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Old 09-13-2017, 07:50 AM   #1
WorldResident
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Mathematical theory PSKO

Hey guys I have a question regarding +$EV decisions in progressive super knockout MTTs.

We discussed it in our MTT study group for a bit. The result doesn't seem right though. So I figured there may be something wrong with our math. Shoot at it!

The information available:
Villain jams 18 bbs(177.121 chips) UTG+2 /w a 1k bounty on his head. Assigned range: QQ-77, 6s6c, ATs+, KQs, AJo+. VPIP/PFR 14/11
Hero looks at 66 with a 203,271 (20 bb) stack on the CO.

UTG+2 59.90%
CO 40.10%

We tried to make calculations based on Apestyles' theory
Buy-in: 500+500+50
Starting stack: 10k

So if I understand it correctly.
10k(starting stack) / 500(bounty) = 20 chips is worth 1 dollar.

Apestyle:
Quote:
But you only get half of the KO money that each player has in the bubble over their head.

So in this tournament, to find out how many chips you add to the pot you just multiply your opponent's bounty number x 11.
In our example we use 20 chips divided by half the bounty = 10 to multiply with.

Chips to add to the pot = 1k * 10 = opponent's bounty number * multiply factor = 10k

Pot + bounty chips = 203.371 + 10.000 = 213.371

Equity needed 177.121/(213.371+177.121)= 45,36%

40.10% - 45,36% = -5,26% equity to call /w 66.


It doesn't seem right. Who knows the correct answer?
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Old 09-13-2017, 08:12 AM   #2
just_grindin
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Re: Mathematical theory PSKO

Quote:
Originally Posted by WorldResident View Post
Hey guys I have a question regarding +$EV decisions in progressive super knockout MTTs.

We discussed it in our MTT study group for a bit. The result doesn't seem right though. So I figured there may be something wrong with our math. Shoot at it!

The information available:
Villain jams 18 bbs(177.121 chips) UTG+2 /w a 1k bounty on his head. Assigned range: QQ-77, 6s6c, ATs+, KQs, AJo+. VPIP/PFR 14/11
Hero looks at 66 with a 203,271 (20 bb) stack on the CO.

UTG+2 59.90%
CO 40.10%

We tried to make calculations based on Apestyles' theory
Buy-in: 500+500+50
Starting stack: 10k

So if I understand it correctly.
10k(starting stack) / 500(bounty) = 20 chips is worth 1 dollar.

Apestyle:


In our example we use 20 chips divided by half the bounty = 10 to multiply with.

Chips to add to the pot = 1k * 10 = opponent's bounty number * multiply factor = 10k

Pot + bounty chips = 203.371 + 10.000 = 213.371

Equity needed 177.121/(213.371+177.121)= 45,36%

40.10% - 45,36% = -5,26% equity to call /w 66.


It doesn't seem right. Who knows the correct answer?
All of your calculations seem right to me but I don't know why you subtracted the equities at the end?

You have 40% equity vs his range and your adjusted pot calculation indicates you need 45% equity to make the call so it's a clear fold even considering the bounty.

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Old 09-14-2017, 09:12 AM   #3
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Re: Mathematical theory PSKO

But don't you think the 45% seems too high? Before I started the calculations I was like this should be a easy call. What about you?

Wanted to show the difference between a call and fold.
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Old 09-14-2017, 09:43 AM   #4
Kelvis
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Re: Mathematical theory PSKO

Well you're playing with a 20x starting stack and the bounty is worth one buy in. Doesn't take too much thought to figure out that this bounty probably isn't going to change too much about your decision. These bounties only become relevant in the start of the tournament.
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Old 09-14-2017, 09:46 AM   #5
just_grindin
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Re: Mathematical theory PSKO

Quote:
Originally Posted by WorldResident View Post
But don't you think the 45% seems too high? Before I started the calculations I was like this should be a easy call. What about you?

Wanted to show the difference between a call and fold.
Well according to the other thread you have converted the bounty correctly into a chip amount (10k).

Since the pot you will win in the end will be roughly 203.371+177.121+177.121 the bounty addition has only effectively added 10.000/557.613 = .0179*100 = 1.79% of the chips in the pot. Not much of an overlay.

So either that method of modeling bounties is incorrect, the method is sound and there is something wrong with the implementation in that specific thread, or your intuition about how much that particular bounty contribute to your $EV relative to the risk of busting out of the tournament and losing your shot at the prize pool is off.

Last edited by just_grindin; 09-14-2017 at 10:13 AM.
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Old 09-14-2017, 10:02 AM   #6
WorldResident
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Re: Mathematical theory PSKO

Thank you for your effort.

There was indeed something wrong with the implementation. The starting stack was 50k instead of 10. Thank you for confirming the math though!
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Old 09-17-2017, 08:58 PM   #7
apestyles
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Re: Mathematical theory PSKO

Hey guys,

Was searching my name and found this thread. When I made that post a long time ago I was fairly certain that was the best way to go about things (50% in psko, 100% in SKO etc.) .
However, based on some work I've done with ICMizer and KOculator I'm reasonably certain my original way of going about it, while intuitive, was actually wrong. The true answer is a bit more complicated because your stack represents your equity in the bounty pool. In the beginning of a pko you probably add more like 25-30% of starting stack, not 50%. I'm still working on the exact answer but didn't want people citing a post of mine that I now believe to be incorrect.

BTW, if anyone wants to get paid to run ICMizer calcs for me PM me. I still want to figure this out and create a more universal tool.
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Old 09-17-2017, 08:58 PM   #8
apestyles
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Re: Mathematical theory PSKO

Hey guys,

Was searching my name and found this thread. When I made that post a long time ago I was fairly certain that was the best way to go about things (50% in psko, 100% in SKO etc.) .
However, based on some work I've done with ICMizer and KOculator I'm reasonably certain my original way of going about it, while intuitive, was actually wrong. The true answer is a bit more complicated because your stack represents your equity in the bounty pool. In the beginning of a pko you probably add more like 25-30% of starting stack, not 50%. I'm still working on the exact answer but didn't want people citing a post of mine that I now believe to be incorrect.

BTW, if anyone wants to get paid to run ICMizer calcs for me PM me. I still want to figure this out and create a more universal tool.
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