how many possible combinations?

[robilaruk]

Hi All

Am trying to figure out how many possible combo's there are please for being dealt premium PP (AA-1010) vs two high cards (AK AQ AJ A10 KQ)

6 ways of getting any PP so 30 in total

16 ways for any AK combo (or am I doubling counting?) so 80 total

Ta

Damo

[PAULM03]

Start with the pocket pair:
2 cards from 4 gives you 6 possible PP for each 'rank'
5 ranks 10-10 to A-A gives 6*5 = 30 possible pocket pairs

Theres 52*51/2 = 1326 possible hole hands so probability of premium pocket pair is 30/1326 = 0.0226(2.26%)

Assuming you have a pocket pair there are now only 50 cards in the deck
For 2 High cards:
First Assuming you have AA
for the AK, AQ, AJ, A10 you have a 2/50 chance of getting your A then a 16/49 chance of your other card
(2/50)*(16/49)=0.013

for the KQ it's 4/50*4/49 = 0.065

Second assuming you have KK-1010
Chance of A = 4/50
chance of other card = 14/49
probability = 0.023

for KQ it's
4/50*4/49 = 0.065
or
2/50*4/49 = 0.003
or
4/50*2/49 = 0.003

SO:
Chances of you holding 10-10 to AA = 0.0226

chances of your opponent holding the hands you mentioned in this case = (I think the sum of all the probabilities mentioned above, although I think I might be wrong on that) = 0.094

Chances of both = 0.0226*0.094 = 0.0022 = about 0.2%

[robilaruk]

Ta

I am trying to figure out a way to beat the continuation bet

and how often I need to bluff at the pot to achieve this

so for instance

I am on the BB with 93, its folded to the CO who raises 4 blinds, folded to me and I call

flop is 10 6 2 - so do I bluff at it now or check raise the 'continuation bet' i expect the CO to make

as you are more likely to get any 2 high cards than Premium PP I think I need to make this move 1 time in 3

yes/no? what do the rest of you think

I realise I am making broad assumptions about what people raise with, but am trying to formulate a theory to discuss first

Damo

Originally Posted by PAULM03

Chances of both = 0.0226*0.094 = 0.0022 = about 0.2%