[Question on combinatorics]

Hey guys! Just registered an account, so please excuse the fact my account is so little customized. I'll get the access to those features soon - I hope ! Ty to all who will read this thread

I've been willing to work on my combinatorics game. So I've selected a couple hands after my session and decided to do some combo work on them to see if I made the right play.

I'm here to ask you guys if I'm doing this the right way, and I'll have a couple questions down the line

My goal is to see whether or not my cbet was a good play and if the sizing was ok.
Here is the hand (5cNL) : http://www.poker-academie.com/poker/...p=ad2d4704&s=6

The following are my calculations on the number of possible combos his range represents after the flop, I'm a little off what Equilab tells me, so if you spot an error, please let me know, because I can't spot it !

***

Hero : As Kd
Vilain call 3b range on BTN = 15%
(77+, A7s+, K9s+, QTs+, JTs, ATo+, KTo+, QJo)
Board : Qs 3h Jd

77+ = 4*6+4*3 = 36 combos
A7s+= 3*4+3*3 = 21
K9s+= 3*2+2*2 = 10
QTs+= 3+2 = 5
JTs = 1
ATo+= 12*1+9*3 = 39
KTo+= 12+9 = 21
QJo = 9

Total is 142 combos, even though equilab tells me there are 132 if we include blockers (which I tried to include in my calculations). Let me know where I screwed up if you spot it !

Hands that beat us :
sets = 2*3 = 6 combos (4.5% out of the 132 combos)
2pairs = 9 combos (6.8%)
Top pair = 3+3+12+9 = 27 (20.5%)
2nd pair = 27 (20.5%)

A total of 69 combos out of 132 beat us, which means 52% of his range beats us.

I didn't include OESD because I still struggle a bit with including them in combo calculations, also my 66% cbet would've denied them good odds to call (implying I'm not offering any implied odds on the turn).

***

Is it correct to understand from this calculation, that a cbet of 50% pot would've been the better play than a 66% cbet ? Maybe I had a little extra fold equity by betting a tad more which could justify the sizing.

I'm a little confused, because I know a 50%cbet needs to work 33% of the time to be profitable. And a 66%cbet needs to work 50% of the time. Can someone clear that up for me please ?

Voilà !

Let me know what you think of this, if you have any advice I would love to hear how you practice these sort of things ! My goal is to get better as a player, and once I get a feel for these I'm sure it will help me greatly in difficult spots !

Cheers

You have many errors in the combo count. For example, for JTs you show 1 combo but there are actually 3 combos, JsTs, JdTd, JhTh. All the offsuit combos are wrong. For QJo you show 9 but that includes the two suited cases, QcJc and QhJh. 77+ and QTs+ are correct.

The first point is that you probably shouldn't include KK+/AK in villain's calling range as he'll typically 4-bet with premiums. In addition, a typical player will fold some of the hands you included (some offsuit Broadways) and call with some other hands not listed (e.g. small pairs, suited aces, suited connectors).

And a couple of quick Equilab tips:
1. Tick the box indicated and little numbers on the matrix will show up so you don't have to manually count the 3 combos of JTs, 7 of QJo etc.


2. The pie-chart button takes you to a powerful new matrix where you can select groups of hand strengths that you think will continue vs a bet (e.g. sets, top pair, OESD) and Equilab will automatically calculate what proportion of the range they make up, such that you can estimate villain's folding frequency.


P.S. This isn't really a theory question, so the thread should probably be moved to BQ.

Ty for your answers, it's very appreciated!

Sorry if I posted this in the wrong sub-forum though ~

I tend to prefer to do things like this as it makes counting easier for me but ymmv.

So for each hand type we have the following number of combinations:

Pair = 6 combos
Suited = 4 combos
Off-suit = 12 combos

So first I like to get the total number of potential combos, not accounting for blockers:


77+ = 7 ranks * 6 combos = 42 combos
A7s+= 7 ranks * 4 combos = 28 combos
K9s+= 4 ranks * 4 combos = 16 combos
QTs+= 2 ranks * 4 combos = 8 combos
JTs = 1 rank * 4 combos = 4 combos
ATo+= 4 ranks * 12 combos = 48 combos
KTo+= 3 ranks * 12 combos = 36 combos
QJo = 1 rank * 12 combos = 12 combos

Next I subtract the number of combinations eliminated by the known cards between our hand and the board:

77+ = 42 - 4 ranks * 3 combos = 30

A7s+= 28 - 7 combos (As) - 1 combo (Kd) - 1 combo (Jd) = 19

K9s+= 16 - 4 combos (Kd) - 1 combo (Qs) = 11

QTs+= 8 - 2 combos (Qs) - 1 combo (Jd) = 5

JTs = 4 - 1 combo (Jd) = 3

ATo+= 48 - 4 ranks*3 combos (As) - 2 combos (Kd) - 2 combos (Qs) - 2 combos (Jd) = 30

KTo+= 36 - 3 ranks*3 combos (Kd) - 2 combos (Qs) - 2 combos (Jd) = 23

QJo = 12 - 3 combos (Qs) - 2 combos (Jd) = 7 combos

Without all the mumbo jumbo:

77+ = 30
A7s+ = 19
K9s+ = 11
QTs+ = 5
JTs = 3
ATo+ = 30
KTo+ = 23
QJo+ = 7

Total: 128

Still off by 3 combos but been through it several times and can't find mistake so I cave :-)

Unless I am missing something, all the tallies are in the picture posted above. For one thing, there are 8 ranks A-7 (not 7). Other discrepancies are possible too.

Edit: Since Hero holds the Ace of spades and the Queen of spades in on the flop, there are only 6 combos of AQo possible. And your KQo tally is off by one as well.

Ty guys ! Especially just_grindin with the very detailled post

They are I started that post way early in the day. Thanks for checking.