Thursday, May 27, 2010

How To Manipulate The Pot Size Effectively

Don’t get lost with your bets.

In poker and many other games, a significant difference between the newcomer and the more experienced player is the ability to devise a plan and anticipate how the situation could evolve. Of course, one does not know (hopefully) what cards will fall or what one’s opponents will do, but it is not too complicated to categorize the various possibilities and figure out how likely each category is. This contrasts with the beginner who simply tries to find the “best move” in each situation (playing quiz poker), with no real plan. The same trait shows in chess, where beginners play mostly for tricks and tactics, and have little understanding of strategical requirements.

This lack of game plan generally translates into the inadequate use of available resources, ie. poker chips. Many beginners bring some chips at the poker table as though it was a second, temporary bankroll for the session. They don’t plan on putting it all at stake unless they have the nuts. Naturally, this is all wrong. Chips are like infantry on the battlefield: you must know how many men you have, and how many assaults you can launch. If a general “throw some forces” at the enemy and he realizes in the middle of the battle that he has no division left for the decisive onslaught, this is very poor planning. Same if he sends a few divisions in some murky situations, only to find out that he cannot back them up with the rest of his troops as he cannot risk losing too many men in such a mess.

In poker, you need to know how many “assaults” you can launch with your stack, and whether you risk getting caught in some predicament where you have already invested many chips in the hand but the situation doesn’t look good anymore. In other words, you should manage your stack adequately to make the most of it.


The usual indicator for measuring your stack size before the flop is the number of big blinds (eg. 100BB stacks), and after the flop it is the Stack to Pot Ratio (SPR). If you have $75 in front of you and the pot is $25, you have three times the pot and your SPR is 3. Naturally, if your opponent has only $25, your $75 won’t be of much use and the effective SPR is only 1.

In big bet poker (NLHE or PLO), bets generally go from half the pot (1/2PSB, ie. half a Pot-Size Bet) to the full pot (1PSB). There can be smaller bets, especially in live games, and larger bets (overbets), but most bets fall into this range. A bet of 1/2PSB lays 3 to 1 to your opponent, and 1PSB lays 2 to 1 — this is enough to prevent most hands from outdrawing cheaply.

Heads-up, if the pot is $1, a PSB is $1 and the pot is then $3 if your opponent calls. If you want to fire another PSB, you would need $3, and the pot would be $9 if you were called. This means you should have $1+$3 = $4 to fire two consecutive PSB. For three PSB, you would need another $9, and your initial stack would have to be $4+$9 = $13 or greater. In other words, with a SPR 1 you can bet the pot one time, with a SPR 4 you can bet the pot two times, and with a SPR 13 you can bet it three times.

It follows a simple geometric progression with a ratio 3: a0 = 1, an = ie. an = 3n. The sum is the geometric series given by the formula: Sn = (3n-1)/2. For instance, firing four consecutive PSB requires a SPR of: S4 = (34-1)/2 = 40.

The Magic Numbers

So the magic numbers for pot size manipulation are: 1, 4, 13, 40. Note that the SPR can tell you how many PSB you have left, but not when the bets occur; a pot-size bet and a pot-size raise count for two consecutive PSB ie. you need a SPR 4 for this betting sequence. A bet/raise/reraise, all to full pot, wants a SPR 13.

In practice, working with a SPR 10 (that is, multiplying the pot size by ten) is faster; this lets you bet two PSB and one 2/3PSB, in whatever order.

If the effective stacks are short, it might be necessary to bet smaller so as to keep three barrels. The same method can be applied to 2/3PSB: the ratio of the geometric series is 7/3, and the magic numbers are then 0.666, 2.222, 5.851, 14.32 (Sn = 2/3×((7/3)n-1)/1.33). This means that with a SPR 5, you can have either two PSB or three 2/3PSB (approximately), and with a SPR 14, you can have either three PSB or four 2/3PSB. However, this supposes your opponent either just calls, or bets or raises 2/3PSB too — if he bets or raises full pot at some point, he can take a barrel away.

Keeping a PSB for moving in next street

Let’s say you want to move in with a PSB next street, so that your opponent face a tough decision. If your SPR is precisely 4, it is trivial: bet the pot now, and bet the pot next street. But what if your SPR is something else?

The formula is: P+2B = S-B, where P is the pot, B is your bet and S is your stack size. This simplifies to: B = (S-P)/3. In other words, you want to bet a third of the difference between your stack and the current pot. If your SPR is 3, you should bet (3-1)/3 = 2/3 now, and you will be able to move in with a PSB next street.

Use your barrels wisely

Calculate as soon as you can how many bets there are left in the hand, considering effective stacks and not only yours. Do not forget that in some situations, it is better for you if you can fire three barrels, while in some others, your hand is actually impaired by the higher SPR. As we previously noted, it might be better to give up the hand early, rather than firing a bet or two and realize you cannot profitably back up your equity with the rest of your stack.


1 comment:

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