Quote Originally Posted by spoonitnow View Post
Part 13: Basic Semi-Bluff Shove Calculation

Now it's time for some poker. Suppose we're heads-up on some street and our opponent has us covered. The pot size is P and we're considering making a shove of size B. Our opponent's chance of folding is F, and when he calls our equity is E. Let's find the EV of this shove.

First we have to figure out all of the possible outcomes. The first decision that happens after we shove is that either Villain folds or Villain calls. If Villain folds the hand is over.

Outcome #1: Villain folds

If Villain calls, either we win the hand or we lose. (Note again we're ignoring ties since that's taken care of in our equity %). Both of these outcomes end the hand.

Outcome #2: Villain calls, we win
Outcome #3: Villain calls, we lose

Now we have to find the chance of each outcome happening. The chance of outcome #1 is just the chance of Villain folding, and we know that's F. The chance of outcome #2 is the chance of Villain calling times the chance we win the hand after he calls (our equity). The chance Villain calls is (1-F) which just means 100% minus the % of the time he folds, and our equity is E, so the chance of outcome #2 is E(1-F), and remember that means E TIMES (1-F). The chance of outcome #3 is the chance Villain calls times the chance we lose after he calls. The chance Villain calls is (1-F) like before, but the chance we lose after Villain calls is (1-E), or 100% minus our equity. So the chance of outcome #3 is (1-F)(1-E). In summary, the chances of each:

Outcome #1, Villain folds: F
Outcome #2, Villain calls, we win: E(1-F)
Outcome #3, Villain calls, we lose: (1-F)(1-E)

(Side note: For this next part, it might be useful for those not super familiar with Algebra to know that (a+b)(c+d) = ac + ad + bc + bd.)

So we need to first make sure that all of these chances added together equal 1. So we have:

F + E(1-F) + (1-F)(1-E)
= F + E - EF + 1 - E - F + EF
= 1
Working my way through this thread and things was going great until I got to part:13.
What I don't understand is what I have highlighted in the above quote. if (a+b)(c+d) = ac + ad + bc + bd.) then what the f*** do I do to F + E(1-F) + (1-F)(1-E) to get F + E - EF + 1 - E - F + EF.

Could someone show me what I should be doing please? I don't get it