Thank u 4 posting.
Have you ever used the cardschat odds calculator? It is a very hand tool and helps us to use math to answer questions like these.
In this hand you ran into a premium hand in the BB, which just sucks. AQ is getting played all day long in tournies for 10 bb
So with this bad preflop result, how much equity did we have?
A whopping 41%, think about that.
Was it a bad play? You tell me.
Hope this helps
Ok, let's use math:
We will assign a percentage of possibilities to each player to pay. We will assume, to make it easier, that anyone would have paid with pairs of 99 or more, AK suited and off and AQ suited and off.
We know there are 1,326 possible
poker hands. However, once two cards have been removed (ours) the 50 remaining cards form only 1,225
hands. Of those hands, how many serve our opponents?
AA: 6 pairs
KK: 6 pairs
QQ: 6 pairs
JJ: 6 pairs
1010: 6 pairs
99: 6 pairs
AK: 16 pairs
AQ: 16 pairs
But now we have to subtract some, since we have a K and a J, then the table would look like this:
AA: 6 pairs
KK: 3 pairs
QQ: 6 pairs
JJ: 3 pairs
1010: 6 pairs
99: 6 pairs
AK: 12 pairs
AQ: 16 pairs
Total: 58 hands serve our opponents. If we said that there are 1225 total hands, the percentage of hands that serve them is 4.74%
We multiply that amount by the number of remaining players and it gives us 33.18%. So we have a 67% chance that nobody will pay.
But this does not end here, because even if they paid against each of their hands we have chances.
Against AA, my KJ wins 18% = 1.08 hands
Against KK, 14% = 0.42 hands
Against QQ, 32% = 1.92 hands
Against JJ, 34% = 1.02 hands
Against 10 10, 46% = 2.76 hands
Against 9 9, 35% = 2.1 hands
Against AK, 29% = 3.48 hands
Against AQ, 31% = 4.96 hands
We add the hands we win and give us a total of 17.74 hands out of a total of 58, that is 30% of the time.
Now let's see if the play was profitable or not.
Everyone folds: 67% chance. Chips after that happens: Pot 2.62bb, plus 9.62 that I had, 12.24bb, multiplied by the 67% probability yields an
expected value of 8.2bb.
If a player pays and wins: Pot 2.62bb, plus 9.62 multiplied by 2 = 21.86 bb. Of the 4.74% of the times that a player is going to pay, 30% will win him, that is a total of 1.42% of the times he calls. We multiply the 21.86 blind by that value and it gives us a total of 0.31 bb. They are 7 players, so we multiply that value by 7, getting 2.17 bb.
8.2 bb if everybody folds, plus 2.17 bb if someone calls gives a total of 10.37 bb. My chips were 9.62 bb, so with 10.37 bb of expected value we can conclude that going all-in is a profitable move.
This analysis is taken from "Holdem harrington Vol. 2"