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Bounties near the bubble: how a PKO changes short-stack shoves and calls

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Two risk premium gauges for the big blind calling a button shove: Vanilla at +3.9% and PKO, with a bounty crown, at βˆ’4.1%

Three places from the money, it folds to you on the button with about 9 big blinds and J9s. In a regular hyper the solver shoves it 100% of the time. In a Speed Racer, with $109.38 on your head, it shoves it 0.1%.

I wanted to know what a progressive knockout really changes at the bubble, so I took the closest pairs of spots I could find in our library: Vanilla Tournament against Speed Racer, both Near Bubble, six-handed, three places from the money (30 left, 27 paid vs 29 left, 26 paid), blinds 0.5/1 with a 0.15bb ante.

I'm going to compare four decisions: a button shove, the big blind's call against it, a small blind against a big big blind, and a big blind who is the shorter stack. The short version: the bounty hardly moves how often the short stack shoves, it changes what it shoves with, and it moves the calling range a lot β€” but only for the player who covers.

Button shove, 9bb, three from the money

The button has 8.9bb in the Vanilla spot and 8.7bb in the Speed Racer spot. It folds to the button and both blinds cover. In the Speed Racer spot the button also carries the biggest bounty at the table, $109.38, which the viewer shows as 4.4x the starting bounty. (Stacks in the text and in the image headers are counted before blinds and antes; the table itself shows the chips left behind.)

9bb BTN open-shove (0.15bb ante): Vanilla Tournament vs Speed Racer, three places from the money

The shove is almost the same size: 26.3% in the Vanilla spot, 26.4% in Speed Racer. But the Vanilla tree also lets the button min-raise to 2bb, and it does that with another 6.4% β€” a split range: JJ+ and AJs+ every time, plus hands like K9o, K5s, K6s and Q5s that would rather not face a call. Count every hand that goes in and the Vanilla button plays 32.7%, the Speed Racer button 26.4%.

9bb BTN open-shove (0.15bb ante): Vanilla Tournament (left) vs Speed Racer with a 4.4x bounty (right)

What surprised me is which hands leave. Suited and offsuit connectors drop out: J9s (100% β†’ 0.1%), 98s (97.5% β†’ 0%), T8s (99.1% β†’ 0%), JTo (100% β†’ 0%), and T9s and Q9s become mixed at 52.7% and 43.9%. Weak aces go the other way: A2o (81.0% β†’ 100%), A7o (91.7% β†’ 100%).

The reason is the big blind. Knocking out this button pays $54.69 in cash, so the big blind calls wider (next section), and a shove that relied on folds loses its fold equity. Connectors were shoved for the folds; against a wider call they are worse than an ace, which also blocks the aces the big blind now calls with. The button's own pressure is also lower: their bubble factor against the big blind is 1.43 in Speed Racer against 1.63 in the Vanilla spot.

A big bounty on your head does not shrink the button's shove so much as change its shape: fewer connectors, more weak aces.

A caveat on the comparison: the two tables are close, not identical. The players who already folded differ (the HJ has 28.7bb in one and 8.7bb in the other), and part of the difference in the button's range is the tree, which offers the Vanilla button a min-raise and the Speed Racer button only fold or all-in.

Big blind against the button shove

Same two spots, one decision later. The button is all in, the small blind folds, and the big blind covers: 22.1bb against 8.9bb in the Vanilla spot, 17bb against 8.7bb in Speed Racer.

17–22bb BB call vs 9bb BTN shove (0.15bb ante): Vanilla Tournament (left) vs Speed Racer, BB covers (right)

The Vanilla big blind calls 22.4%; the Speed Racer big blind calls 29.2%. The hands it adds: A2o (0% β†’ 100%), A3o (0% β†’ 100%), A4o (73.7% β†’ 100%), and K9s, Q9s, J9s, T9s and QJo, which go from almost never to always.

The bubble factors explain it. In the Vanilla spot the big blind's bubble factor against the button is 1.17, a risk premium of +3.9%: the call needs a little more equity than chip-EV pot odds. In the Speed Racer spot it is 0.85, a risk premium of βˆ’4.1%: the call needs less than chip-EV pot odds.

17–22bb BB call vs 9bb BTN shove (0.15bb ante): the big blind's bubble factors and risk premiums, Vanilla Tournament (top) vs Speed Racer (bottom)

A bubble factor below 1 is what a bounty does. With payouts alone, losing a flip near the money costs more than winning it gains, so the factor sits above 1. In a PKO the bubble factor counts the bounty too, and this one pays $54.69 in cash β€” about two thirds of the $80.48 min-cash. Look at the button's column: every bigger stack is below 1 against the button (LJ 0.89, CO 0.84, SB 0.90, BB 0.85).

Covering a big bounty took the big blind's bubble factor from 1.17 to 0.85, and the call from 22.4% to 29.2%.

My opinion, not the solver's: this call is built against a button who shoves 26.4%. Many players with a big bounty on a PKO bubble shove tighter than that. Against a tighter button I would cut the bottom of this range first, the A2o and the suited gappers, before touching the pairs.

Small blind against a big big blind

Now the blind battle. It folds to the small blind with 9.3bb in the Vanilla spot and 9.5bb in Speed Racer, and the big blind has 29.9bb and 33.9bb. The small blind's bounty in Speed Racer is $25.00, the starting head and the smallest at the table (1.0x in the viewer): knocking the small blind out pays only $12.50.

9bb SB open (0.15bb ante): folded to the small blind, big blind covers, Vanilla Tournament vs Speed Racer

The small blind plays far more hands in Speed Racer: 56.9% against 43.0%. The shove itself grows only a little, 36.4% β†’ 39.2%, with offsuit kings like K5o (0% β†’ 100%) and K3o (0% β†’ 74.6%) joining it. The rest is a 17.7% limp.

9bb SB open-shove (0.15bb ante): Vanilla Tournament (left) vs Speed Racer, smallest bounty at the table (right)

Read the pairs carefully. 99 goes from a 99.0% shove to a 0% shove, but it does not fold: the Speed Racer tree has no 2.5bb raise for the small blind, so its strong hands limp instead. AA, KK, QQ, JJ, TT, 99 and 88 all limp every time, where the Vanilla small blind raises AA 97.2% and KK 91.0% of the time.

Then the big blind faces the shove. The Vanilla big blind calls 28.8% with a bubble factor of 1.11 (+2.6%); the Speed Racer big blind calls 34.6% at 0.98 (βˆ’0.4%). The extra calls are kings and broadways: K7o (0% β†’ 100%), K8o (0% β†’ 100%), JTo (0% β†’ 100%), K3s (0% β†’ 100%), Q8s (0% β†’ 100%).

30–34bb BB call vs 9bb SB shove (0.15bb ante): Vanilla Tournament (left) vs Speed Racer, BB covers (right)

Why so much movement for a $12.50 bounty? Part of it is that bounty. The other part, as I read it, is the ladder: in a PKO half of the prize money is in the bounties, so the payout ladder that ICM taxes is smaller (the min-cash is $80.48 here, $110.00 in the Vanilla spot). You can see it in the small blind's own bubble factor against the big blind: 1.75 in the Vanilla spot, 1.42 in Speed Racer. Both players are under less pressure, so both play more hands.

Even the smallest bounty at the table moved the big blind's call from 28.8% to 34.6%.

When the big blind is the one covered

The last pair flips coverage. The LJ shoves 11.4bb in the Vanilla spot and 10bb in Speed Racer (8.2% and 9.0% of hands), and the big blind has only 8.3bb and 8.4bb. If the big blind wins, the LJ is still in the tournament, so there is no bounty for the big blind to collect.

8bb BB facing a 10–11bb LJ shove (0.15bb ante): the shover covers the big blind, Vanilla Tournament vs Speed Racer

The two calling ranges are the same hand for hand: 77+, AJo+ and AJs+, with one exception, ATs (0% β†’ 99.9%). That is 7.2% against 7.5%. The bubble factors stay well above 1 in both: 1.54 (+10.6%) and 1.41 (+8.6%).

8bb BB call vs 10–11bb LJ shove (0.15bb ante): Vanilla Tournament (left) vs Speed Racer, BB covered (right)

This is the other half of the bounty rule: only the player who covers can win a bounty. A covered big blind is playing for their tournament life, and the LJ is the one with a bounty to gain: $34.37 in cash for winning the pot. Nothing in that pushes the big blind wider.

No coverage, no discount: the covered big blind calls 7.2% in Vanilla and 7.5% in Speed Racer.

The same pattern across the library

Four pairs could be luck, so I ran the same walk over every six-handed Near Bubble spot of the two formats that is exactly three places from the money with 30 or fewer players left: a player with 8–12bb shoves first in and it folds to the big blind.

Big blind facing an 8–12bb shove, three places from the money
FormatBig blindSpots (decisions)Average callAverage bubble factor
Vanilla Tournamentcovers the shover25 (32)15.4%1.25
Speed Racercovers the shover7 (9)22.0%1.00
Vanilla Tournamentis covered8 (9)38.7%1.42
Speed Raceris covered7 (10)34.5%1.39
Plain averages over every matching decision; the stacks differ from spot to spot, so read the direction, not the decimals.

When the big blind covers, the average bubble factor falls from 1.25 to 1.00 and the average call rises from 15.4% to 22.0%. When the big blind is covered, the bubble factor barely moves (1.42 and 1.39) and the call does not get wider. The Speed Racer side has only 9 and 10 decisions, so treat it as a direction, not a rule.

Near the bubble, a PKO changes who calls more than who shoves. The short stack's shove stays about the same size, loses its connectors and keeps its aces. The player who covers calls wider, by a lot when the bounty is big and still visibly when it is the smallest one at the table. The player who is covered plays almost exactly as in a Vanilla Tournament.

So the first question in a PKO bubble spot is not "how big is the bounty" but "who covers whom". Open the spots below and click through the same decisions; the bubble factor panel in the viewer shows the coverage effect in one number.