The Statistics Behind Bluffing: As Crucial As Understanding Pot Odds

Author: Simon Dexter

Regular players soon discover that poker is more than just a game of cards. Part of the game’s skill lies in understanding that every time you make a decision to play or respond to what another player does, you are taking or laying odds.

Some games, such as No Limit Hold’em, often come down to one of those “Do they or don’t they have it” scenarios loved by movie-makers. Usually though, the poker player’s decisions are determined by basic maths and a rapid calculation of the pot odds; indeed, in some situations there might be no point trying to bluff a player because the odds are stacked against you, whereas in others, you could virtually call blind.

It follows that it is important to have a good idea of the odds of making or, just as importantly, defending, your hand in any given situation, together with an ability to quickly compare them to the pot odds you are getting or giving.

Being aware of your chances of success in common poker confrontations is absolutely essential and the good player will submit the odds of winning in such situations to memory.

For example, in Texas Hold’em there are 1,326 possible two-card combinations for your starting hand, and 1,225 for any one of your opponents once you have taken a glance at your cards. Should you play a hand through, there are 19,600 possible flops and 2,118,760 total full board combinations. Got that?

They’re worth remembering because these numbers are poker’s basic arithmetic parameters. Within them, the chances of opening with a pocket pair are 16/1 and of upgrading it to trips on the flop some 12%. If you don’t have a pair, you can bank on making one on the flop around one third of the time; you have a one-in-two chance of getting a pair by the river. With suited cards, you will make a flush by the river 8.4% of the time, but only flop a flush once every 119 hands.

While your situation also depends on what cards your opponents are holding, an understanding of poker’s arithmetic is, ironically, the most effective way of learning how to bluff – and here too, some basic maths apply.

Bluffing is actually an over-hyped poker skill. It will serve you well in high level, No Limit games, but you can’t bluff players who don’t know what they’re doing. This makes bluffing virtually useless in low stakes, Limit games, where it may only cost to see a pot containing .

Essentially, bluffing is the most effective use of betting to represent a hand you don’t have. If you suspect your opponent has a better hand than yours, but detect a lack of confidence in his betting - a succession of calls, checks or a very low raise is usually a good sign - you can convince him of the strength of your hand, even if you hold absolutely nothing.

Nevertheless, although it feels wonderful to pull off a successful bluff, it should only be used by experienced players at higher level tables. If you try bluffing at low stakes Limit games, you’ll get called time and again and watch as your stack fritters away, which is why a number of players believe it would be useful to have an invisible, pocket-sized mentor sitting on your shoulder whose role would be to advise where and when to take specific action.

“See that mistake you’re about to make” your mentor would whisper, just before you plunged headlong into some disastrous situation, “I made the same one myself once back in 1985. Let me show you how to avoid it…” whereupon he would explain in detail how to extricate yourself from the impending mess.

Unfortunately, life isn’t like that. We must learn from our own errors, although the intriguing possibilities for a mentor appear endless. Indeed, I suspect the question he (or she) would be asked most frequently would concern bluffing - or rather, when and when not to bluff.

In truth, it’s something to which there is no definitive answer, although as a rule, it pays to bluff sparingly, mainly because you can push your luck too far and bluffing can only be considered successful when you get away with it. Do it too frequently and you’re bound to get found out.

Many poker players bluff out of desperation, especially if they’re on tilt. It’s a classic poker / gambling reaction: “Right, I may have just lost a shed load of money, but now I’ll show ‘em.” In such a situation, your mentor would be urging you to leave the table as quickly as possible, take a break, have a drink, anything, because opponents who recognise that you’re on tilt will call you at every opportunity and eventually bleed you dry.

But not only is it foolish to bluff when opponents expect you to, as in the above instance, statistically, bluffing can be a mug’s game, a fact which has been known to poker mentors for more than eighty years.

Let me explain. Back in 1925, a lady named Ethel Riddle wrote a PhD thesis entitled Aggressive Behaviour in a Small Social Group, published by Colombia University in New York.

It was a relatively short psychological study designed to measure the effectiveness of bluffing, but its results hold true to this day.

Riddle wired six poker players up to lie detectors during a protracted series of five-card stud games and studied their reactions when they examined their cards and those eventually revealed by opponents. She found that in general, poker players are actually poor judges of the bluff, concluding that most overestimate the attempts at bluffing by infrequent bluffers and underestimate the attempts of the frequent bluffer.

Indeed, Riddle arrived at a conclusion which suggested that poker players will be most effective and, therefore, richer, if they bluff exactly 6% of the time, or once every 17 hands in which they participate.

I’m not suggesting that this is a formula which should be mechanically adhered to irrespective of the conditions under which you’re playing, but it’s worth remembering that if you play say, 200 hands during an average poker session lasting a few hours, you probably shouldn’t bluff in many more than 12 of them.

Any poker mentor, invisible or otherwise, would tell you that, adding that in addition to having an ability to calculate pot odds, knowing when to bluff (or not) is yet another of those arithmetic skills crucial to poker success.