Found very nice old article https://www.pokerstrategy.com/strate...probabilities/

But what i currently want to understand is cooler probabilities

for instance very well known AA lost in 19% of the time, stupid to complain if you loose AA 1 from 5, i would not call it as a true cooler.

But for instance you have a nut flush on a paired board, what is the chance that your opponent will have a full house at the same time ?

What is the chance that one of your full house will be beaten by another one (also interesting to know what will be real chance to have a jack pot in some casinos -)) )


When people are talking about online bad beats most of the people reply that game is for sure correct, because you are playing too many hands per hour. But math is very stubborn science, i think we need to calculate probability of cooler situations and compare them with what we really see. That's applicable also for live game too: especially when casinos using sophisticated shuffle machines with card recognition system.

Am I correct that i should multiply probabilities of having one combination by another one ?

Thinking about writing simple software with RNG to calculate it with several millions hands, and also wondering if such data sets not nessasarry from named persons available online to download

This wouldn't be a cooler in my opinion. Depending on the betting, it could easily be bad play.

A cooler is when you get AK all in on a AKxx board against 77 and the villain spikes the 7 on the river. That's pretty easy to calculate since they had 2 outs. Equilab will give you the odds of losing any type of hand vs. a range of hands. No need to simulate it.

I'm just going to say, you can try to figure this out, but it doesn't matter and it won't help your game.

The reason is because you aren't factoring in the distinction between probability and conditional probability.

In other words, you don't want to compute the overall probability that a cooler scenario happens. You want to compute the probability that you have been coolered, given the action that has gone down so far.

Let's use your nut-flush-on-paired-board example. Imagine it's the river. You have the nut flush, and you want to know what the chances are that your opponent has a full house. Well, this is sort of a trick question, because it depends on what "chances" you care about.

Let's say you are first to act on the river, and you bet. Then your opponent raises you all-in. What's important to recognize is that the chances of you being coolered are different once you know your opponent's action. They've (probably) gone up, because you can take certain hands out of your opponent's range that you thought were in there before.

The same holds for past actions too. How did you even get to the river? What was the action beforehand? Maybe you are able to remove certain combos based on that, and that will change the probability you're beat too.

In short, it seems like you're asking the wrong question.

If you get all of your money in preflop, losing with AA is a pure cooler. You lost because of a bad run out of cards when you knew you had the best hand going in.

Most of the rest of it is not only conditional on action but abstract percentages would be misleading. Having the nut flush when the board is KQQJ is not the same in practice as when the board is T773. An abstract count of outs will produce the same results but in practice in the first hand you are way more likely to already be beat.

That's a bad beat, not a cooler. A cooler is when both players have very strong hands. Set over set is a great example. AA vs KK is another. Nut flush vs. straight flush. Top boat vs. quads.

Not a two-outer on the river.

+1

A cooler is when you are ahead when the money goes in, and your opponent sucks out on you.

Since you would have always wanted to get the money in anyway, it isn't fruitful to worry about it.

Yeah, I agree that a cooler is when both sides had no choice but to get the money in, regardless of who was ahead when it did, but I also agree with CMV's point about why doing the math on this is pointless, because it doesn't happen in a vacuum.

Fair enough, that's correct.

Well initial question was about probabilities:
Of course a lot of spots could be just tough spots not a coolers.

In the paper i posted above author calculated some simple ones.

But most of the time money changing the owner in case of 2 strong hands
1. One pair against two pairs.
2. Two pairs against set
3. ...
4.flush against full house
5. Full house against full
6. Flush against straight flush
7..quads vs full house

The higher combination you have thereoretically chance of having stronger hand at the same time imho even smaller. Thats why some casinos like Commerce giving you up to 200k for quads vs quads.

So i think its good to know how frequently you should be beaten in such cases.

And also if you see on the table that staight flush beats flush in one hour 3 times, something wrong about it, and you should be cautions about playing at that place.

This is good stuff... Thanks for posting.

Question: How many straight flushes are allowed before we should question the integrity of the room? 2 ok, 3 warning signs, 4 panic?