My question is the following :
What is the probability of facing a pocket pair (preflop phase) with an off-suit hand?
I made some calculations considering a single adversary. I display them here.
Initial problem data :
Only two players are considered.
- Player 1 receive two offsuit cards (this is important).
- Therefore the remaining deck of cards contains 50 cards as they remain:
- 11 card values with 4 suits. So 44 cards.
- 2 card values with 3 suits. So 6 cards.
Direct calculation of the probability of event A :
This calculation can be verified by determining the complementary case :
Attempt to calculate with two opposing players
Main question :
The simple addition of an opposing player seems to make this calculation much more complicated (or so I'm doing it wrong). Moreover, the calculated probability decreases whereas intuitively it should increase.
Would there exist a calculation formula making it possible to obtain "simply" the result for a number n of players ?
Temporary Answer :
Thanks to BowlOfRed's formula, we can have an approximate but nevertheless precise value of the answer to my question.
Moreover, we can perform a relatively reliable linear regression on these values to obtain the following formula :
Probability = 4 x "number of players" + 3
We get the following table :
If we can see that the relative error is not negligible on a certain line, it remains very acceptable for a mental calculation (which is the goal) and the rapid obtaining of a useful value.
I am still working on a numerical calculation method. I will post the result once the work is finished.
Do not hesitate if you notice any calculation errors or for any other remarks or questions.