Converting Bounties to Chips
A critical skill in knockout tournaments is being able to gauge the value of a bounty in chips, so you can weigh everything along a single axis. This is why bounty power conversions exist: they let you translate a bounty into chips, then drop that directly into the reward side of a pot odds equation.
Exchange Rate
The basic idea is that you can always define an exchange rate between chips and dollars at any point in the tournament. This is a chip EV approximation.
Exchange Rate = Chips/Prizes
Bounty Prize Pool Decay
The bounty prize pool decays according to this equation, as posted earlier.
B ≈ F ^ K
Starting Stack%
However, knockout specialists don't care about bounty prize pool%. They care about the value of a bounty as a startstack.
By combining the pool decay law with the exchange rate, you get a general equation that works for any bounty format:
Bounty as StartStack% = (K * B * m) / ((1 - B) + B * f^K)
Variables:
- B = Fraction of buy-in going to the bounty pool (ignoring rake)
- F = The percentage of runners remaining = remaining entries / total entries
- K = The percentage of a bounty you cash upon knockout (typically 50% for PKO, 100% for SKO)
- M = the number of bounties a player has on their head = target’s bounty / starting bounty
After the bubble, just replace (1-B) in the denominator with the percentage of the remaining regular prize pool.
Average Stack
You can also express the same thing as a percentage of the average stack by multiplying by F:
Bounty as AvgStack% = (K * B * M * F) / ((1 - B) + B * F^K)
Canonical Shortcuts
In practice, this reduces cleanly for the standard formats:
One Bounty as StartStack%: (Before bubble)
- SKO (B=0.5, K=1) = 1 / (1 + F)
- PKO (B=0.5, K=0.5) = 0.5 / (1 + √F)
- TKO (B=1, K=1) = 1 / f
Bounty Calculator
Of course we don't really want to manually calculate this each time. Best practice is to just memorize some milestone values at various points throughout the tournament. So I've included a bounty power calculator to make that easy.
2 Replies
The Big Question: Do Bounties Get More or Less Valuable?
This is a bit of a "yes and no" answer. Two things are happening at once:
- 1. The Absolute Value Increases: As the bounty pool decays chips deflate in value, so the value of a single bounty is worth more chips.
- 2. The Relative Value Decreases: At the same time, the average chip stack is growing. The average stack tends to grow faster than the average bounty value does.
The key takeaway is that in practice, bounties become less relevant as the PKO progresses. While the bounty itself is worth more chips, those chips mean less when compared to the massive stacks in play later on.
This graph shows it perfectly: the bounty's value as a percentage of a starting stack goes up, but the average bounty compared to the average stack goes down (blue line).
Updated spreadsheet showing average bounty as a percentage of average stack:
Converting bounties to chips sounds like possessing someone's soul.
