs/AJs/ATs, that's going to affect the combos.

It is also the question how reliable the 7% number is.

He is 3betting an UTG+1 open from the big blind... I don't know if he is 3betting all his range, I don't even think AK, 99+ is accurate.

Bear these things in mind.

1) If he has a wide value range for 3betting PF - he will not always get to the river this way. So of course - you can look at total number of possible combinations but some of the time he will check give up 99 sometimes he will bet/flop try and get to showdown. Thus the calculation is usually - if he always has all the full houses and given it is nano-stakes poker and a board that smashes our range given Kx is going to be there alot so we can expect him to monkey shove overbet given 10NL call a straight here almost always. So all FH are likely there - but not all bluffs are there be it AQ AJ or 99 - given it is a 3bet pot on a 4 straight board in a game where players dont often fold 5 card hands - so he prolly does not bluff always......thus if they are there they ar e not all there - so frequency of bluffs has to be accounted for when assigning hand combos.
2) Our EV - if he never bluffs - of a call is for a split. Which means our 0EV is not 50%.

So if
x= 0 or times we lose
y= 0.5 or times we split
z = 1 times we win (he is bluffing)

Then the proportions are different from a stardard EV calc.

Standard visualisation would be

XXXZZZZ more combos of we win than lose + existing pot = +EV
Here e.g. (note not exact combos)
XXXXYYYYZZ
4 combos we lose
4 combos we split
2 combos we win

So I suggest relook at frequencies then apply the visualisation technique.

I was working under the assumption that he b/c/os with his whole 3b range. I obv never see him do this with 99.