Is My Shove Profitable? (Equity Calculations)

_red_dog · Last edited by _red_dog on Wed Mar 03, 2010 6:12 pm; edited 1 time in total

I see alot of people asking about scenario's where it is a push or fold decision and they seem unsure. So I am going to explain how to calculate whether or not a shove is profitable.

EV of open shoving

1). Calling Ranges.

What are your opponents going to call a 8xBB shove with? These types of questions often generate great discussion within the forums, unfortunately there is no definitive answer. The best you can do is assume an appropriate calling range gathered from the reads that you have on your opponent. Is he tight, is he loose these sort of things.

Once you have established a range, you need to figure how your hand plays versus said range. To figure this out you need pokerstove. If you don't already have this program you are costing yourself money. It is free, so there is absolutely no reason to not have it. You can find the program here http://www.pokerstove.com/.

2) Card Combinations.

Once you establish a calling range, you need to find out the percentage of the time you will be called.

There are 6 ways to be dealt a pocket pair, and 16 ways to be dealt an unpaired starting hand. (12offsuit, 4 suited). If you have an A in your hand then there only 3 ways your opponent can have AA, and 12 ways for him to have a hand like AK (9offsuit, 3 suited). This is called card removal.

Say we are shoving A2 and believe we are being called by 22+ KT+ A5+

that gives us the card combo's of:
6 ways for each pocket pair 33-kk (66)
3 ways for 22 and AA as we have one of each (6)
16 ways for KT
16 ways for KJ
12 ways for each A5-AK (108)

This gives us 212 card combinations.

There are now a total of 1225 card combinations. This is found by multiplying 50*49. Because we have taken 2 cards out of the deck for our hand.

Divide 212 by 1225 to get the percentage of hands our opponents are calling with. In this instance: 17%.

3) The Formula.

To put it all together you need the following formula:
Overall Equity = (odds of no one calling * stack increase when no one calls) + (odds of someone calling * odds of you winning vs opponents calling range * stack increase when called and you win) - (odds of someone calling * odds of you losing vs opponents calling range * stack decrease when called and you lose)

So for the above example in part 2 the equation would look like this:

Overall Equity = (0.83*1BB)+(0.17*0.36*8BB)-(0.17*0.64*8BB)
= 0.83 + 0.49 - 0.87
= 0.45BB

Therefore every time u make this play u are expected to make 0.45 Big Blinds.

Now I don't expect you guys to be doing these complicated calcs at the tables when you are playing but I think it helps explain the "why" behind some of the advice given to you. It is also a great way to analyze your own play, after a while you will get a feel for what hands you can shove versus different calling ranges.

There are also some equilibrium solutions to shoving. Nash Equilibrium is one. Sage is another. These are good outlines for shoving, try to avoid using the calling charts unless ur opponent is shoving exactly according to nash or sage.

This calculation can also be extremely useful in figuring out which hands to 3bet shove. 3bet shoving is vitally important when stacks get to 25BBs or less. If you are unsure of how to apply this formula to 3bet shoving PM me, post here or hit me up on skype.

Hope this wasn't too long winded and that it helps a few of you out.

EV of 3bet shoving

I shall use an example from a hand of mine tonight.

When considering 3bet shoving u must consider 2 things: How often ur opponent opens and how often he calls ur shove. Obviously these two things vary greatly from opponent to opponent. Our assumptions of their range can never be 100% accurate but with keen observation of ur opponents tendencies u can put together a reasonable estimation.

The formula does not differ from the one above.

Example:
Blinds: 25/50
Stacks:
Hero: 2025
Villain: 975

Hero is dealt 6c7c in the BB

Villain opens to 100, hero shoves.

Ok, so this looks kinda spewy at first i know but with the information i had at my disposal i assumed a reasonably wide opening range for villain, as he was an aggressive player who opened almost all his buttons, and had been doing so even as stacks became shorter.

I gave villain the range: 22+,A2s+,K4s+,Q6s+,J8s+,T9s,98s,A2o+,K6o+,Q8o+,J9o+,T9o
This accounts for 39.1% of starting hands.

This was my first 3bet shove of the match, so i gave villain a slightly tighter calling range of: 22+,A6s+,KQs,A8o+,KQo

14.9% of starting hands.

**Whether my assumption of his calling range is accurate or not is not important here it is merely an example.... (although its pretty close
Wink

)

Versus this calling range 67s has 36.95% equity.

so our equation looks like so:

EV = (0.619 * 150) + (0.381 * 0.3695 * 975) - (0.381 * 0.631 * 975)
= 92.85 + 137.26 - 234.4

= -4.29

However, folding nets us a loss of T50, whilst jamming nets us a loss of T4.29

Therefore shoving is the least -EV play.

I couldn't think of a easy way to explain it so i just went with giving an example, hope u guys get it. It really is a simple equation, the hard part is range assumptions.

Again, if u have any problems or want to go over it more feel free to talk to me on skype "mathew.brown2" i'm on almost always (sadly) and am more than happy to talk poker math/strat.

Mat.
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Check2DRaiser · Reader of Souls Joined: 04 Nov 2009 Posts: 578

Great article. If you aren't intimately familiar w/ the concept of EV, then study this post!

Thx red_dog!

rjello76 · Posted: Sun Feb 14, 2010 9:26 am Post subject:

Red Dog put the subject of equity into greater perspective last night during a sweat session. Believe me when I say that this is one guy you need to listen to!
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Check2DRaiser · Reader of Souls Joined: 04 Nov 2009 Posts: 578

Bump. Only 17 views, yet probably the single most profitable article on the site except for the "non existent player strategy".

forced · Posted: Tue Mar 02, 2010 8:04 pm Post subject:

can you 'sticky' this?

rjello76 · Posted: Tue Mar 02, 2010 11:49 pm Post subject:

forced · Posted: Wed Mar 03, 2010 12:44 am Post subject:

lol.... not quite what i meant.... all the math in there hurts my brains though...

and not that in that head...
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icemanv6 · Posted: Wed Mar 03, 2010 1:16 am Post subject:

This thread confuses me Smile

Need to read up on it more this weekend..
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_red_dog · Posted: Wed Mar 03, 2010 1:40 am Post subject:

If u're having trouble with it, hit me up on skype.
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Brokerstar · Posted: Wed Mar 03, 2010 11:57 am Post subject:

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