? About Shoving and FE

Alright I was going to hijack Razvan's thread about the nit turn raise with his set, but figured it more appropriate to just start a new thread. But for the sake of ease I'll be using the numbers from his hand to ask this question since the cards aren't entirely necessary here.

What I'm wondering is that obviously when we are shoving for value we want to beat >50% of villains calling range since we stand to win any money in the pot over half the time if this is the case making us $$$ over time, okay basic.

However, is there a time when we'll shove that might look like a value shove when we have less than 50% equity? Suppose we only have 40% equity vs Villain's calling range can we figure out a BE point of FE we need from our shove to cover the difference?

Using Razvan's example, he got raised on the turn and has $8.17 left behind. The pot at that point is $6.25. So here's my maths for this, just checking to see if this makes sense though...


If on a shove we only beat 40% of villains calling range, we stand to only make 40% of the pot over time so total pot is (6.25 + 8.17 + 8.17) = 22.57 * 40% = $9.04

If we had the 50% we needed to break even it would be 22.57 * 50% = $11.30

The difference between the two being $2.26. So we need to make that amount in FE out of the original pot which was $6.25. So 6.25/2.26 = 36% FE required to break even.

Or do we calculate our FE from the risk 8.17 to win 6.25 idea where we have 8.17/(6.25+8.17) = 56% FE required to make a EV play here with our only have 40% equity vs Villain's calling range? I feel like it's the first idea on FE I presented... but am definitely open to being wrong. This second FE calculation I think assumes we have relatively 0% equity against villains calling range.

So beyond the math here, does this idea even make sense or am I just completely off track here?

so, pot is 6.25 and we have 8.17 behind that opp can cover. we shove and he calls. pot is now 22.57. if our equity vs his calling shove range is 40% that means we win 40 times out of 100, or easier, 4 times out of 10.

math for 10 runs same hand he calls shove all of his range:

we win 4 times * total pot 22.57=90.28 $

we lose 6 times * money left behind 8.17=49.02

total profit when he calls his entire range is 90.28-49.02=41.26 so we make a very good profit and our shove is + EV.


now, same numbers, but villains doesnt call a shove with all of his range, let's say he folds 20% of his range and continuos with the rest of 80% of his range.

another math:

in 10 cases he fold 20% of his range, so 2 times out of 10 and calls the shove with 80% of his range, that is 8 times out of 10. so in these 8 times we win 40%* 8 (our equity * times he calls) and we lose 60%* 8 .

math for 10 runs , opp folds to shove 20% and calls 80%

we win folds 2 * pot 6.25= 12.5 $

we win 0,4* 8* 22.57=72.22$

we lose 0,6*8*8.17=39.21

so, total profit 12.5+72.22 - 39.21=45.51


so in both cases, when we have FE or not vs his range our shove is + EV. but you have to do the math for every hand. in time i hope to get them fast and in time play as accurate as possible for myself also, but this only comes with experience .

Razvan -- when doing these calculations off the table, you want to figure out what is the *best* EV. Just proving that a decision is +EV isn't sufficient. You need to prove that the decision has a higher EV than your other choices.

For the original question, I believe your fold equity can compensate for your lack of pot equity only if you're folding out enough better hands. Otherwise, checking is the better option. In other words, if you only fold out hands you are already beating, then just check.

I don't feel like plugging in the numbers for you, but you need to factor in your risk when doing your calculations. You're only figuring out how much of the total final pot you get back, but then you can't compare the different decisions because you put different amounts of your stack into each choice.

E = your equity for that decision
P = starting pot size
F = villain fold %
B = bet size

EV(check) = E*P
EV(bet) = F*P + (1-F)*( E*(P+B) - (1-E)*B )

OP and Razvan, it's easy to get mixed up in these maths. The trick to figure it out initially is to learn to do proper EV equations (like Nightgizmo did above). An excellent thread to learn how to do that is http://www.flopturnriver.com/pokerfo...ht=mathematics and an excellent book is Sklansky's no limit theory and practice.

OP your first error above is when you say

If on a shove we only beat 40% of villains calling range, we stand to only make 40% of the pot over time so total pot is (6.25 + 8.17 + 8.17) = 22.57 * 40% = $9.04

The correct way to do this is to calculate your EV: 40% of the time your profit is 6.25+8.17=14.42 and 60% of the time your loss is 8.17, so your EV=0.4*14.42-0.6*8.17=$0.866. Although this is a positive EV, which is good, it would be more profitable to check down the hand vs the same range because 60% of the time you loose $0 investment and 40% of the time you win $6.25 so your EV would be 0.4*6.25=$2.5 >>> $0.866. It can easily be demonstrated with these equations and some algebra that checking is always better than betting if your equity against a given static range (he always calls a bet) is less than 50%, regardless of how much money already is in the pot or your bet size (as an exercise, do the same equations with P for pot size before any betting, B for bet size and E for equity and figure out for what E the EV of betting is equal to the EV of checking: you should find E=0.5 or 50%).

Raz you made the same mistake. You don't win 4 times $22.57. You should say "4 times, your profit is $14.42"

This is a very common mistake from beginners in EV calcs. Always use your profit and loss in the EV equations, not the total pot including your bet.

Next step will be to come up with the EV equation of a semi-bluff (range is not static anymore, he folds a fraction F of it to a bet, so note that our equity vs the calling range is not anymore the same as our equity vs the range against which we could check). Gizmo wrote the EV equation above, and how to get there is explained in Spoon's EV thread in one of the more advanced posts. Finally, as Gizmo very rightly said, it is not just a matter of figuring if a semi-bluff has an EV>0, it is a matter of figuring whether it is the most +EV play (checking may still be better).

Also see this post for the simplest and most elegant shortcut for calculating semi-bluffs. This is an elegant shortcut, but at the end of the day it is nothing more than a rearrangement of the same semi-bluff EV equation as above.

Another important skill for figuring out what actual % of a range an opponent folds is counting combos. No better place to start than: http://www.flopturnriver.com/pokerfo...light=blockers

The two Spoon posts that I linked to above are fantastic detailed explanations of two huge pillars of poker math and Spoon went to great lengths to make these understandable by people without a lot of math background. Read, re-read, understand and practice.

edit: and here is a link to a post where I do an EV calc for a semi-bluff, including counting combos (and I first make a mistake that I correct later).

re-edit: the cherry on the cake for EV calcs is to take rake into account. Rake has a much bigger influence on EV than you think before you calculate it!

Believe it or not one of my degrees is actually in Math so it doesn't scare me at all, I actually enjoy it. Sometimes I just get lost in the nitty gritty of it, especially when trying to teach myself all the stuff.

Okay so for clarification, equity as I understand in laymen's terms is "our share of the pot." So if we have 40% equity then we can use this to determine quickly if a call is +EV, but not anything else correct? So if our call is equal to 40% of the to bet pot, aka call/(current pot+call) = 40% we have a BE move? Just trying to get all these things straight in my head.

Yep that's correct. So if you are 33% to win and someone bets pot. You break even.

Originally Posted by lombracremisi

Believe it or not one of my degrees is actually in Math so it doesn't scare me at all, I actually enjoy it. Sometimes I just get lost in the nitty gritty of it, especially when trying to teach myself all the stuff.

Okay so for clarification, equity as I understand in laymen's terms is "our share of the pot." So if we have 40% equity then we can use this to determine quickly if a call is +EV, but not anything else correct? So if our call is equal to 40% of the to bet pot, aka call/(current pot+call) = 40% we have a BE move? Just trying to get all these things straight in my head.

That is correct, but even that is a shortcut resulting from the underlying EV equation, as you can see in this other epic post by Spoon: http://www.flopturnriver.com/pokerfo...ll-173396.html
(see the "extra credit: proving the shortcut" paragraph)

It is also incorrect to think that equity is only used in the above case: you will be using equity in all the EV equations you will be making. Equity is indeed your "fair share" of the pot, and it differs from win% only because you sometimes tie.

So EV equations are very much the cornerstone of pokermath and it is important to master them.

Thanks for the clarification guys. I've read many of the articles you've posted daviddem, however I think I didn't read them critically enough and just got lost with the math and why it means what it means. I think this thread has in all reality clarified a lot for me and I should be able to get a lot more out of Spoon's threads now.

Cool. The only way to get this right is to get your hands dirty and actually do the calcs and write down the equations.. Keep posting your equations here, we'll have a look and help you if you have difficulties or questions, and we can correct if you made mistakes.

Actually doing the math is a very good way to develop "in play" intuition. With experience, you'll often be able to tell at a glance whether a choice is +EV or not. Look at the top players: lots of them are number freaks (unfortunately for me, not all number freaks are top players...)

Lots of swinging from spoon's nuts itt

I hate to flatter your ego, but those threads of yours are pure gems. I can't think of a way of explaining these concepts to non-mathematicians better than you did.

I stole them from Al Gore

The guy who invented the internet?