[Slim Pickens]

Here's the original hand for discussion.
blinds 300/600
UTG (t3000)
UTG+1 (t3900)
Button (t4000)
Hero (t6100)
BB (t3000)

Hero posts SB of t300
BB posts t600

Preflop:<font color="gray"> 3 folds</font>, <font color="red">Hero raises all-in</font>

Which hand do you feel the best about pushing?
a) QJs
b) 22
c) A4o

As a basic review, here's how to calculate Hero's tournament prize pool expectation ($EV). This is the same process programs like SNGPT or SNGWhiz use. Since this is blind-v-blind and all the possible action is described perfectly (at least as far forward in time as we go) by our three possible outcomes, SNGPT, SNGWhiz, a hand calculation, and any other method should get the same answer to within the numerical precision.

1) What are Hero's options?
In this case, the action has been folded to Hero on the SB. He may either push or fold. With the lone remaining opponent sitting on 5 BB, Hero really shouldn't be considering any other option outside of a few specific circumstances, all involving some fairly advanced reads and strategies. Push/fold is simple and effective with the blinds this high.

2) What are the possible outcomes that result from each option, and what is Hero's prize pool equity in each possible outcome?

2a) Hero folds
There's only one outcome. BB wins the hand and picks up Hero's t300 small blind.

2b) Hero raises all-in
There are three possible outcomes. BB can fold, BB call and Hero can win, or BB can call and Hero can lose.

3) What is the tournament prize pool expectation of each option?
This has to be divided into two parts, one for each option Hero has.

3a) Hero folds
If Hero folds, the hand is over. The stacks will look like this for an instant before the button moves and the next hand is dealt.

UTG (t3000)
UTG+1 (t3900)
Button (t4000)
Hero (t5800)
BB (t3300)

Putting all five of those stacks into an ICM calculator gives Hero's prize pool equity as 26.19% of the total prize pool. This is EV_fold.

3b) Hero raises all-in

3b-i) Hero pushes, BB folds
UTG (t3000)
UTG+1 (t3900)
Button (t4000)
Hero (t6700)
BB (t2400)
Hero's $EV in this case, $EV_push/nocall, is 28.88% of the total prize pool.

3b-ii) Hero pushes, BB calls and Hero wins the hand
UTG (t3000)
UTG+1 (t3900)
Button (t4000)
Hero (t9100)
BB (t0)
Hero's $EV in this case, $EV_push/call-win, is 35.34%.

3b-iii) Hero pushes, BB calls and Hero loses the hand
UTG (t3000)
UTG+1 (t3900)
Button (t4000)
Hero (t3100)
BB (t6000)
Hero's $EV in this case, $EV_push/call-lose, is 16.65%.

4) How likely is each outcome within each of the available options?

4a) Hero folds
BB will win the pot 100% of the time, obviously.

4b) Hero raises all-in
Here's where your skill as a poker player comes out. It is necessary to determine a range of hands with which BB will call. For simplicity, assume BB will call with 100% of the hands in his range and 0% of the hands not in his range. Say Hero was dealt Q[img]/images/graemlins/diamond.gif[/img]J[img]/images/graemlins/diamond.gif[/img]. Let's also say, based on what Hero has seen BB do over the course of the tournament, that he thinks BB will call with this hand range: {22+,A7s+,A9o+,KJs+}. Now, we go to PokerStove or any accurate holdem EV calculator and see that...

{22+,A7s+,A9o+,KJs+} constitutes 12.9% of possible starting hands given Hero holds Q[img]/images/graemlins/diamond.gif[/img]J[img]/images/graemlins/diamond.gif[/img] and QJs will win 40.5% of the time against {22+,A7s+,A9o+,KJs+}.

4b-i
BB will fold 87.1% of the time (P_push/nocall)

4b-ii
BB will call and Hero will win 40.5% of the 12.9% of the time BB calls, for a total of 5.2% (P_push/call-win).

4b-iii
BB will call and Hero will lose 59.5% of the 12.9% of the time BB calls, for a total of 7.7% (P_push/call-lose).

Check that 100% of the time, something happens... good.

5) What is the $EV value of each option.

5a) Hero folds
$EV_fold=26.19%

5b) Hero raises all-in
$EV_push=(p_push/nocall*$EV_push/nocall)+...
(p_push/call-win*$EV_push/call-win)+(P_push/call-lose*$EV_push/call-lose)
=(0.871*0.2888)+(0.052*0.3534)+(0.077*0.1665)
=28.27%

6) Which option has the higher $EV value?
28.27&gt;26.19 therefore pushing&gt;folding

OK, this is all background to help answer the original question of which hand would you rather have and why. This is the process that we'll have to do many, many times, and display graphically.