Getting to grips with the mathematics of bounties

October 08, 2020inStrategy

Bounty Builder Series kicks off this Sunday and there’s more than $30 million up for grabs. In this article, you’ll learn how much a bounty is really worth in chips, how much equity you need to call to win a bounty, and more.

One quick glance at a Bounty Builder / Progressive Knock-Out (PKO)* lobby never gives you the whole story. The payouts may seem smaller than you’d expect considering the tournament’s guarantee, particularly the min-cash (which is often less than the buy-in itself).

But that’s because unlike regular tournament structures, you don’t have to wait until the bubble bursts to make money. Half of your buy-in goes to a regular prize pool, while the other half goes into the bounty prize pool.

*Bounty Builders and PKOs are exactly the same format but you’ll usually find larger starting stacks and bigger guarantees in Bounty Builders.

In a Bounty Builder/PKO tournament, the second you knock a player out, half of their bounty is added directly to your PokerStars account in cash, while the other half is added to your own bounty.

This drastically changes the way you have to have to play. We have to aggressively try and knock out as many people as possible, and that means we have to crunch the equity numbers.

Get to grips with PKOs: The maths behind bounties

Let’s say you’re playing a $55 Bounty Builder Series event.

Bounty Builder Series starts this Sunday (11th October)

$25 of your buy-in goes into the main prize pool, while $25 goes towards the bounties.

The starting stack is 25,000, and a PKO of $12.50 will be awarded for each player eliminated.

As the amount available to win is only half of the overall bounty, that means a $12.50 bounty equals 12,500 (or half the starting stack) in chips.

So, 25,000 in chips equals $25.

You have 25,000 in chips and the player to your left has 10,000 chips with a $12.50 bounty.

The blinds are 250/500 and you open to 1,000. They move all in and everyone else folds.

The pot is now 11,750 (including the big and small blinds) and you have to put in 9,000 to win 20,750.

Here’s how to work out your odds:

Total Pot (11,750) ÷ Amount to Call (9,000) = 1.3 = 1 to 2.3 odds

Now we need to convert that into hand equity.

Here’s how to work out the equity your hand needs to call:

1 ÷ 2.3 = 43%

So your hand needs 43% equity to make your call profitable.

But remember: their $12.50 bounty is also up for grabs.

The $12.50 bounty equals 12,500 in chips, so you could say they’re actually all in for 22,500 (10,000 + 12,500).

Let’s do the maths again:

Total Pot (24,250) ÷ How Much To Call (9,000) = 2.69 = 1 to 3.69 odds 

1 ÷ 3.69 = 27% 

With the bounty in play, your hand now only needs a 27% chance to win to make your call profitable.

This is why it’s so important to hunt bounties aggressively. The nature of Bounty Builders/PKOs means the variance is higher, but the more bounties you win, the more money you take out of the tournament and the less other players can win.

An easy way to remember in-game:

The starting bounty equals half a starting stack.

Double the starting bounty equals a complete starting stack etc.

For more hand maths examples from bounty tournaments, check out Pete Clarke’s mathematics of bounties article over at PokerStars School.



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