The Betfair Prof: "Is there a favourite-longshot bias in no-limit Texas hold'em poker?"

The Betfair Prof / Leighton Vaughan Williams / 03 February 2009 / Leave a Comment

The Betfair Prof takes a look at poker, odds, value, the right play and what this all means for the favourite-longshot bias...

You're in the big blind at the low stakes no-limit Texas Hold'em table, costing you a dollar for the hand, and you are holding the seven of clubs and seven of spades. Everyone, except for the player on the button, folds. You've seen that look in her eyes before and you know it means that she's picked up a big pair, at least Jacks, perhaps Aces. She raises five dollars. Do you call, raise or fold?

Well, if you raise all-in and are called, there will be a showdown and the probabilities tell you that you are a four-to-one underdog or slightly worse. Similarly, calling the raise is almost surely ill-advised. After all, paying five dollars into a pot of six plus the small blind is not, in these circumstances, obtaining value. Your only hope of winning is a bluff, or a slice of fortune, on the flop or later.

This assumes, of course, that you know your opponent is holding the higher pair. But what if the gleam in her eye almost certainly betrays top suited connectors, perhaps the Ace and King of Hearts? Now you're the marginal favourite and facing a whole different proposition. Calling or even raising all-in is a real option.

The problem in a real game of poker is that you are unlikely to be that sure of what you are facing across the board. A pair of sevens is a very big hand against two unsuited undercards (about an 85-15 chance), but almost as big an underdog against a pair of eights. So what's the optimal play?

There's no definitive answer to this question, but if raised by a tight-aggressive opponent the sevens hardly constitute the strongest hand, certainly when you are as out-of-position as the big blind. Substitute a 2-9 offsuit for the pair of sevens and the decision is much more straightforward. In almost all circumstances, a fold would be the advised play. That's because you're almost certainly the underdog (you could be facing a 2-7 offsuit, but unlikely), and you're obtaining little more than even money on your stake. Such a play would, in fact, be roughly the equivalent of accepting 6 to 5 and a bit about what should really be a 3 to 1 shot in the opener at Carlisle.

Now we know from decades of research into the so-called favourite-longshot bias at the racetrack that horse players tend to over-bet the longshot and underbet (relatively) the favourite.
It's interesting to ask, therefore, whether this also applies at the No-Limit Hold'em tables. Casual observation of the low and medium stakes online game suggests to me that it is indeed very much alive and kicking (often literally by players over-valuing their big picture card-little kicker hands).

If so, it follows that exploiting this sort of bias can be a key part of establishing a long-term profitable poker strategy. And more than that - it can be a whole lot of fun!

Professor Leighton Vaughan Williams is the Director of the Political Forecasting Unit and Betting Research Unit of Nottingham Business School, Nottingham Trent University