CardSharp

I want to make sure everyone is familiar with the concept of the “structure” of a poker game.  The structure of a game is simply a shorthand for a few related rules for a given game:

1. The number, location and size of the antes and/or forced bets (blinds and bring-ins) in a game
2. The rules for bet sizing in that game
3. The restrictions, if any, on minimum and maximum buyin amounts and rebuy amounts
4. In a tournament, the way these things change as the tournament progresses

These four rules, along with one concept I’ll discuss in a minute, are important to consider as a group because they all factor into one decision: whether or not to voluntarily put money in the pot with a given hand.  The connection between structure and the correctness of entering the pot may not be obvious, so I want to present some hypothetical games with strange structures.  We’ll see that correct strategy must change to match the structure.

The first hypothetical game is limit holdem with no blinds or antes but an otherwise typical structure.  Preflop play simply starts to the left of the button with an empty pot.  Otherwise the game is normal – everyone has sufficient stacks to play a hand to the river, the bet doubles on the turn etc.  In this structure, I claim it’s correct to enter the pot only with pocket aces.  Any lesser hand will not do.  And even when you do enter the pot with pocket aces, you can expect to make no money, as your opponents if they play correctly will only enter the pot with the other two aces.

To see why the aces-only strategy is correct for this game, we need to think about what would happen if you ran some other hand up against aces.  The best types of hands for running against aces are medium pocket pairs (ie. 66) and medium suited connectors.  In both cases you want no shared suits with the aces.  Now, both these types of hands are roughtly 4:1 against beating the aces.  But we shouldn’t be so eager to crown the aces king.  Since they’re being played as part of an aces-only strategy, they’re effectivly being played face up.  It’s reasonable to ask if the knowledge that an opponent holds aces, plus the prospect of future bets, is enough to make up the gap in hot and cold win rates.

It turns out that it’s not enough, although it’s closer than many people would think.  The player with aces can for simplicity’s sake adopt this strategy: put in the preflop bet, and then check and call all the way down.  The player with the drawing hand has only one good postflop option at that point: bet when an equity favorite to aces, check when not a favorite.  If you run the math on these two opposing strategies, it’s close but the aces come out ahead against both suited connectors and pairs. As such, it doesn’t make any sense to take any other hand up against aces in this structure.  And there’s no cost to prevent one from waiting for aces.

What we have here is a degenerate strategy rho with only one item in the head of the rho.  The head is “play only aces” and the tails are everything else.  This example illustrates a key poker priciple:

The presence of money in the pot at the start of the hand motivates action.  Without such money in the pot, the only strategies in the head of the rho for that game involve either no action at all, or only meaningless action (such as AA vs AA in holdem).

The second hypothetical game is the opposite situation where there is a ton of money in the pot at the start of play.  Imagine an otherwise normal limit holdem game where each player is required to post a 50 big bet ante before the start of each hand.  We’ll asume all players have deep enough stacks to play out the hand, and that the table is a typical 10-handed one.  In this case, correct strategy indicates that you must play every hand, regardless of what cards you hold.  With a standard Vegas 4 bet cap, it will take at worst 12 big bets to see the hand to conclusion.  If you choose to play, you will win an absolute minimum of 500 big bets if you win.  It’s a basic fact that no holdem hand is a 500:12 or worse dog to win the pot, so you have no choice but to play the hand out.

One more hypothetical game is in order.  This one is basically a limit game, and has a fractional small bet ante. But the hands are resolved differently.  At the end of the hand, instead of awarding the pot to the best hand a fair die is rolled to determine who wins the pot.  The cards simply don’t matter.  It should be obvious that in this game it is never correct to fold.  Earlier I said there was one other concept that affected the decision to play or not.  That concept is the idea of expected edge.  The bigger one player’s edge typically is over another’s the less often you want to play under anything but the best of circumstances.  In this admittedly absurd circumstance where there is no edge, you should always play.

Hopefully these examples have got you thinking about the effects of structure and in particular the way structure interacts with the expected edges one might see in a given game to determine if a hand should be played or not.  I’ve given the extreme ends of the spectrum here – a situation where no hands are meaningfully playable, and two situations where every hand is playable.  As you might expect, this is in reality a continuum, or actually two of them:

As the amount of money in the pot from antes and forced bets at the start of a hand increases relative to the amount you might have to put in later, correct strategy requires that you play more hands.  When there is less money in the pot, correct strategy is to play fewer hands.

In a game where there are big edges between good and bad situations and hands, correct strategy is to play only the best ones.  When the edges are small, correct strategy is to play frequently.