Situation – 27 man mtt, top 5 get paid – 15 players left, 4th level – 7 minutes until blinds double.
 
Hero has 1100 chips, BB has 1700 chips.  Blinds 50, 100.
 
Folded to hero on the SB with J8 (11BB stack) against a semi-tight opponent (17BB stack) that hero thinks villain may defend his BB with any A any broadway any pair 77 plus.  This means he’s calling 25% of the time, possibly less given his stack size and stage of tourney.  Giving these stats, and reads, should hero shove?  Did hero correctly estimate villain’s calling range given villain’s stack size?  Would villain tighten up or loosen up with this stack size, and no reads on hero?  What if villain thought hero was a solid player, playing 27/17 (vpip/pfr), no steal reads?
 
 I thought the above hand was a +EV shove.
 
These are situations that should be studied prior to being faced with them.  Off the top of your head, is this a +EV play?  If not what would be the minimum hand strength not including suited cards, needed to shove?
 
Below are my calculations.  I’m not sure if it is the best way to figure this problem out, but I believe it gets to the correct answer:
 
J8 has 34% equity given the hands I think villain will call with.  He will call 25% of the time.
 
34 x .25 =  8.5 (hero)            pot will have 1150 + 1150 = 2300
66 x .25 = 16.5 (villain)         villain needs to invest 1050 to win 1250 (needs 46% equity, EV wise)
 
75% of the time hero wins 150 (75 x 150)                         +112.50
  8.5% of the time hero wins 2300 (.085 x 2300)               +195.50
16.5% of the time hero loses 2300 (.165 x 2300)              - 379.50
                                                                                            -   71 EV
 
I was sure K9 would be +EV, but:
 
K9 has 38% equity
 
38 x .25 =  9.5 (hero)            pot will have 1150 + 1150 = 2300
62 x .25 = 15.5 (villain)            
 
75% of the time hero wins 150 (75 x 150)                         +112.50
  9.5% of the time hero wins 2300 (.095 x 2300)               +218.50
15.5% of the time hero loses 2300 (.155 x 2300)              - 356.50
                                                                                            -   25.50 EV
 
With a 9BB hero stack, (finally an almost break even situation, but does villain loosen up?):
K9 has 38% equity given the hands I think villain will call with.  He will call 25% of the time.
 
38 x .25 =  9.5 (hero)                pot will have 950 + 950 = 1900
62 x .25 = 15.5 (villain)              villain needs to invest 850 to win 1050 (needs 45% equity)
 
75% of the time hero wins 150 (75 x 150)                         +112.50
  9.5% of the time hero wins 1900 (.095 x 2100)               +180.50
15.5% of the time hero loses 1900 (.155 x 2100)              - 294.50
                                                                                             -     1.50 EV
 
Should this deter me from stealing on SB over a BB that will call 25% of the time?  Math says yes.  Looks like this will only be +EV against a NIT.
 
 
I also figured K9 (J9 was -EV) against a loose player that will call with the top 70% of hands:
 
K9 has 54% equity given the hands I think villain will call with.  He will call 70% of the time.
 
54 x .7 = 37.8 (hero)              pot will have 1150 + 1150 = 2300
46 x .7 = 32.2 (villain)             villain needs to invest 1050 to win 1250 (needs 46% equity, EV wise)
 
30% of the time hero wins 150 (.3 x 150)                          +  45
37.8% of the time hero wins 2300 (.378 x 2300)               +869.40
32.2% of the time hero loses 2300 (.322 x 2300)              - 740.60
                                                                                            +173.80 EV
 
The villain’s call is also correct (EV wise) if he feels we will be shoving with the top 45% of our hands.  He is getting 46% equity needed to break even (EV wise).
 
All that being said, I feel knowing your opponent, and knowing if he is willing to risk crippling himself in this situation, plays a big part in your decision to shove, if on the SB.  The same is true on the BB, is your opponent willing to end his tournament with this shove?

I welcome any and all feedback - I hope this isn't too long or has too much math