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I decided to do a small recap about the chances in poker because I started experimenting with PokerStove and the best way how to really think about it is also write about it. We will start with pre-flop. Comments I have are only related to 2NL full ring cash game, the only one I have experience with.  I am also using default hand range from PokerStove; it is good enough for our simple explanation because I know some players tend to play any pair pre-flop trying to hit set for example.
And also I don’t want to prove anything here. This is only what I was curious about, that is all. Comments and correction are welcomed!


Pre-Flop


Pair vs Pair (AA vs KK)
Everyone knows it, you have KK, all in, and villain call and he has AA. So what are the chances?

AA vs KK: AA is a big favorite here, 80%. But the same applies to any other pair vs pair. If a villain has AA, it does not matter if you have KK, TT, 88 or 22.  It is actually slightly better to have 88 rather than KK. The chance for KK is around 18% but the chance for 88 is around 19% but it is not worth to bother with such a small difference here.
This applies to any higher pair to lower pair (TT vs 77, KK vs TT and so on). Interesting is pair against the same pair – there is 96% chance for tie but 2% chance you can win! Also 2% you can loose


Pair vs higher connectors cards (AK vs TT)
Probably the most common all-in in poker. AK vs pair (not including AA and KK).

AKs vs TT: 45% vs 55%.The difference between AKs and Ako is very small, around 1-2% so for our purpose it is not really important. The same applies to any other higher connectors to pair, like KQ vs 99 or JT vs 55 and so on. So AKs or Ako vs any pair without AA and KK is still around 55% for a pair.


Pair vs lower connectors (KK vs 87)

KK vs 87: 80% for KK. The difference between suited connectors and off suite is still around 2%. This applies to any other combination like JJ vs 56, AA vs QJ.  You are a big favorite.


Two higher cards against two lower cards (AK vs JT)

AKs vs JTs: 60% vs 40%. So you are favorite, but not so big one as before. The difference between suited and off suite is small. This applies to any other combination like Q9 vs 56. The chance for you to win is larger around 4% if the villain is not holding connectors for example Q9 vs 63 but this is very hypothetical, I don’t think someone is playing those cards


Top card, low card  vs middle cards (AT vs KQ)

AT vs KQ: 57% vs 43% AT is a favorite here but not so big one. This applies to any other combination like K7 vs T9. There is also a small change if you have like suited connectors vs off suite K7 but as before I would not bother with such a small difference.


I think I used all common combination so let’s have a look on hand range instead of specific cards.

 

EP – AK, AA and KK

Very common situation, someone on EP bets, we are sitting on button and we re-raise him and villain goes all in. Very likely he has AA, KK sometimes AKs/Ako. Let’s not to think about KK, everyone is willing to go all-in, but what abour pairs and suited connectors:

         Pair: It does not matter if we have QQ or 77.  The chance for us to win is always 40%. On the other hand, if you know his range and you hit the flop it is usually easy to get all the chips into pot.

         Suited connectors without AKs: The chance for us to win is only 30%. Very small. Not   worth of trying it.

         Ax: Very bad idea trying to outplay this range with something like AQs-A2s, AQo-A2o. The chance for you to win is only 25%!

I am not including AKs, AKo, AA and KK into our range because it is much simpler to play those cards.


Against 5% hand range (99+,AJs+,KQs,Ako)

         vs 88-22: The chance for us to win is small around 33%. A bit small

         vs QQ-99: This is better, we are in his range and we also can be ahead in few hands. The chance for win improved, we have 46%

         vs suited connectors below his range (QJs,JTs,T9s,98s,87s,76s,65s,54s,43s,32s): We have less than 30% chance to win. We are terribly behind.

         vs KQs: 35% chance to win, Still behind a lot. I am not including AKs because that hand is very strong itself and with AKs against this range is a coin flip.


Against 10% hand range (88+,A9s+,KTs+,QTs+,AJo+,Kqo)         

          vs 77-22: Our chances are around 41% so almost coins flip.

          vs QQ-88: 52% for us to win! We are in his range and we already beating some combination with those cards.

          vs suited connectors below his range  (JTs,T9s,98s,87s,76s,65s,54s,43s,32s): Don’t be a hero here. Our chances are still very bad, 34%

          vs KQs, QJs: 38%. Not good

Against 15% hand range (77+,A7s+,K9s+,QTs+,JTs,ATo+,KTo+,Qjo)

           vs 66-22: 42%. Our chances are better and better.
           vs QQ-77: 54%. We adding another pair, pair is better than non-pair combination so our chances are getting higher.
           vs suited connectors below his range (T9s,98s,87s,76s,65s,54s,43s,32s): 35% very small chance. Nice to see that we need to be very careful when playing suited connectors.
           vs suited connectors in his range (KQs, QJs, JTs): Even we are in his ranger already, still very bad, 41% only.

Against 20% hand range (66+,A4s+,K8s+,Q9s+,J9s+,T9s,A9o+,KTo+,QTo+,Jto)

          vs 55-22: We have last four pairs that are probably not his range. We have still only 44% chance to win.
          vs QQ-66: We are in a good shape here, 56%.
          vs suited connectors below his range  (98s,87s,76s,65s,54s,43s,32s): 36% is not good enough.
          vs suited connectors in his range (KQs, QJs,JTs, T9s): 42%. Our chances are getting higher but very slowly


Against 30%hand range (55+,A2s+,K5s+,Q7s+,J8s+,T8s+,98s,A7o+,A5o,K9o+,Q9o+,J9o+,T9o):

          vs 44,33 and 22:  we have 46% chance to win with these cards.
          vs QQ-55: 58%, chances are good here.    
          vs suited connectors below his range (87s, 76s, 65s, 54s, 43s, and 32s):  36% still very low.
          vs suited connectors in his range (KQs, QJs, JTs, T9s, 98s): 44% This is still very low.


Other info

When holding pair (AA-22):

        Chance for two pair: 40%
        Chance for set: 12%
         For Flush: 2%
         For straight: 1.5% (or 2.2% if you hold TT-55)
         For full house:  8.55%

When holding suited cards (A6s for example):   

        Chance for flush: 7%

When holding two non-pair cards (AK for example):      

        Chance for a pair: 44%
        Chance for two pairs: 22%
        Chance for a set: 4%
        When holding middle connectors the chance for a straight:
                   AK: 3%, KQ: 5%, QJ: 7%, T9: 9%, The rest is almost the same.


Some chance are vary because for example if you have a pair the chance that you will have a pair after the river is only 35% because you have also a chance for two pair, set, flush….

Used software: Pokerstove (www.pokerstove.com)

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