KO maths
Posted by hennerz0
Posted by
hennerz0
posted in
Mid Stakes
KO maths
Hey guys trying to figure out how to quantify the value of a bounty in terms of chip expectation.
For example in a super knockout, the bounty is worth half the buyin and starting stacks are 3000. Is it correct to equate the bounty then to 1500 chips? Aka to make a breakeven call you can take a -1500 chip edge?
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No, half of you buy-in goes to your chips and half of it goes to the KO bounty.
At the start (assuming a deep field far from the money, so no ICM effects) doubling lets you take all the equity from your opponent, your chip EV doubles and you collect the KO bounty. All that you have to do is to value the potential to KO other players as a function of your stack. At the beginning everyone has equal chances to knock someone out, if you lose a flip on the first hand that value goes to zero. So that adds up to doubling the KO EV.
But in reality, having a slightly bigger stack matters a lot, especially at significant blind pressure, since with a 3100 stack you can take out all the 3000 stacks, whereas with a 2900 stack you can't. Of course this changes if there are a lot of smaller stacks than you.
This is a great breakdown of the future value of the stack
But i think you forgot to include the dollar value of the bounty in the equation.
I think the equation needs to be something like:
Prob needed=(current tournament $value)/[(tournament $ if win)+ $bounty earned].
So in the $20SuperKO, a $10 bounty makes an early call break even at 40%. Wow.
So how much we should add to the pot when we cover opponent? 3k or 1,5k?
Much less than 1500 chips, probably closer to 0 than that.
Suppose you value a knockout at 1500 chips more and start calling with 40% equity where you would normally call only with 50%, you will lose 60% of the time. If you played normally, assuming equal skill, you would have a 50% chance to knock someone out with those 3000 chips at a later opportunity. So you just cost yourself 10% chance of collecting the bounty and you made a -600 cEV call.
You should compare calling with folding and how much chance you have to collect bounties if you fold. For instance if he has a 300 chip stack and you cover, calling with 40% only costs 60 cEV, and in a super knockout a bounty is worth as much as a start stack (3000). Losing 300 chips will cost you far less than 3000 in terms of opportunities to knockout other players.
In an extreme example, suppose you only have 200 chips left, and the big blind is (effectively) all-in with 100 chips and everyone else has a much larger stack. Then your cEV value is very low (less than 1/10th of your starting stack) and almost all the value from being able to knockout other players comes from being able to knockout the big blind. So you should probably go all-in with every hand because this is your last opportunity to collect this bounty with a worth of a fresh 3000 starting stack since it costs you so little.
I think I'd add 1500 in the early stages. This drops as ICM kicks in and/or the bounty pool shrinks...
very complete video about it: http://www.runitonce.com/pro-training/videos/pudge3/
Ill watch the video next, however disagree w/ you gametheory. You're sacraficing a lot of $EV by not factoring in the KO value. Say its the first hand of a 20$ SKO, 3k starting, your 3k stack has a $ EV of 10$ in a vaccuum, doubling your stack will put your $EV at 19 or something most likely, KO is worth exactly 10$ EV, you get it instantly. So if you're making an AI or F decision pre just run an equity calc and see which $EV is higher...which means using 3k chips as that is equivalent to 10$ EV, and actually, the larger your stack (if its very very large) the larger # of chips, slightly, that 10$ represents.
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