This problem is from the book "application of NL hold'em".

From the book:

Let’s now analyze the profitably of 4-betting with the intention of calling a 5-bet. To accomplish this, assume we win 12.5 big blinds total for the hand when our 4-bet is successful and that our 4-bet is successful 60 percent of the time.

We will thus win on average 7.5 big blinds from our fold equity alone every time we 4-bet.

7.5 = (0.6)(12.5)

The remaining 40 percent of the time our opponent will jam and we’ll call, and our expectation will be decided by our equity times the final pot-size. For example, in a 201.5 big blind pot, if our 4-bet has 45 percent equity against our opponent’s 5-bet jamming range, the total amount we will expect to win with our hand will be -9.325 big blinds.

-9.325 = (0.45)(201.5) - 100

And since this only occurs 40 percent of the time (with the remaining 60 percent producing a profit of 7.5 big blinds), our overall expectation is 0.77 big blinds.

0.77 = (0.60)(7.5) + (0.40)(-9.325)

My questions:

  1. why did we subtracted 100 big blinds instead of 96.5(considering our 3 bet was 3.5BB)

  2. why we multiplied folding equity by .60 twice. I get it why we multiplied showdown equity by .40 but we have already did that with the folding equity(that's how we got 7.5BB instead of 12.5BB)

when i searched online, i found other formulas for finding EV but with them the EV came different than what is given in the book. so what is the right way to find EV?

the formula i found on internet is EV = F(pot) + C((WW%) - (LL%))

where, F is frequency an opponent will fold C frequency when an opponent call W how much we win W% our hand equity L how much we risk(in case of all-in, we risk our current stack) L% opponent's hand equity

in my case i will be calling 5-bet(all in) and my folding equity will be coming from 4-bet as opponent can fold 60% of the time and shove 40%. which we will call

PS: in this question we are considering that our opponent will not flat call 4-bet(all-in or fold) and we are ready to call all-in.

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