How does a poker odds calculator work?

[Constantinos]

How does a poker odds calculator calculate the probability for a specific hand to win against another hand or hand distribution like example PokerStove does?

Does it simulate the hand with the selected hands or does it use a special algorithm?

If I for example want to calculate the probability of QQ winning against AKs, does it then simulate:

Case 1: QQ vs AKs, simulates the hand with a flop, turn and river and sees which hands win (or split) and makes the simulation for example 1 million times to get an accurate probability value?

(PokerStove says 53.951% vs 46.049%)

Case 2: QQ vs AK, same procedure as above.

(PokerStove says 56.758% vs 43.242%)

Does it then combine the probabilities? In other words in the QQ vs AKs case it said that QQ wins 53.951% of the time, which means in 100 000 games it will win 53951,
and in the other case with QQ vs AK, QQ will win 56758/100000 times.

Conclusion: QQ wins against the hand distribution AK or AKs 53951+56758 = 110709 / 200000 times, which gives a probability of 55.354%.

The reason why I'm asking how to calculate the probability is because when I run the simulation QQ vs (AK or AKs) it gives the probability 56.056%, while my calculation gives 55.354%.

Am I doing the calculation correct? Thanks in advance!

[Norb]

Such kind of Calculator like PokerStove simply just evaluate all possibilities and count the wins, ties and losses of each hand and display those probabilities in percental values.

Some time ago, I programmed something like this for my own personal use. Therefore I know, that PokerStove uses a highly optimized algorithm to perform high numbers of combinatorial evaluations in a quite short time.

If you like to have 100% exact results, you need to switch PokerStove to the "Enumerate All" mode, press the "Evaluate" button and wait, until PokerStove has completed calculating all results (100%). This might take quite long time if no board cards are specified.

Otherwise, I recommend to change to the "Monte Carlo" method. Then PokerStove will approximate the result continuously while calculating.

[_D&L_]

The version of poker stove I have, there is no "AK". AK is ambiguous because it could stand for either AKs or AKo. If you just put AK (on my version) it rewrites to AKs, AKo when you hit evaluate. Try selecting AKo...and see if you run into the same problems.

[Constantinos]

[ QUOTE ]
Such kind of Calculator like PokerStove simply just evaluate all possibilities and count the wins, ties and losses of each hand and display those probabilities in percental values.

Some time ago, I programmed something like this for my own personal use. Therefore I know, that PokerStove uses a highly optimized algorithm to perform high numbers of combinatorial evaluations in a quite short time.

[/ QUOTE ]

By "evaluate all possibilities", you mean testing all different 7-card combinations (flop+turn+river+holecards) of the remaining cards in the deck and sees who has the best hand each time?


[ QUOTE ]
If you like to have 100% exact results, you need to switch PokerStove to the "Enumerate All" mode, press the "Evaluate" button and wait, until PokerStove has completed calculating all results (100%). This might take quite long time if no board cards are specified.

Otherwise, I recommend to change to the "Monte Carlo" method. Then PokerStove will approximate the result continuously while calculating.

[/ QUOTE ]

The "Enumerate all" mode went < 1 sec when trying with QQ vs AKs, but the "Monte Carlo" method did not move over 1% complete after 1 minute so I canceled it, but you said that the "Enumerate all" mode would take time.. [img]/images/graemlins/confused.gif[/img]

[Constantinos]

[ QUOTE ]
The version of poker stove I have, there is no "AK". AK is ambiguous because it could stand for either AKs or AKo. If you just put AK (on my version) it rewrites to AKs, AKo when you hit evaluate. Try selecting AKo...and see if you run into the same problems.

[/ QUOTE ]

I used AKs and AKo, I just misstyped AKo for AK in my post [img]/images/graemlins/wink.gif[/img]