Betting Archetypes

An e-mailer who recently had been snowbound with his brother in a mountain cabin in Colorado asked my opinion as to the best strategy to use in a heads-up one-card poker game they invented using a deck consisting of only seven cards. They each anted $5, received one card, and then could check or bet either $5 or $10 – a very simple form of poker. That game reminded me of an information theory example I had once discussed (while majoring in poker) at MIT that helped me, and might help you, understand several fundamental concepts about betting.

If two players each received one card from a (known) two-card deck, they would know each other's card; hence, there would be no contest. If two players each received one card from a three-card deck, the betting strategies with the top and middle cards would be obvious. The player holding the top card should simply bet (he can't lose). The player with the middle card should not bet, since he would not bluff out the top card and the lower card would certainly fold to a bet (it would be foolish to bluff-raise with the low card since the bettor would usually have the top card).

One skill situation in playing with a three-card deck is how frequently to bluff-bet with the low card (since you can't win if you check). And what percentage of the time one player bluffs with the low card should determine whether or not the other player should call a bet with the middle card.

If a player never bluff-bets with the low card, his opponent should never call a bet with the middle card. If a player always bluff-bets with the low card, his opponent should always call with the middle card. If the ante and the bet are both one unit, and if one-fourth of one player's bets are bluffs when holding the low card, the other player holding the middle card will have the same long-run result either calling or folding. Thus, if your opponent's bets are bluffs more than one-fourth of the time, you should call with the middle card. This simplistic game makes it easy to see that you must bluff with the bad hand at least occasionally or your opponent will know what to do and will have a substantial edge.

When playing one-card poker with an abbreviated deck, most of the betting situations are relatively easy to analyze, and the results often yield betting principles that are also applicable to the usual, more complex forms of poker. Should you bet with the highest card or should you check (trap) some of the time? Should you bet with the second- or third-best card (and then fold if you are raised by an opponent who would be unlikely to bluff)?

Is it ever cost-effective to bet with one of the middle cards (since you are unlikely to get called by a lower card)? And how frequently must you bluff so that your opponent will not have a clear action when you bet.

If you were to play this simple version of poker with a seven-card deck, it would be relatively easy to figure out the odds of your opponent holding a better or worse hand than yours. You might even be tempted to formulate a simple game plan or mental list of what you consider to be the best action with each of the seven one-card hands.

But perhaps the most important overall lesson taught by this primitive form of poker is that poker is not a static game in which there is one best play with any given hand! If you know what your opponent usually does with any given hand, you can usually "outplay" him by adjusting your own strategy.

For example, suppose you are playing with a seven-card deck against a player who never bluffs and who always bets when he holds one of the top two cards (analogous to a weak-conservative poker style). You should fold middle cards whenever he bets and you can safely bet with the third-best card after he checks. You obviously have a huge advantage.

Even if your opponent is somewhat more sophisticated, if you know what he does with certain hand types, you have a significant advantage. Suppose your opponent consistently bluff-bets with either of the lowest two cards, checks with all the middle cards, always bets with the second-highest card, and randomly checks or bets (each about half the time) with the highest card. Based on that profile, when your opponent bets, he will have a weak hand slightly more often than a strong hand. Thus, you would certainly show a profit by calling him with medium cards (note that the amount you win is twice the bet you lose).

These concepts can be readily extended to simple straight poker (aka, "Bet Your Hand" or "No Draw"). If your opponent bets with only jacks or better and never bluffs, you should never call him with a medium hand (for example, a pair of eights). But if your opponent's bets are bluffs (for example, less than queen high) more than one-fourth of the time, it would be correct to call with medium hands. If the betting limit allows your opponent to bet twice the amount of the ante, you will show a profit by calling if his bets are bluffs more than one-third of the time.

These simple poker games make it very clear that knowledge of your opponent's tendencies gives you a substantial advantage. And, of course, that is also true in the more complex forms of poker. So, whatever your level of play, it probably costs you money if you are too consistent or too predictable.