Burst the bubble

Trying to protect your tournament life at the expense of acquiring chips is a misguided gamble based on a lot of blurr y assumptions and an underestimate of the luck element in poker. However, when you’re on the bubble the value of your tournament life leaps sharply into focus.

Simply put, tournament strategy begins at the bubble because that is the first point at which you can make money by not playing a hand.

At the start of this series of articles I defined tournament strategy as being anything that would make no sense in a cash game. In a cash game, passing your hand can only save you money; it can’t make you any. So a good pass on the bubble is a genuine example of valid tournament strategy. If you pass your hand at the bubble when two players are all-in, you acquire equity.

BUBBLE BASHING

Much has been written on bubble play, some of which is merely people passing off their own particular style of play as the correct one. I take a more rigorous, analytical approach that makes no assumptions about how opponents are going to play. However, two pieces of conventional wisdom are still worth remembering.

First, tightening up to make the money reduces your chance of making the higher big spots. Second, if you adjust at the bubble you should adjust in the opposite direction of other players: if they tighten up you should use that to acquire chips, if they play the bubble aggressively you should exploit that to move into the money for free.

To this, I’ll add a third piece of wisdom. Recall that at the bubble you hold a small amount of equity in every pot in which you muck your cards. It’s not a flat rate because it varies according to the likelihood of a player getting knocked out, but it is always positive. This means that at the bubble there must be some hands which could be played with positive expectation, but which will still hold less than the expectation gained by passing.

The exact nature of when the positive expectation is exceeded by the negative expectation depends not only on the cards, but how well you play. But the strategic consequence is this: once you have adjusted your play in whichever direction best exploits other players’ bubble behaviour, on top of that you should tighten up slightly. That is not opinion. It’s a consequence of the fact that you can’t lose chips from folding but you can gain equity by moving into the money.

In a tournament you are only ever paid according to the place you finish, and acquiring chips is just a means to that end. Accumulating a large chipstack is usually to optimise your finishing place is to pass.

Interestingly, while tournament strategy begins at the bubble, it does not end there. As long as the money increases according to finishing place, you gain expectation by not playing. A rising payout structure creates a series of bubbles. If the first player to get paid gets £1,000 and the next £2,000 then, while it’s nice to get paid, the importance of not getting knocked out does not diminish immediately after the bubble.

MID-STACK BUBBLE PLAY

There is a common misconception among tournament players that there is something advantageous about reaching the bubble. That depends very much on the distribution of chips and this is best represented by Independent Chip Modelling (ICM) calculations. ICM can tell us the equity of any stack size, provided we know the other stack sizes at the table.

Imagine there are 1,000 chips in play and payouts are £500, £300 and £200. If everyone has 250 chips at the bubble, everyone has £250 equity and nobody gains anything extra by being at the bubble. But as soon as there is an uneven distribution of chips, equities at the bubble swing about wildly.

The thing to remember is this: at the bubble the small stacks acquire a lot of extra equity and the large stacks lose it (they must do since all gains must be matched by losses). But it’s a mistake to overstate the importance of the equity gained or lost on the bubble. For the majority of medium-stacked players the bubble brings few rewards.

What is perhaps surprising is how little extra equity is gained by moving ever closer to the bubble when sitting on an average stack. Instinctively it feels like there is a surge in equity as more short stacks fall, but the maths does not bear this out.

Here’s a question that reveals the truth about bubble bias. A tourney pays six places in the following amounts: $400, $250, $150, $100, $60 and $40. You believe the field to be of an identical standard to you. You have average chips and the other stacks vary from half your stack to one and a half times it in balanced increments.

Would you rather there were seven players remaining (putting you on the bubble), ten players remaining (putting you three off the bubble) or seven players remaining with only three places paid (placing you four off the bubble)?

While most people will choose to be on the bubble, in fact it makes almost no difference. In each case your stack has slightly more equity in it than the actual chips it contains, and this is because the big stacks have chips that are worth less.

The extra equity you gain on the bubble is 2.4%; in the other two scenarios it is 1.6%. So the value of being on the bubble in real terms is worth less than 1% of your stack.

SHORT-STACK BUBBLE PLAY

The players that specifically benefit during the bubble period are the small stacks. As previously mentioned, they gain a lot of extra equity at this point. But it’s important to note that it’s equity that cannot be actively used because it’s not contained in their chips. Rather it is their tournament life itself that is of value.

This places them in a strange position whereby they gain least from risking their life, since a double-up is not a true double-up because it is only the equity in the chips that gets doubled (and this is not where the true value lies at this point). But poker is not a game of absolutes, so be aware of playing too cautiously at this point with a short stack.

I’ve used ICM heavily for this article because as far as it goes it is mathematically perfect. But ICM won’t tell you how to play poker. If you are the short stack at the table then as long as you fold, the other stacks may just pass to each other and then all call when you finally have to make a stand.

This brings me round to a final point: don’t pre- empt the bubble by tightening up before it actually arrives. Some people figure that if you get fold equity on the bubble then you must get fold equity a bit earlier too. But remember that it is only the small stacks that really benefit at the bubble and if you are a small stack right now you will probably expire before the money if you tighten up before it.

If you are a medium stack you might gain from the bubble if it arrives with very uneven stacks but you can’t know that will be so. Indeed you don’t know how big your own stack is going to be either. If you get a premium pair it’s likely to change your stack one way or another.

VALUE YOUR LIFE

If we were to sum up the correct approach to bubble play, then ‘tight is right’ would be a good catchphrase. However, poker is rarely that simple. Often tightening up at the bubble will be exactly the wrong thing to do. For example, if you are a big stack you may find it easy to run over the medium stacks who are waiting for the short stacks to bust out. But tread lightly, and be aware for the first time of the value of your tournament life.

By all means let the cash player in you go chip-hunting at the bubble. But let the tournament strategist within you tighten your play up a little bit. The maths will be on your side. And if you’re still confused then just ignore the whole concept of bubble play and play your natural game. You’ll rarely be doing much wrong.