Let's say the flop is 999.

If V play all the 9 (92o+), it actually has a lot of combos of 9 in V range? (26 combos).

If a flop come AKQ. V can have 9 combos of set. (V play QQ+).

Once the flop come 999. It is not difficult for V having a quads?

It's actually more difficult having a set on AKQ? only 9 combos of set compare to 26 combos of 9x(assume V play all the 9) on 999.

Thanks!

it's more difficult because you need both your cards to be specific in the option with a set - while it's harder for one of your cards to be a 9, the other one can be literally any other card in the deck (although your 26 number seems horribly wrong, should be 48)

If someone is playing 92o+ then yeah they have a dece number of combos of 9, but they are playing everything else.

Pro tip: Don't play 92o

oh yes you are right should be 48 combos of quads

If someone is playing 92o in a certain situation, then they are probably playing pretty much any two cards in such situation. If in a given situation someone's range is any two cards, then such person has 48 combos of quads on a 999 flop and such person's range consists of approximately 3.6% quads and 96.4% of other, with most of the other being air.

If in a given situation someone's range is QQ+, then such person has 9 combos of sets on an AKQ flop and such person's range consists of 100% sets.

I'm re-iterating what others have said, but it's not the total number of combinations that's important. It's the proportion of the entire range that those combinations make up.

If someone plays any two cards, then the number of combinations in their range that make quads on 999 is 48, but there are over 1100 combos that didn't.

To use another illustration that might help OP understand the concept, imagine that UTG (6-max) opens with a fairly standard range of 55+, A2s+, KTs+, QTs+, JTs, AJo+, KQo.

There are a lot of Ax, big pairs and Broadway combos in that range, so when the board comes AKQ, almost 60% of the range made at least top pair. It's a great board for the UTG opener's range.

If the board had come 932, however, only 21% of the range made top pair or better, because UTG doesn't have many 9s in his range (just A9s and 99), and can't even flop a set of 3s or 2s, because he folds those pre-flop. His range is heavily weighted (41%) towards ace high.

FWIW, these combo calculations can be done instantly by inputting a range and flop texture into Equilab and pressing the pie-chart button.

To put it another way, OP, you are answering the question

'Given the following two flops 999 and AKQ, out of all possible combination of two hole cards, which hand is more likely to be made, quads with 999, or a set with AKQ?'

This is a meaningless question, as in poke, you should be working to narrow people's ranges.

That being said, if the board is three of a kind, and the preflop action was soft with a lot of limpers or flatters, I will likely give credit to anyone who calls flop and turn and then gets aggressive on the river. So many combos that make quads, as you have identified.

just want to have a idea how often people can have quads on 999. I was thinking that its really rare for people to have quads but actually not. There are actually 48 combos of quads. If it is a limp pot and many players in the pot. It's not that hard for people to have quads.

Let's put it this way. Let's assume that players are really playing any two cards. Assuming that you don't have the fourth quad, the odds of a villain having quads is approximately 4.2% with one villain, 8.5% with 2, 12.8% with 3, 17% with 4, 21.2% with 5, and 25.3% with 6. So, not likely, but really not uncommon.

thanks, how u get these number tho? I lost to quads on 999 and 555 this week on 1/2 live cash so I start to think about this...but it's so hard for people floping a quads, I think is 17,295 to 1? (search on google). so what number should we look at it? combos vs chance of flopping quads. yes, there a ton of combos of quads (48). BUT it so hard to flop a quads...should we still pay them off...let's say we have AA.

There are 1326 combinations of 2 cards. If you have a XXX Flop then you can eliminate about 150 of them (3 x 48), which leaves 'only' 4% of them (48) that could be quads. That is 'not' a ton ...

Let's say we 'force' all pocket pairs to continue playing this Flop. There are 66 combos of pocket pairs plus the 'other' AA. Would you like to play a hand where you win 67 times and lose 'only' 48? I think that shows a profit. Now add all the times a player will call with just an Ace or King trying to hit or doesn't believe you have a pocket pair.

When you assume that play will only continue when someone has quads or a pocket pair then, yes, it will appear that quads happens 'a ton' .. 48 out of 115 times. But in the long run you will be a winner with AA. So feel safe playing it.

Oh, and don't forget .. Your opponents are folding almost 1100 other times when the Flop comes XXX and you have AA per 'our' pocket pair rule. Those may be seen as missed opportunities, but hopefully they all add up to make up the difference of what you lose 4% of the time to quads.

Yes, it's hard to hit quads .. but it's real easy to continue when you do. GL

Again, you have to work with the right numbers. You are looking at it backwards. You don't look at the liklihood of flopping quads, you look at the liklihood that someone has the fourth quad card if the flop is trips.

The way I get those numbers is by finding the odds that a player does NOT have the fourth quad card, and then subtracting that from 100%.

If you know that there are 3 nines on the flop, and you know that you do not have a nine, that means there are 47 unknown cards, and only 1 nine. The liklihood of the villains first card NOT being a nine is 46/47, or 97.87%. The liklihood of him not having a nine on his second card, is 45/46 , or 97.82%. So the liklihood of him not having a nine on either card is the liklihood of both events multiplied together, or 95.7%, which means that the liklihood of him having a nine is 4.3% (some rounding errors between this and my first set of numbers). You can continue this logic to include 2,3, or more players.

You seem to be wanting to compute the liklihood of events without taking into account information that changes the possible outcomes. Yes, it is unlikely to flop quads with any two cards (I have it as 1 in 9800), but, once a flop has come up with trips, you have to look at it the other way, what are the odds that someone holds that 4th quad card.

Action influences those odds, of course. If the board is 555, and you raised from middle position and got only one or two callers, you can reduce likely combos down to A5s, 45, 56, and 57, and those might be eliminated based on the situation (for example, late in a tournament, where stacks are 20 to 30 bb, it is less likely that players will have those hands in a calling range).

There's a trick I like to teach beginners for combo counting that is admittedly cumbersome for figuring out quad combos on the 999 flop:

If you want to figure out the number of combos of a given hand there are in your opponent's range, do this:

Get a pen and paper and draw three dots. Connect the dots as many times as possible. Hint: you can only connect three dots three times. This will allow you to visualize set combinations without having to do algebra. Three sets * three combos per set = 9 set combos on an unpaired flop.

Or to figure out how many AK combos there are in your opponent's range on the 954r flop:

Draw eight dots four by two like this:

* * * *
* * * *

then connect the dots the short way. This will help you visualize unpaired hand combinations in your opponent's range. You'll quickly find that there are sixteen combinations of AK in your opponent's range on the 954r flop.

Or if you want to find out how many AK combinations there are in your opponent's range on the A45r flop, you draw seven dots with three in one row and four in another row like this:

* * *
* * * *

Connect the dots again and you'll quickly find that there are twelve combinations of AK in your opponent's range on the A54r flop.

This trick works for many different combinations of things that you may encounter. Like when choosing side dishes at a restaurant. You have two sides to choose from out of five possible side dishes:

Draw five dots in a circle and connect the dots to see how many times you can eat out at this restaurant without having the same thing twice, even if you get the same entree every time.

FWIW, Ryan Fee posted a free beginner's guide to hand combinations and blockers/card removal on Upswing today: https://www.upswingpoker.com/how-the...-combinations/

* Get Equilab (it's free).
* Study how ranges work on different flops.
* Profit?

The poker principle here is that the more people there are in the pot, the more likely it is that the winning hand will be the best possible nut hand, because there are more "opportunities" for someone to have it. Flopping quads is rare for one person, but if 9 people are in the pot and one or two of them are piling a lot of money in, it's usually because they have very strong hands. A small full house (with an underpair), for example, is relatively worthless multiway if two other players are going crazy on a board where flopped quads and many better full houses are possible.