I'm working on an excel sheet to calculate ranges and remaining combinations on certain boards. Things are going pretty good so far.

I think I'm stuck at calculating the remaining amount of combinations after a certain flop. I'm not going through the exact excel setup (formulas etc.), I do however have a question. I experienced the card removal factor influences PP's/suited/offsuit ranges on different ways. So I'm going to have to separetly calculate them (which I have been able to in my excel sheet so far). But my math skills are kind of letting me down here.

So I'm following an example in a book to make sure the numbers are right in order for my excel sheet to be correct. So I built my range (amount of combinations are all fine so far). Now I'm trying to count combinations after a certain flop. The flop comes Q 10 6 (using the book's example). I wrote a formula to count all Q's, 10's and 6's in my ranges. So far so good.

What's the exact influence on the PPs, suited hands and offsuit hands?

Am I right when I say I multiply all PPs that contain a Q by 2 (same for the 10 and 6, and add them all up). Multiply the suited combinations that contain a Q by just 1 (same for 10 and 6, and add them all up). Multiply the offsuit combinations by 3 (I'm not really sure about this number..), and ofcourse same process as the above (I add up the other flop combination removals). In the end I add up all results and substract them with the initial amount of combinations.

Having done all of this, I'm left with 133 combinations (I started off with 158 hand combinations range), compared to 136 combinations on this flop stated in the book. This means that I removed to many combinations, 3 to be precise.

So my question in a nutshell: how many combinations of PPs, suited hands and offsuit hands do I lose when one (or more, but I'm guessing that's just going to have a lineair effect) card hit the flop.

I think you are asking the following; given a hand type in a range, how many combinations remain if some of the included cards in the hand type fall on the flop. Anyway, that’s what I’ll answer.

Let’s start with a simple case. Someone’s range is only AA. We know there are C(4,2) = 6 AA combos; choose 2 of 4. Now if an ace falls on the flop, there are only 3 remaining so the remaining number of ace-pair combos is C(3,2) = 3, so you lost 3. This is true obviously for any pair, so the number of pair combos is 3 for any rank that falls on the flop and is just 1 for any rank where 2 of that rank fall.

For any suited hand with the suit specified, such as one in diamonds, there are C(13,2) = 78 combos. If a diamond falls on the flop, then the number of suited diamond combos in a range is C(12,2) = 66 so you lost 12; for 2 flopped diamonds, it is C(11,2) = 55 and C(10,2) = 45 combos for a monotone diamond flop.

For a specific suited hand such as AKs, there are 4 aces and only 1 king with the same suit for a total of 4. If either an ace of king falls on the flop, then the number of AKs combos is 3, with a loss of 1. With 2 of one rank or 1 of each rank with different suits, there are only 2 remaining AK combos. For example, if the flop were Ac Kd x, then the remaining AK suited combos is AhKh, AsKs. You should now be able to figure out other possibilities.

Offsuit hands: assume an offsuit like AKo; there are 4 aces that are paired with 3 kings of a different suit for 12 combos. For either an ace or king on the flop, there are now 4*2 = 8 combos, a loss of 4. If there is A and K flopped cards of the same suit, then there are 3*3 = 9 remaining unsuited AK combos For one of each on the flop with different suits there are 3 *3 = 9 total AK combos but 3 are suited, leaving 6 unsuited. Another way - there are 3 aces but of the 3 kings, only 2 will not match suit, so the number of off-suit AK combos is 3*2=6. I'll let you work out the combos if all three flop cards are aces or kings.

Unless I am losing my mind, this does not seem right to me. If AKo is in the range, for which there are 12 combos preflop, and exactly one ace and no kings comes on the flop, there are 9 offsuit AK combos still possible (not 8).

If exactly one ace and one king of the same suit come on the flop, then there are 6 offsuit AK combos still possible (not 9).

If exactly one ace and one king of different suits come on the flop, then there are 7 offsuit AK combos still possible (not 6).

Anyway, here is a sketch of an example I came up with that has (I think) 158 combos possible preflop, and then shrinks to 136 combos postflop with a QT6 rainbow flop. These ranges may not make sense from a poker perspective, but I wanted to try out the combo removal method on something and this was the first that came to mind.

Suppose PP range is TT+. Suppose suited range is K8s+. Suppose unsuited range is KTo+. Then, I think, there are 5*6=30 pair combos in the range, 11*4=44 suited combos in the range, and 7*12=84 unsuited combos in the range (30+44+84=158).

Now suppose flop is QT6 rainbow. Two pair combos are shrunk by 3 each, so a total of 6 pair combos vanish. Four suited combos are shrunk by 1 each so a total of 4 suited combos vanish. And four unsuited combos are shrunk by 3 each so a total of 12 unsuited combos vanish. 6+4+12=22. 158-22=136.

Hopefully, I didn't screw this up.

P.S. As posted above, OP needs to consider all the possible combos for the flop, all possible rank overlaps, and all possible suit overlaps. For example, if QT was in the preflop range, special care must be taken to properly count the suited and/or unsuited QT combos that vanish on a QT6 rainbow flop. This is a straightforward but very tedious task (and do not assume any effects are "linear").

@OP:
You will double-count some combinations in the process you outlined. Let's start with a very simple example that should cover all important scenarios and see if they match your process.

Range:
KQo, KQs, QTo, QTs, T8o, T8s, 88

Flop:
QsTd8d

Note the differences between QT<->T8 hands.

The initial problem is indeed solved. The PP removal was the problem. I am however facing two new problems: paired boards and the double removal. It's pretty near impossible to make a woring excel sheet I think.

When I plug in the flop K 9 9 for example (and 99 is in our range), the result will be 0 combinations (instead of 1) of pocket nines (using the same template as unpaired boards).

Also, the QT etc. example showed a different result for me.

whosnext made the right corrections to my posting for AK offsuit combos. I have to remember not to post combinatorial calculations at a 1AM.

Can I ask why you're using a spreadsheet, when Equilab and Flopzilla do this automatically?

Yeah man, use those computer programmes and memorise Janda's preflop ranges from his book. IMO they are the best balanced ranges I ever saw written out.

It's funny you should say that when that's the part of the book he himself likes least and has 'retracted' in as many words.

Please do show me a better preflop balanced range??

Will be good for my student, I'm teaching him GTO atm... I could write one out myself but can't be arsed.

If you can't be bothered to make a hand chart I hope the student isn't paying much.

yeah guys, feeding yadoula seems like a great choice of how to spend one's time

In the past I taught my players to make their own plays. Instead of handing them a fish, I taught them to fish.. Coaching this way is about 1 billion times more effective then teaching somebody what to do in every single spot. You have fun writing your hand charts, when you cover all 60 billion situations please do post it to me so I can make a big bonfire!

I simply don't teach GTO, that doesn't mean I'm not good at poker. As I am the highest level of exploitative player I can actually write you up a remarkably accurate GTO preflop range. I understand how to do it, but doing it would take much more time than it's worth for me (especially as I only really teach on here atm and you guys arnt even asking me, let alone politely).

Wat ?

+1

Link to coaching thread plz

"hey coach did you do my database review yet?" " sorry man CBA at the moment but here is some great ranges from someone else's book"

I got one padwan... I explained GTO to him one day a few weeks back, as he rejoined the tables, and then I pointed him to Janda's book. I only really taught him for a few days anyway lol but he's really good n now I'm leaving him to it. I do still help stake him.... I'm just too fast for you lol.

Just stop, man.

Stop what?

I don't lie... I don't spend hrs getting every word right on my posts but I do correct my mistakes.

I mean stop with the "I'm a next level player above everyone else ya'll just don't get me" schtick.

I would also add in an avert chart. It helps set the frequency to bet lightly as a category. I like what you have so far though.