In using the same equations and inputs as you I have different answers, I think you made a math error somewhere. I’ve also never seen calculations done quite this way, and I’m not sure how relevant the results are. Sidenote, as of a few months ago, the bounties displayed at the table are now the bounties that you win immediately. Also, since $500 from each buy-in goes to bounty pool, each KO must pay >= $250.

EV1: 0.3564($0.03 * 27525) + $575 = $869.30

EV2: 0.2883($0.03 * 10158) + $325 = $412.86

EV3: 0.3553(-$0.03 * 18554) = – $197.77

Total EV = $1084.39

I think the EV in this equation is only relevant in relation to the $ value of your stack at the start of this hand, which is ~$500 + X. I’ve got X representing the value of your ability to collect bounties in future hands, which is probably impossible to put a number on, except to say it is a lot larger than $0. If this was the first hand of the tourney, I think X is always $500. X will begin to fluctuate after a few hands (even if we pretend your stack never changes), as the stacks and bounties at your table change, and is also affected in some infinitesimal way by players busting from other tables. That being said, you are left with some chips even after losing both pots, which is also worth > $0.

I think any simple calculations of $EV in PKOs are misguided. There is a ton of value in collecting bounties sure, but there’s also a ton of value in sticking around to collect much bigger bounties later in the tournament. If we try to play a strategy that would be suitable to a normal KO tournament, we are giving up a significant amount of $EV by not accounting for the nebulous EV of potential future opportunities. Even harder to estimate (but probably unwise to ignore entirely) is the +/- EV of players gambling against us more often when we accrue a big bounty early on.

Thanks Andrew, that’s some great insight. PKOs are my favorite online format, but I’ve rarely found strategic advice that I didn’t think was flawed or flat out wrong. I like how you show the math while also pointing out other things that should influence our decisions, even if they can’t be mathematically calculated. Although I realized there was more incentive to play for 1st in a PKO, I can see that I need to emphasize it even more. Nice work in the $44 Bounty Builder!