Bluff in Poker. Evaluating a Bluff in Real Money Poker Game
There’s lots of strategy writing online that lauds bluffing; some writers hold it up on a pedestal, as though it were the be-all and end-all tactic of poker. I’m not going to write a bunch of crap about soul-reading, being a hero, or keeping opponents honest in this article. I’m going to tell you how it is.
Here’s the deal: bluffing is great, but only when well-planned and well-executed. There is no worse play you can make in poker than a hasty bluff – such a play is literally throwing away money. You certainly want to be deceptive at times; but you want to calculate your deception and use it profitably.
There are certain scenarios in which you should bluff, and other scenarios in which you shouldn’t. Let’s take a deeper look at some examples of both, and figure out how we can optimize our poker bluffs in today’s online games.
Expected Value of a Poker Bluff
The key to proper bluffing is knowing the expected value of the play before you make it. If the expected value of a poker bluff turns out to be higher than the EV of other actions, then you should bluff.
A lot of the time, it will be easier to figure out how often a bluff needs to work to be profitable, and to act based on that heuristic. This is because we obviously can’t do complicated math at the tables in real-time. But we can certainly refer to benchmarks numbers we calculate off-table, just like most players do when estimating equity in a hand.
To calculate how often a bluff needs to be profitable, you basically need to subtract the amount you lose when a poker bluff fails from the amount you win when a bluff works. In mathematical form, this looks something like.
EVbluff = (Pwork)($win) – (Pfail)($lose)
Where Pwork equals the probability our bluff works, $win is the pot we take down when our bluff works, Pfail is the probability our bluff fails, and $lose is the amount we lose when our bluff fails (generally the size of our bet).
Let’s look at a common application of this formula, and try and discern some patterns in optimal bluffing frequencies.
Poker Bluff on the River
Often times, we’ll end up on the river with a marginal hand; or sometimes — although not often, let’s hope — even with total air. In these situations, we’ll almost always want to at least consider a bluff. If we don’t consider a bluff, we basically throw the pot at the mercy of our opponent; and that’s something we want to avoid at all costs.
We can set up the equation for a river bluff as follows:
EVbluff = (Pfold)($pot) – (Pcall+Praise)($bet)
Where Pfold equals the probability that villain will fold, $pot is the amount of cash up for grabs, Pcall equals the probability villain will call a bluff, Praise equals the probability villain will raise a bluff, and $bet is the amount we bet as a bluff.
We can figure out how often a 1/2 pot bluff needs to work as such:
EVbluff = (Pfold)100 – (1-Pfold)50
EVbluff = (Pfold)100 – 50 + 50(Pfold)
50 = 150(Pfold)
1/3 = Pfold
So a half-pot bet needs to be successful 1/3rd of the time to be profitable, or 33%.
We can figure out how often a 1/5 pot bet needs to work as follows:
EVbluff = (Pfold)100 – (1-Pfold)20
EVbluff = Pfold(100) – 20 + Pfold(20)
20 = Pfold(120)
1/6 = Pfold
So a one-fifth pot bet needs to work about 1/6th of the time, or ~17%, in order to be profitable.
Comparing Poker Bluff Frequency with Equity
Once you’ve figured out how often a poker bluff needs to work to be profitable, you need to compare the equity you’ve got in the hand in order to determine the overall EV of the play.
If you figure that there’s a 25% chance of your opponent folding to a bluff given his range, for example, a 1/5th-pot bet would be profitable. As we calculated above, a 1/5th pot bet needs to work about 17% of the time in order to be profitable. Since in this case your opponent will fold well over 17% of the time, you can go ahead and fire a barrel on the river.
Figuring out when to bluff and when to hold back is just a matter of keeping these calculations in mind. Practise them off-table in order to commit the common patterns to memory. Eventually, figuring out when to bluff will be second-nature to you at the tables.