Push EV Theory

In an online poker tournament blind stealing is paramount. But when should you steal and with which hands. It's all simple math. When you're in the SB, and you have X BB for your stack, your shove EV w/ any given hand is easy to calculate if you know the range of hands your opponent will call with.

X= your stack size (in terms of BB, assume the BB has an equal stack or has you covered. If you have the BB covered, X = the size of the BB's stack)
C = Percent of the time you are called
W = Percent of the time you win when you're called (use poker stove to figure this out)

Your EV is then:
(1-C)1.5 + WC(X+.5) - C(1-W)(X-.5)
translated this is:
1-C = % of the time you are steal the blinds
1.5 = the amount you win when you steal the blinds

WC = the percent of time you are called and win
X+.5 = the amount you win when you are called and win

C(1-W) = the percent of time you are called and lose
X-.5 = the amount you lose when you are called and lose

This formula simplifies to:

SHOVE EV = 1.5 - C + CX (2W-1)
X= stack size
C = % of time you are called
W = % of time you win when you are called

Example: You have 32o in the SB, and your opponent will call you with 22+, 54+, 86+, T7+, J6+ Q2+

According to poker stove, 32o wins 31% of the time against this range of hands, therefore W=.31

This range of hands accounts for 64% of all hands (13 pocket pairs x 6 combinations)+ (48 non pair hands * 16 combinations) = 78+768 = 846 combinations.

846 / 1326 = .64
Note that 1326 = total # of combinations of hands.
C=.64

Let's say your stack size is 10x BB.
We now have X=10
C=.64
W=.31

SHOVE EV = 1.5 - C + CX (2W-1)
Shove EV w/ 32o and 10x BB = 1.5 - .64 + (.64)(10)(.62-1)
Shove EV w/ 32o and 10x BB = -1.572 x BB

Thankfully a company has developed some software to do this match quickly and easily for you. Visit this website to get this powerful tool. http://sitngo-analyzer.com/

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