The bubble in a tournament: how the pay jump changes correct play

In a cash game a chip is a pound and a pound is a chip. In a tournament it is not, and on the bubble the gap between the two becomes the main feature of the game. We work one bubble through with actual figures, because the conclusions — fold more, shove wider, stop taking flips — are repeated everywhere and justified almost nowhere.

The hand we are costing

Four players left, three paid. A prize pool of £1,000 pays £500, £300 and £200. Chips are 15,000, 10,000, 5,000 and 1,000, which is 31,000 in play. If chips were money, each player’s share of the pool would simply be his share of the chips. They are not, because fourth place pays nothing and nobody can finish better than first.

The standard way of converting stacks into money is the Malmuth–Harville model, which works out the probability of each finishing order from the chip proportions and weights the prizes accordingly. It is a model, not a law — it ignores position, blind level and skill — but it is accurate enough to show the shape of the thing, and the shape is the point.

Stack	Share of chips	If chips were money	Equity under the model	Difference
15,000	48.4%	£483.87	£375.15	−£108.72
10,000	32.3%	£322.58	£325.37	+£2.79
5,000	16.1%	£161.29	£243.87	+£82.58
1,000	3.2%	£32.26	£55.61	+£23.35

Read the last column twice. The chip leader holds 48 per cent of the chips and 38 per cent of the money: more than a hundred pounds of his chip value has been redistributed to the people he is trying to eliminate. The 5,000 stack is worth half again as much as his chips say. And the 1,000 stack — one hand from the exit — is carrying 72 per cent more than face value, because the three stacks above him are all vulnerable to each other.

Why the flip is a disaster for both players

Now the actual hand. The 10,000 stack moves all in and the 15,000 stack is deciding whether to call. Treat it as a coin flip and run the model on both outcomes.

For the big stack: he holds £375.15 now. Winning takes him to 25,000 and £460.13. Losing leaves him with 5,000 and £257.57. A fifty-fifty is worth the average of those two, £358.85 — so an even-money flip costs him £16.30, and he needs 58 per cent equity to break even on the call rather than the 50 per cent a chip count would suggest.

For the shorter stack it is far worse. He holds £325.37. Winning takes him to 20,000 and £419.00; losing takes him to nothing. A flip is worth £209.50 — a loss of £115.87, more than a third of everything he has — and to break even on getting his stack in he needs £325.37 out of £419.00, which is 77.7 per cent equity. There is no hand that holds 78 per cent against a calling range. Which is the real lesson: on this bubble, the 10,000 stack getting called is already the mistake, whatever two cards he is holding.

What follows from the table

• Medium stacks fold. The 10,000 and the 5,000 are being paid for other people’s risk. Every hand that passes with the 1,000 stack still alive is pure profit for them, and getting involved converts a large, safe equity into a coin flip at bad prices.
• The short stack shoves wide, and only when nobody is committed. With 1,000 chips he cannot fold his way to the money, and his equity is already above chip value, so the chips he can win are worth more to him than they are to anyone else. The hands to pick are the ones where the players behind can fold.
• The chip leader presses, but not against stacks that must call. His weapon is the fold, not the showdown: raising to take blinds from players who cannot afford to flip is where his position is worth money. Calling all-ins is where he gives it back — he needs 58 per cent, and almost nothing he can be shown offers it.
• Everyone waits for the short stack. The single most valuable event on the bubble is the 1,000 stack busting without your chips involved, and the model prices it: it moves everybody into the money at once.

Where the model stops being right

Three places, and they all matter at the table. It assumes no skill edge, so a strong player’s chips are worth more than it says. It ignores the blind level — at 500/1,000 the 5,000 stack is three hands from being the short stack, and its comfortable equity evaporates with the clock, a pressure our column on playing poker against the clock describes. And it ignores position entirely, which is the one variable the players themselves can use. Treat the numbers as the shape of the incentives, not as a strategy: the shape says survival is worth more than chips near the money, and more than that it does not claim. The general tournament principles the figures reinforce are in our pages on no-limit tournament tips and playing a big stack.