Ok,so literature says that with a pocket pair you flop a set about every 1 out 8 times right?

What if you add in the turn as well?

Say you got those 1/8 odds on the flop,but flop is checked so you get a free turn.So flop and turn combined,what are the now the odds of hitting a set after seeing 4 cards?

Can anybody guys do this calculation?

Thanx in advance!!

If you ask what is the chance to hit a set if checked to you at flop and the flop didnt give a set already so you are set mining on turn then its clearly 2 outs and there are 52-2-3=47 cards left. So you have 2/47=4.26% chance to get there.

If you ask what is the chance to get there by turn regardless of flop action (say you are willing to accept most bets or the situation preflop was such that you will rarely face a donk bet and can almost count on seeing turn then you ask what is the chance that it wont happen which is easier to calculate ie what is the chance all 4 cards not your own pocket pair rank. Obviously this is the number of ways you can select 4 cards out of 48 non set providing cards divided by the total possible boards of 4 cards ie 4 out of 50.

So 1- (48,4)/(50,4)=1-48!/4!/44!/(50!/4!/46!))=1- 48!*46!/44!/50!=1-46*45/50/49=15.51%


Notice you can see that also as 1-48/50*47/49*46/48*45/47 in the sense of looking each card dealt to not be the rank you have (ie chance to not have a set is first card is 50 cards available so you need to draw from 48 of them so 48/50 chance , second is 47 out of 49 etc all the 4 terms in product and you subtract that from 1 for opposite probability and after some cancellation you get the same expression).


Now keep in mind that this includes also the probability to have a better than set by turn which we didnt consider but we can examine if you want (ie quads or fh). The 15.51% is all the sets and better (not the just sets number). By the way the just set number implies out of 4 cards 1 is your rank and the other 3 are not. So its 2 (2 left of your rank) times (48,3) divided by (50,4)=15.02%. This number still includes the chance of a full house though (if the other 3 make a pair or better and sometimes that can even counterfeit your fh). I wont try to take out the fh here because they are part of your unavoidable overall objective by turn as sometimes the other pair is already on the flop and you still look for a 3rd card of your rank to appear at turn even if you are drawing for fh rather than set as the best hand you can improve to now. In fact a pair at flop may allow you a higher chance to claim opponent didnt connect etc, that may allow you to get to turn without a lot of stress (even if there is still a small chance they have trips or quads even depending on the exact board and preflop range).

Thanx man that was very helpful!