Give them enough rope

I promised, implicitly at least, to provide some illustrations of how concepts from combinatorial game theory (which, need I remind you, you can learn from the marvelous new book, Lessons in Play) can be related to poker, despite the fact that the description of combinatorial games (two player, perfect information, no chance elements) scores 0/3 as a description of most common poker games.

Of course these illustrations would work perfectly well, and in much the same way, if the source were the I Ching, Tarot cards, or your favourite religious tract. The benefit is largely in thinking about it -- I'd include advice from the magic eight ball, except it doesn't allow for much in the way of reflection. Anyhow, back to the story.

I'm going to cheat (another way in which poker is unlike combinatorial games) and start with a principle which is not about the theory of combinatorial games, but about their play.

Give them enough rope (to hang themselves with)

In combinatorial games, this is used to describe how to play when you, because you've read the book and become a combinatorial games guru, recognise that, somehow, you manage to find yourself in a losing position. Chess players know it as “playing for complication” and it's a particularly effective tactic there, especially if your opponent is under time pressure.

The basic idea, is that if you are losing, you need to make it as easy as possible for your opponent to make a critical mistake. So, you should play in a way that leaves the maximum number of possibilities open to your opponent -- or, at the very least, which presents a number of plausible but losing options. As I said, in competitive chess, this is a well recognised ploy. Before moving on to poker, a small digression (gosh, I really am settling back into academic mode).

The oriental game of go is, arguably, the most complex pure strategy game (a.k.a. combinatorial game) that is played competitively. It has a rich literary and philosophical tradition, which includes a significant amount of game etiquette. Central to this etiquette is the idea of showing respect to your opponent. For instance, the first move is traditionally played in the corner of the board closest to your opponent's right hand (where, should he choose to respond locally, it will be easiest for him to play). I never did sort out if you were supposed to adjust to left handed opponents! Anyhow, the enough rope principle is completely antithetical to this etiquette -- since it implies that you believe that your understanding of the board position is superior to that of your opponent (yes, I know, this is precisely what playing the game is supposed to prove -- but you're not supposed to be obvious about it!) The “proper” play in go, when you recognise that your position is lost, is to resign.

So, what has it got to do with hold 'em? A fairly common situation heads up on the river, is to suspect that you have the second best hand, but that your opponent's hand is not overly strong (for example, you have second pair, you suspect that your opponent has top pair). If you are in position and your opponent checks on the river, then a check by you can never make life difficult for your opponent. But, if a bet by you might plausibly represent a better hand (e.g. the river has completed a flush draw, present since the flop, or filled some sensible straights), then a bet might be just the rope that your opponent needs.

Of course, this is probably not the most common interpretation of the phrase “give them some rope” in poker. More obviously, it can be applied to the slow play. Here, with great strength, you represent weakness in an attempt to induce bets, or calls from your opponents. But really, this is just another view of the same principle: you wish to ensure that your opponents are faced with difficult decisions, not easy ones.