So, you have 5 big blinds left in your stack and you are utg.  The range of cards you want to shove with is +A7 suited and offsuit and any pocket pairs.  With 5BB left you are probably left with 9 hands left in the tournament to play before you get blinded out.


So, what are your chances that your card will come in those hands.

1. First we need to know what percentage of our hands we are playing.

The combination of A7 are as follows:

Ah7h,Ah7c,Ah7d,Ah7s,Ac7h,Ac7c,Ac7d,Ac7s,Ad7h,Ad7c, Ad7d,Ad7s,As7h,As7c,As7d,As7s

There are 16 A7 play cards. Likewise, there are 16 A8,A9,A10,AJ,AQ,AK. So from A7 to Ak there are 16 x 7 hands = .112.


Now let's find out how many AA there are:

AhAc,AhAd,AhAs,AcAd,AcAs,AdAs, so there are 6.

Likewise there are 6: KK, QQ, JJ, TT, 99, 88, 77, 66, 55, 44, 33, 22

So there are 6 x 13 = 78 hands of pocket pairs.

So combined with the number of hands we can play for aces we have 112 + 78 = 190.

There are 1326 possible starting hands.  There fore 190/1326 *100 =  14% of all possible hands.


2.  Next we need to calculator the probability that our cards don't show at all in those 9 hands:

So the probability our cards don't show one hand is 86%.  For two hands it is 0.86^2 = 0.74 or 74%.  For nine hands it is 0.86^9 = 0.26.

So, there is 26% chance we don't hit our card, which means there is a 74% chance that we do.


So in conclusion there is a 74% chance of hitting a +A7 or pocket pair if you are short stack with only 9 hands left.