## Infinite Stacks – A Thought Experiment

### No Limit Texas Holdem, Strategy

October 4, 2007

Many of yesterday’s Things You Should Know about NL Holdem focused on the effects of deep stacks and implied odds on the game. I think one of the easiest ways to get your head around the effects of deep stacks is to consider what would happen if the stacks were infinitely deep. As you might expect, stacks that are merely very deep have the same properties, but sometimes not to quite the same degree. If the idea of “infinitely deep” stacks bothers you, just think about a stack that’s 1 million big blinds deep – ie. a 2 million dollar stack at 1/2 NL. Here are some effects of those huge stacks:

You can’t move all-in without the nuts, or call an all-in without the nuts

This stems from the very large ratios between the pot size and the stack size. If you move in 1 million BB to win a 200BB pot, your opponent has a simple strategy: call with the nuts and fold everything else. If they adopt this strategy, you will have a negative expectation (infinitely negative with the infinite stacks) every time you bet all-in without the nuts. And if you only bet all in with the nuts, clearly it would be dumb for them to call with anything but the nuts (and an assurance you can’t be freerolled). This logic may appear circular (I would say it has no loose ends…) but that’s the nature of poker strategies. There are only two strategies in the head of the rho when considering all-in bets – bet the nuts and call with the nuts. Everything else is out in the tails.

A side-effect of this is that you can’t bluff all in unless you have conclusive proof your opponent doesn’t have the nuts, which rarely occurs in holdem.

The “big game” for stacks never happens between good players

In yesterday’s article I made a distinction between the “big game” for stacks and the “small game” for pots. Because correct strategy requires that you almost never move all-in or call all-in with infinite stacks, the big game essentially never happens between good players and when it does they’ve both got the nuts and the pot is split. Unskilled players at our million dollar 1/2 game may not grasp this concept however, so against them the big game may still occasionally occur, and they will always get the worst of it.

The “small game” for pots becomes far more intricate

Because the big game never happens, the small game IS the game. And it’s far more interesting than with smaller stack sizes, because it continues for more streets. When stack sizes are small, only a certain number of bets can go in during the small game before it becomes the big game. This limits the intricacy of the small game. But with infinite stacks, the small game can continue for all 4 betting rounds, and indeed with raises on multiple rounds as people represent various different hands and see if they can get their opponent to fold or reach a showdown with a superior hand.

Bluffs on middle streets have a huge amount of additional weight

Because you need the nuts to call an all-in bet, you have to give additional respect to non-all-in bets on middle streets. The spectre of an all-in bet on the next street makes trying to call down on the current one tougher.

Preflop raises do not have the effect you’d think

In shorter NL games, and especially in limit games, opening raises tend to make a statement that you believe you have the best hand now, and that you want to narrow the implied odds by getting more money in while you know you’re best thereby making it less profitable to draw. This drives out drawing hands that would played if you hadn’t raised. They chose not to play because your raise has increased their upfront cost a lot, but increased what they stand to win much less (proportionally) and thus made the implied odds much worse.

This effect doesn’t happen when playing with infinite stacks. The only difference between playing a 3BB pot and a 10BB pot before the flop is that everything will be scaled up in size by a factor of 10:3 from that point forward. Aside from that, nothing will change about the postflop play because bet sizing will still be a function of the pot size rather than stack size. What this means is that preflop raises, instead of being a way to limit the implied odds and drive out inferior hands and thereby reshape play, simply mean that you think you have the better situation. This means that all sorts of drawing hands can raise and call raises, and that things like position raises with weakish cards become correct.

On the other side of the coin, if you have strong cards (say, aces) you can’t make it wrong for your opponents to draw at you just by raising sufficiently preflop. No matter how big you raise, it has no effect on your opponent’s implied odds to try to crack those aces. This makes big made hands much more difficult to protect – in fact, you really can’t protect them at all. You just have to fold on a later street if you become convinced you’re beat.

Implied odds are not based on stack depths

In the discussion of the 5/10 rule, we used stack size as a proxy for potential implied odds when contemplating preflop calls. That’s correct reasoning because with small to medium stacks the stack size is the bound on your implied odds. When you move to infinite stacks, the 5/10 rule still gives correct results – you should call with a positional advantage with all those hands. But when considering calls with even weaker hands that need even more dramatic implied odds, you can no longer use the stack sizes as a bound. Otherwise you’d call behind with everything, and in most cases that’s wrong. Instead the bound on your implied odds is how likely our opponent is to call a big (much larger than pot) value bet on later streets with a weak hand. This means that against certain very poor players, you really do have odds to play every hand, but against tougher opposition you need to stick to the more reasonable nut-making type hands the 5/10 rule suggests.

Take-away

As you might guess, no one ever plays with infinite stacks. But games with very deep stacks (often more than 1000BB) often crop up in casinos. As I said before, all the effects that infinite stacks have on the game also apply to merely huge stacks, just to a lesser degree. Huge bets require huge hands to make, and huge hands to call. Intricate bluffing and counter-bluffing across multiple streets are the tactics of the day. Calldowns are difficult to make. People raise, reraise, and call before the flop with speculative hands because their implied odds are still deep enough and they think they have an edge (often positional). And big hands are more difficult to protect. These are all important concepts to keep in mind for future discussions of deepstack play.

This article is part of Project Cash Game No Limit Holdem - You can find more great strategy articles there.