In Exercise 6 we made sure everyone knew how to count up hand combinations. Now we're going to apply that knowledge to simple bluffing situations in a vacuum.

For a pure bluff to be +EV in a vacuum when we bet some amount S into some pot P, our opponent needs to fold more often than S/(S+P) for the bluff to be +EV. Or you can remember this as bet/(bet+pot). We figure out how often our opponent is folding in our analysis by putting him on a range, deciding what part of that range folds to our bet or raise, and counting up the hand combinations to see what percentage of the time he's folding.

For example, if there's some spot where the total pot is $6 when it's your turn to act and you bet $4 as a pure bluff, you need your opponent to fold more than 4/(6+4) = 4/10 = 0.40 = 40% of the time for it to be +EV. If we hold 43o on a board of J95r and our opponent's range (as a simple example) is {99+, AJ+, KQ} and he folds everything that doesn't make top pair or better, that means he's folding {TT, AQ+, KQ}. His starting range is 90 combinations if I counted it right, and he's folding 54 of those combinations (again, if I counted it right), so he's folding 54/90 = 0.60 = 60% of the time. We need him to fold more than 40% of the time, so this would clearly be a +EV bluff in a vacuum.

Now here are today's exercises:

1. Find a situation where you 3-bet bluffed pre-flop, or could have 3-bet bluffed pre-flop and chose not to. Analyze whether the bluff would have been profitable in a vacuum.
2. Find a situation where you made a c-bet bluff. Analyze whether it would have been profitable as a pure bluff in a vacuum.

When doing these exercises, you should write out your opponents entire ranges, how many combinations each hand is when finding your totals, and how often you would need him to fold based on the bet sizing and pot size. Then make your conclusions.

Afterward: Pure bluffing assumes you'll never win the pot if your opponent doesn't fold. Bluffing in a vacuum assumes that your play won't change how your opponents play in the future. You'll rarely be betting on a pure bluff, and sometimes your bluffs will change your opponents' play in later hands even at microstakes. We'll look at these ideas in greater detail in the future.