? About Shoving and FE

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!