Progressive Knockout Bubble Math: Why 99 Is Still a Fold
A $15 bounty changes the price on a progressive knockout bubble. 99 still falls short. The stack, ICM and bounty calculations are below.
Ten players remain in a $22 progressive knockout and nine get paid. Hero is in the big blind with 99 and 14 big blinds. The cutoff shoves 12 big blinds with a $15 bounty on their head.
The chip math says call. 99 has 57.1% equity against a 19% shoving range, and chip EV needs only 45.3%. ICM raises the required equity to 63.3%. The $15 head lowers it to 60.5%, which still leaves 99 short. The calculation below uses the stack sizes and payout structure.
The spot
- Tournament: $22 progressive knockout, 180 runners. The $1,800 prize pool and the $1,800 bounty pool are split evenly.
- Situation: 10 players left, 9 paid. Tenth place gets nothing; ninth pays $100 and the winner takes $480.
- Blinds: 500 / 1,000 with a 100 ante, so 2,500 is in the middle before action.
- Hero: big blind, 14,000 behind after posting.
- Cutoff: 12,000, shoves. The $15 head is a $10 starting bounty plus one knockout.
- Range: about the top 19% of hands, something like
22+, A2s+, K9s+, QTs+, JTs, T9s, 98s, ATo+, KJo+.
Hero covers the cutoff. The call is 12,000 into a final pot of 26,500.
Step 1: the chip-EV price
Calling 12,000 to win 26,500 needs 45.3%:
Price:
12,000 ÷ 26,500 = 45.3%
Against that range, 99 has 57.1% equity from a seeded 60,000-run Monte Carlo. In chips, the call returns 3,129:
Chip EV:
0.571 × 26,500 − 12,000 = +3,129 chips
The margin is 11.8 points, so chip EV makes this a call.
Step 2: ICM changes the price
ICM converts each stack into a share of the prize pool. With 10 players left and nine paid, the three outcomes are worth:
| Outcome | Hero’s stack | Hero’s ICM equity |
|---|---|---|
| Fold | 14,000 | $190 |
| Win the all-in | 28,500 | $261 |
| Lose the all-in | 2,000 | $68 |
The break-even equity between folding and calling:
Break-even equity:
(190 − 68) ÷ (261 − 68) = 63.3%
At 57.1%, the call is worth about minus $12 in prize equity. The 18-point gap between 45.3% and 63.3% is the risk premium.
Most of that gap sits in the losing branch. A 2,000-chip stack with 10 players left is 1.5% of the chips in play, and the next two hands put 1,700 chips into the middle in blinds and antes. Folding keeps a 14bb stack. The bubble factor for a transfer this size is about 1.23, so a chip lost costs about 23% more prize equity than a chip won adds.
Step 3: pricing the bounty
Half of the $15 head is paid in cash on the knockout. The other half is added to the winner’s bounty and pays out only if that player wins the tournament. The model values the added half at 20.8% of face value here.
- $7.50 cash on the knockout.
- $7.50 added to the winner’s bounty, worth about $1.56.
- Total bounty value: about $9.06.
Adding $9.06 to the win branch lowers the required equity from 63.3% to 60.5%. 99 at 57.1% is still below that line:
Bounty-adjusted call:
0.571 × (261 + 9.06) + 0.429 × 68 − 190 ≈ −$7
The same threshold across a few hands:
| Hand | Equity vs range | Call at 60.5%? |
|---|---|---|
| 69.5% | Yes | |
| JJ | 65.3% | Yes |
| TT | 61.0% | Yes, barely |
| AKs | 60.9% | Yes, barely |
| AKo | 58.9% | No |
| 99 | 57.1% | No |
| AQs | 56.7% | No |
| 77 | 52.2% | No |
| AJo | 51.1% | No |
| 33 | 42.9% | No |
At this price, the calling range is about TT+ and AKs. With the $15 head included, the rest of the list loses money.
When the bounty changes the decision
The bounty moves the threshold in this spot by 2.8 points. Several other inputs move it further:
| Change from the baseline | Required equity | 99 decision |
|---|---|---|
| Cutoff’s head is $30 | 57.9% | Fold, by less than a point |
| Cutoff’s head is $40 | 56.3% | Call |
| Cutoff shoves 6bb instead of 12bb | 44.1% | Call |
| Hero has 30bb instead of 14bb | 46.0% | Call |
| Cutoff shoves a wide 35% range | 60.5% (99 has 61.9%) | Call |
- A $30 head lowers the threshold to 57.9%, which is 0.8 points above 99.
- A $40 head lowers it to 56.3%, and 99 becomes a call.
- Against a 6bb shove the threshold falls to 44.1%, since a loss leaves an 8bb stack.
- With 30bb behind, the threshold is 46.0%, since a loss no longer ends the tournament.
- Against a 35% shoving range, 99 has 61.9% equity and clears the 60.5% threshold.
The four inputs
Four inputs decide a bubble call like this one:
- Chip-EV price. The call amount divided by the final pot. It sets the baseline.
- ICM price. Rebuild the fold, win and lose stacks, then compare prize equity. A direct bubble with a short stack usually adds a double-digit risk premium.
- Bounty value. Half of the head is cash. The added half is tournament equity, so it is worth less than face value.
- Elimination risk. A loss that leaves a playable stack reduces the ICM cost. A loss that leaves 2bb raises it.
Both the bounty and the ICM cost belong in the same prize-equity calculation. In this spot, the $15 head moves the threshold from 63.3% to 60.5%, and 99 needs another 3.4 points. Folding is worth about $7 more than calling.
How these numbers were produced
The stack equities use the Malmuth-Harville ICM model, computed exactly for the 10 remaining players. Hand equities are seeded Monte Carlo runs of 60,000 showdowns against the stated range. The progressive knockout model pays 50% of the eliminated player’s bounty in cash and adds 50% to the eliminator’s bounty, valuing that added half by the eliminator’s post-hand chip share, which is 20.8% in this spot. The model covers one hand and does not simulate future game states, so treat it as a single-hand estimate. The numbers are rounded, so differences under a tenth of a point are noise.
Written by
Jake Rivera
Poker writer
Jake Rivera writes about poker strategy across No-Limit Hold'em, Pot-Limit Omaha and Short Deck. His work covers preflop ranges, ICM and bubble decisions, and postflop lines, along with the adjustments that separate tournament play from cash games.