CardSharp

Last Time we talked about top-pair and overpair type hands, and the desirability of keeping the pot relatively small post flop with these hands. I want to continue that discussion, and provide some additional details and specifics that weren’t in the first article:

Effects of Stack Size

You’ll note that last time I worked with a very specific stack size and preflop raise – 100BB stacks and a 3BB preflop raise called by one caller. It’s legitimate to ask what happens if we vary those numbers. The surprising answer is that changing the stack sizes doesn’t change much – redid the math from the previous article but made the stacks 200BB, we would want to get .12 * 200BB in preflop, or a total of 24BB. We would only get 1/8 of that in, so we would have an effective payoff cap of 1/8 of our stack, which just happens to be 25BB – the same number we got with 100BB stacks. The conclusion here is that a given made hand (unimproved aces after the flop) plus a given preflop raise size yields a very specific size of pot you want at the end regardless of the stack depth. If you only had 25BB stacks, you’d want to get all the money in every time. If you had a million-BB stack, you wouldn’t want to get more than 25 in on the aces on average.

This logic may seem fishy to you. It initially did to me as I was developing the current form of the payoff rule, and the reason is that it closely mirrors some bad logic a lot of players use. Specifically, fish will often justify calling with a bad hand based on the total cost to them alone (“this is a $10 hand”) while ignoring their odds of wining and expected win size. This tends to lead to overly loose play. Similarly, they’ll fold (“well, it’s not a $100 hand”) based on pure $ amount even if the odds are in their favor. The resemblance between what I’m saying and that fishy logic may at first appear strong, but there is in fact a difference. The difference is that the fish are applying this logic when on the draw, and I’m applying it when on a made hand. Simply put, made hands less than the nuts want to get fixed amounts into the pot regardless of stack size whereas draws become more attractive the more money there is behind to potentially win if you hit. This distinction is lost on many beginning deepstack players. Trying to “stack” someone with top pair, top kicker when the stacks are 300BB deep is folly – the strength of the hand just dosen’t scale up that far. If someone goes along with you, you’re beat. But trying to stack someone with the nut flush when you think they have a smaller flush DOES scale up. Or put another way, non-nut made hands want to play just the top of the stacks. Draws to the nuts (or close, under some circumstances) want to play the entire stacks if they hit. These are opposing goals, and in draw vs. made hand confrontations, the side that is more successful at getting their desired amount of chips into play will be the long-term winner.

Effects of Preflop Raise Size

It turns out that you can change the eventual target pot size by changing the size of your preflop bet. In the aces vs. set farming example, if the guy with aces bet 5BB instead of 3, it would be correct to put over 40BB into the pot in total without violating the payoff rule. This has some dramatic strategic implications in games with loose opponents where you’re trying to balance not paying off sets with extracting value from weaker top-pair type hands. Specifically, in these games a slightly oversized preflop raise works miracles. The opposite is true in tighter games where a big preflop raise will run off the competition. In those cases sticking to the standard 3 to 3.5 is more effective.

Position & “Sensible” Bet Sizing, And The Role of Opponent Slowplay

Successful pot control is based almost entirely on three things:

1. Your opponent’s desire to slow-play
2. Your opponent restricting himself to “sensible” bet sizing
3. You being in position

Consider the following plausible continuation of the previous scenario:

Hero is on the button with the same aces he started with. Villain set-farmed from the big blind and hit a set of fours. The preflop pot was 6BB (we’ll ignore the 1/2 BB from the small blind). On the flop, villain checks, hero continuation bets 5BB, and villain calls. On the turn, villain checks intending to check-raise. Hero checks behind. On the river, villain realizes hero may not bet again, and bets the just under 2/3 pot (10BB) in an attempt to get paid off. Hero calls with the aces.

Now clearly, hero lost money in this pot, but in fact he came out ahead – villain paid 3BB for an 8:1 draw, and got paid off only 18BB when it hit. He needed to get 24BB to break even on average. By the fundamental theorem we know villain’s loss was hero’s gain. Notice however that hero’s victory here required all three of the elements numbered at the start of this section. Had villain decided not to slowplay, and instead led out with his set, pot control would have failed, and hero would have had to make a difficult decision on either the turn or river about possibly folding his aces. Similarly, if villain had abandoned sensible bet sizing and overbet the river by a large amount, hero would have a difficult choice. And if position were reversed, hero’s check would not eliminate the turn betting, and pot control would again fail. This leads to two important facts about pot control:

Pot control by means of checking behind on a street prevents an opponent with a monster from getting a lot of money in if and only if the street you choose to check on is the street when he planed to reveal his slowplay by checkraising. Usually that means it’s best to eliminate the turn betting.

and

Pot control requires position. Without it, pot control simply doesn’t work. This is perhaps the most concrete advantage conferred by position in big bet games.

I’ll have more to say about pot control in the near future.