“Honest Villain” Is Not An Oxymoron

The Break-Even Formula Applied To Bluff Catching

“If you suspect your opponent is bluffing more than one-third of the time [on the river], you should call every time. If you think your opponent is bluffing less than one-third of the time, you should fold every time.” —Ed Miller, The Course

This breakeven percentage value of one-third that Miller cites for villain bluffing frequency derives from an assumption that the villain has made a full pot-size bet into you on the river. For example, let’s say you flopped a set, but now the board has four-flushed on the river. Unfortunately, you don’t have the flush, so you’re either way ahead or way behind (WAWB). The villain’s bet is representative of a strong made flush–or he’s bluffing. You’ve seen the villain play mostly straightforwardly for the past few hours at the table, but you’ve also seen him make a few bluffs, too. So, should you call? 

Well, like most things in poker, it depends. In this case, it depends on how likely you think it is your opponent is bluffing in this situation. If it’s greater than a third of the time, you should call. If it’s less, you should fold.

So this means you should almost always fold. Let me explain…

Poker’s Break-Even Formula

The expected value break-even formula in poker is:

Breakeven % = Risk/(Risk + Reward)

In this specific example, above, let’s say the pot was $100 before the bad guy bet. He then makes a full pot-sized bet of $100 into us on the river. It costs us $100 to call and potentially win the $200 sitting in the middle. Therefore, the “risk” to us in this situation is $100. And the potential “reward” is the $200 currently sitting in the middle of the table. Therefore, the breakeven percentage for us to call is:

Breakeven % to Call = $100/($100+$200) = 33%

In other words, if we think our opponent is bluffing at least one-third of the time in this specific situation, we should make the call. Conversely, if we don’t think he’s betting at least one out of three times on average in this spot, we should fold.

So then why did I say you should fold? Answer: because small-stakes villains bluff far less than 1/3 of the time in general, especially on the later streets.

Breakeven % For Different Villain Bet Sizes

Astute readers will notice that the larger the villain’s bet size, the more often he has to be bluffing for this to be a breakeven call for us. In other words, the risk has gone up more than the combined risk+reward. On the flip side, the smaller the villain’s bet size, the less frequently he has to be bluffing for this to be a breakeven call. Here’s a plot of breakeven required villain bluffing percentages as a function of bet sizing: The reality of small stakes poker games is that most of the opponents we face simply don’t bluff very much in general, and in fact they bluff very rarely on the river, especially if their bet is large.  Their fifth-street bets usually mean what they look like– strength. The vast majority of opponents you play against don’t bluff even close to one-third of the time; they bluff far less than this. Which means you’re almost never getting the right price to call.

I don’t have the hard data to prove it, but from my 3M+ hands of poker played over the past 1.5 decades, I would hazard a guess that most small stakes villain’s bluff on rivers around 10% of the time, max. Per the chart above, this means you should not be calling in river WAWB situations unless the villain is making a very small (<20% of pot) bet into you on the river. If the bet is greater than 20% of the pot–which it usually is–and you don’t have a near-nut hand, you probably should just fold. The risk is mathematically too great for the potential reward; i.e., it’s negative EV to call. Remember, it’s always zero EV to muck; it literally costs you nothing to fold your hand.

Most small-stakes villains bluff on rivers much less than the required 33% of the time. They have the goods far more often than 33% of the time, so the safe play for us is to just fold and don’t look back. The vast majority of villains you face at the small stakes tables are, ironically, pretty honest on the river.

Exceptional Poker — Learn. Master. Crush.

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