We need to start with the standard B/E Formula.

**B/E Formula for Fold Equity**

The basic B/E Formula is Win Value = Lose Value or Win Value – Lose Value = 0

If you introduce b, where b = B/E Fold Equity %, the formula changes to

Win Value x b – Lose Value x ( 1 – b ) = 0

AND

Lose Value x ( 1 – b ) = Lose Value – ( Lose Value x b )

*Therefore the formula Win Value x b – Lose Value x ( 1 – b) = 0 can be expressed differently and converted to the formula for both a Cold and warm Bluff.*

Win Value x b – Lose Value x ( 1 – b )

equals

Win Valuex b – (Lose Value – (Lose Valuex b))

equals

Win Value x b + Lose Value x b – Lose Value

equals

b x ( Win Value + Lose Value ) – Lose Value

**Therefore**

b x ( Win Value + Lose Value ) = Lose Value

And

b = Lose Value / (Win Value + Lose Value) where b = B/E Fold Equity

If we consider the pot and a bet to try and win it, the win value = money in the pot and the lose value = the bet cost (cost of bluff).

**We use this to build our formula for both Cold and Warm B/E Fold Equity**

B/E Fold Equity = Cost of Bluff / (Money in Pot + Cost of Bluff) (**This is the Cold Bluff Formula**)

B/E Fold Equity = Average Loss / (Money in Pot + Average Loss) (**This is the (warm) Semi Bluff Formula**)

**Average Loss**

If we go back to basics and the standard B/E formula for the fold % in a Cold Bluff

Money in pot is Cost of Bluff = Cost of bluff / (Money in pot + Cost of bluff)

If we move to the Warm or Semi Bluff formula for the fold %, the Cost of Bluff is replaced by Average Loss (our true bet cost or EV when called), but what is Average Loss?

**Average Loss is equal to our (winning) equity in the current pot and (winning) equity in villain calling cost, less the losing equity of our bet cost**

(Current Pot x Equity) + (Calling Cost x Equity) – (BC x (100% – Equity))

However the (BC x (100% – Equity)) can be expressed as

BC – (BC x Equity)

**Therefore the Warm or Semi-Bluff Formula can now be expressed as**

(Current Pot x Equity) + (Calling Cost x Equity) – (BC – (BC x Equity))

OR

(Current Pot x Equity) + (Calling Cost x Equity) – BC + (BC x Equity)

The equity figure is a constant, amending the formula

Equity (Current Pot + Calling Cost + Bet Cost) – Bet Cost

The Current Pot + Calling Cost + Bet Cost is equal to the Final Pot and this reduces the Average Loss formula to

(Final Pot x Equity) – Bet Cost

**Therefore if we replace the Cost of Bluff in a Cold Bluff with the Average Loss in a Warm or Semi-Bluff, our Ratio and Formula to determine the villain fold % is**

Money in Pot: Average Loss equals Average Loss / (Money in Pot + Average Loss)

OR

Money in Pot is ((Final Pot x Equity) – Bet Cost) equals ((Final Pot x Equity) – Bet Cost) / (Money in Pot + (Final Pot x Equity) – Bet Cost)

**We have hero covered after calling a squeeze bet preflop – how often does villain need to fold on the flop to make a bluff profitable?**

Hero Hand 9d8d

Villain Squeeze Range 10%

Flop 2d5h6h

Effective Stacks 58.05

Current Pot 23.50

Final Pot 139.60 (23.50 + 58.05 + 58.05)

Bet Cost 58.05 (This is also the calling cost)

Equity 33%

(The flop equity is from Poker Stove and increases by 1% if you ignore the flop cards).

Average Loss is (139.60 x 33%) – 58.05 = 46.07 – 58.05 or – 11.98

Fold % is 23.50: 11.98 equals 11.98 / 35.48 or 33.76%

Therefore the opponent needs to fold more than 33.76% to make the semi bluff profitable and the true bet cost is 11.98 to win 23.50