If we make a bet or raise as a bluff, it is necessary to calculate how often your opponent needs to fold in order for the bluff to show an immediate profit.
Immediate profit = When your opponent folds
It does not consider anything else (for example, your possible outs to improve).
This is useful for a cold bluff where your opponent will either fold or raise (and you always intend to fold to a raise).
Step 1
There are no EV calculations, only a price calculation to find the B/E point or how often your opponent needs to fold for the bluff to be profitable:
The price = Money in pot: Cost of Bluff
This is a ratio and can be converted into a % by the formula:
B/E Formula = Cost of bluff / (Money in pot + Cost of bluff)
Example:
Blinds...................................$5 (1 Bet)
Hero open raise.....................$15 (2 Bet)
Villain re-raise.......................$45 (3 Bet)
Pot is now.............................$65
A 4-bet bluff raise to $110......$95 cost
Ratio....................................$65: $95
Percentage............................95 / (95+65) = 95 / 160 = 59%
The opponent needs to FOLD more than 59% of the time to make the bet IMMEDIATELY profitable.
The opponent has a MAXIMUM CALLING RANGE of 41% to make the bluff profitable (100% - 59% folding range).
The B/E Fold Equity and Call Equity for immediate profit is an investment decision based on Risk and Reward. The 2 downloadable spreadsheets calculate Equity in advance for all situations between 10bb and 200bb in 10bb steps of bet size and pot value.
Step 2
Calculate your opponent's MINIMUM overall pre-flop re-raising range % for the bluff to show an immediate profit, using the formula:
% of hands opponent will CALL / Maximum % opponent can call before the bluff becomes unprofitable.
a) Estimate the hands your opponent will call with and use Pokerstove or Stoxpoker Combo to determine what % of all possible hands this is (the shortcut described in an earlier section could be used - Number of Hands / 13 = Range %).
b) Subtract the MINIMUM % you need your opponent to fold from 100% to find the MAXIMUM amount your opponent can call before the bluff becomes unprofitable (This has already been done above).
Example (continued from above)
You estimate the Opponent will call with 88+/AJs/AQ+
This is 5.9% of all possible hands (42 pairs, 4 suited, 32 non suited = 78 hands / 1326 hands)
[A very close shortcut is to divide 78 by 13 = 6%]
% hands opponent will call.......................5.9% (say 6%)
Maximum % opponent can call.................41%
Minimum Overall Range...........................6/41 = 14.4%
Therefore the cold bluff will show immediate profit if the opponent has re-raised with AT LEAST a 14.4% range.
Cold Bluff Calculator
This downloadable spreadsheet allows you to enter the key data and obtain the Minimum Overall Range and Minimum Fold Equity required (or Maximum Calling Equity) for immediate profit based on your estimate of the opponent's calling range, Bet Cost and Pot Value (including results for 5 other possible ranges).
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