The General

Stratego, like poker, is a game of incomplete information. Each player starts with 40 pieces of various ranks, which they arrange as they like. The rank of each piece is concealed from the opponent. There is only one general (the strongest piece), but the threat of the general commands respect. Until it has been revealed, any piece could be the the general, so the opponent must proceed with some degree of caution.

The general is comparable to the nuts in poker. If you are capable of having the nuts, even if it’s unlikely, you have a certain degree of protection. Some percentage of the time you have a hand so strong it can not only withstand pressure, you actually want to get as much money in the pot as possible. But if you cannot have the nuts, and your opponent knows it, he can attack fearlessly, both by bluffing and by value betting thinly and correctly.

This principle makes sense both in terms of psychology and game theory. Psychologically it’s far more difficult to bluff someone who might be lying in wait with a huge hand. Even if the actual chance is small, the possibility of walking into an ambush makes running a bluff way scarier.

From the game theory perspective, the possibility of running into the nuts puts limits both on bet sizes and on betting frequency. As I mentioned in my post about playing against someone who’s turned his hand face up, if you know for certain whether or not you have the best hand, the theoretically optimal bet size is to go all-in regardless of how much is in the pot. But if your opponent might have the nuts, you can’t know for certain that you have the best hand, unless you also have the nuts. It would clearly be foolish to bet a thousand times the pot if there is any chance your opponent has the nuts. In fact, if 

 your bet / (your bet + the pot) <= chance opponent has the nuts

then you don’t stand to make anything by betting. For example, if you bet the size of the pot and your opponent has the nuts at least half the time, he can at least break even against your strategy just by calling with the nuts.

Because the possibility of having the nuts is so important, if you’re playing against a tough player, it’s important to manage your hands so that you can have the nuts on a variety of board textures and runouts. This idea has far-ranging consequences.

One consequence is the idea of board coverage: selecting your pre-flop hands so that you can connect well with the flop whether it comes high or low cards. Say you observe (correctly) that it is difficult to play weak hands profitably in early position. Accordingly, you trim your under the gun opening range to just the very strongest hands, JJ+ and AK. That’s only 3% of starting hands. Over time an observant opponent will recognize that you are playing extremely tight in early position. If you open under the gun, the flop comes 765 and continuation bet, your opponent can raise and make your entire range into a bluff catcher. This puts you in an extremely tough spot, which only gets worse the deeper you are. If you raise 77 and 98s, at least some of the time, it makes it far less appealing to attack you on this flop.

Another consequence is that it’s important to play the flop so that you’re capable of having a strong hand no matter what the turn card is. I recently wrote about slow-playing and why it’s usually not a good idea. It is however important to sometimes slow-play sometimes against tough opponents so you can represent a strong hand if the board texture doesn’t change. For example, if you never check back top pair+, you check, and the turn pairs the top card, your opponent can put you in a tough spot by betting twice no matter what he has. If you check back top pair every now and then, sometimes he’ll just be walking into a minefield.

Likewise, you want to be able to have some strong hands if the board texture changes. Many players, as the pre-flop raiser, habitually continuation bet all of their flush draws. That means if a flush draw is possible, they check behind, and the flush comes in on the turn, they can never have it. Again, the opponent can put them in a tough spot by betting twice. Against tough opposition you should check back a flush draw every now and then.

Ensuring you can have the nuts in any situation is easier said than done. It requires careful planning and management of your ranges. Often the crucial decision is counterintuitive and arises before the need for such a strategy becomes apparent. Building these concepts into your game requires experience and planning away from the table. Nonetheless, it’s necessary if you want to defend yourself against tough players.

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