Chips are not money: the final table

At an example final table you hold 5,000 of the 10,000 chips in play. Is your stack worth half of the prize money?

The stacks are the same in both circles, and only the yardstick changes: measured in prize money, the leader’s slice shrinks and the two shorter stacks’ slices grow. The prizes are an example, not those of any room. Amounts are in betting units, not pesos: a unit can stand for any amount, and the arithmetic is the same at any scale.

Leoformer dealer · rules and maths

At final tables I watched people count their chips as if every chip were a unit, and then make their calls on that count. The number worth working out is what a stack is worth in prize money, and a chip count does not tell you that number.

Tournament chips are not money

The players in a tournament usually start with the same stack of tournament chips, the chips in front of one player. A player whose chips are gone goes out, and the prizes go to the places in the order the players go out, the last player left taking first place.

The Sit & Go rules of the Buenos Aires province lottery say this in so many words: every player starts with 5,000 points in chips, and the chips used in a Sit & Go have no monetary value, belong to the casino and cannot be taken from the table.

The prizes add up to the prize pool, and the prize pool is what is left of the buy-ins after the room takes its fee, which is lesson 7.11. Taken together, the players in a tournament finish behind by that fee: nothing at a final table turns a tournament into income.

From chips to prize money

To turn a stack into prize money we count with a model, not with a rule of any room. ICM, the independent chip model, is the name players use for working out what tournament chips are worth in prize money, and the version here is the Harville model, after a 1973 paper on the outcomes of competitions with many entries. The steps below are our reading of how the model works.

1. First placeEach player’s chance of finishing first is that player’s share of the chips.
2. Each next placeTake away the player who finished above, and run the same rule among the players still left.
3. Prize moneyEach place’s prize, times the chance of finishing there, added up across the places.

The leader finishes first exactly as often as its share of the chips, and the shorter stacks pick up most of the second and third places.

• Leader, 5,000 chips383.93 unitsin prize money.
• Second stack, 3,000 chips327.50 unitsin prize money.
• Short stack, 2,000 chips288.57 unitsin prize money.
• All three stacks1,000 unitsthe whole prize pool.

Each figure is the prizes weighted by the chances in the table above, counted exactly over every order in which the three players can finish.

So the leader holds 50% of the chips and 38.4% of the money, and the short stack holds 20% of the chips and 28.9% of the money.

An all-in call at the final table

In the same example, take the second stack’s seat: the leader moves all in against your 3,000 chips. You either call, matching the bet, or fold, giving up the hand. Calling puts all 3,000 at risk: if your hand comes out higher you double to 6,000 chips, and if it comes out lower you are out in third place. Suppose your hand comes out higher exactly half the time; in chips the call is even, because you stand to gain as many chips as you stand to lose.

• Fold327.50 unitsYour 3,000 chips, as they are.
• The call holds410 unitsYour stack doubles to 6,000 chips.
• The call loses200 unitsYou go out in third place.
• The call, on average305 unitsHalf the hands one way, half the other.

The chips at stake are the same either way, and the prize money is not: going out costs more than doubling up adds, so the average of the call falls below the fold.

• How often your hand comes out higher50%
• Needed, counting chips50%
• Needed, counting prize money60.7%

The third bar is the share of hands your call would need to be worth as much as the fold in prize money; the chips ask only for half.

Where that share comes from: call it p. The call is worth as much as the fold when 410 units × p + 200 units × (1 − p) = 327.50 units. Solved for p, that share is 60.7%.

With two players left the gap closes: the second prize is certain, and the rest of the prize money moves in a straight line with the chips, so chips and prize money give the same answer. A call worth more in prize money can still lose the hand: these figures are averages over many such hands, and one hand is decided by the cards. How often one hand comes out ahead of another before the flop is lesson 7.6.

Who sets the prizes

How the prize pool is split by place is the room’s payout table. In the Sit & Go rules of the Buenos Aires province lottery, in every case, the entry money goes 50% to first place, 30% to second place and 20% to third. The example prizes here, 500 units, 300 units and 200 units out of a pool of 1,000 units, are that split. How a pool is built and paid is lesson 7.11.

A split like this is a room’s rule, and other rooms and other tournaments split the pool differently.

Mayaformer floor supervisor · manners, money and breaks

A final table is exciting, and excitement is when limits slip. The buy-in and any re-entries were decided before the first hand, and what your stack is worth now does not change that amount: the money is already spent, and the prize is not yet paid.

If the evening has started to run on the hope of a final table, stop and look at the plan you made at home. Losing the tournament after a long run is the moment lesson 7.13 is about.

Practice: what are your chips worth?

Level 1 sets an example final table, with stacks and example prizes, and asks what your stack is worth in prize money, to the nearest unit; the answer gives the exact figure. Level 2 has a player move all in against you, says how often your hand comes out higher and how often the prizes need it to, and asks whether to call or fold: in most of its moments the chips say one thing and the prize money another.

Nothing is bet here, and no card is dealt: each moment stops at the decision. The stacks and prizes are examples, not those of any room.

Check yourself

Mayaformer floor supervisor · manners, money and breaks

Three quick ones. Pick an answer, then check it. No timer, no points: just whether it stuck.

Back to the question we opened with. Half the chips at the example final table is worth 383.93 units of the 1,000 units prize pool: less than half, because the prizes are paid by place.

Help, tools and further reading

18+ under each province’s rules · Play responsibly · the helplines are further up this page

Further reading

• Resolución 1452/12, Anexo I: Central Póker Holdem, modalidad Sit & Go (Reglamento del Juego) · Instituto Provincial de Lotería y Casinos de la Provincia de Buenos AiresThe Buenos Aires province Sit & Go rules: 5,000 points in chips each, chips with no monetary value, and the entry money split 50, 30 and 20 per cent.

How it’s worked out