I am working on how to adjust the nash shoving ranges in a PSKO tournament. And was wondering if you guys think my approach is sound.

Say we play a 90man PSKO far from the money. We are in the SB with 10bb and we got the BB covered (he has 9bb). Blinds are 100/50/10

The normal nash range for the SB (assuming that the BB calls nash) is that we should shove 73.5%.

Now lets assume that the BB has a single starting bounty on his head. I model this bounty by assigning it a number of additional chips (750 chips in this case).

HRC does not have an option to add additional chips. So we have to cheat a little and use the antes field for this. There are 9 players at the table and 750/9 = 83.

So i upped the ante from 10 to 93. To represent the extra virtual overlay. This is not entirely correct of course. (maybe even completely wrong?)

Now HRC gives the SB a pushing range of 100%.

What do you think of this method? Outcome is not important.

Not sure if my math is right but let's say we have 22 in the SB in your example and BB will call 58% of the time and we have 47% equity vs his range.

EV_shove= EV_win + EV_lose + EV_FE - EV_fold= 1970*0.47*0.58 + 100*0.53*0.58 + 1180*0.42 - 940= 123

If we convert 1$ bounty to 375 chips, we should have (1970+375)*0.47*0.58, so our shove will make 102 more chips than in a normal, non pko situation.
So, if math is correct, I don't think the bounty equity is a fixed number, I think it will depend on our equity when we get called, mainly because we'll win the bounty more often with, say AA than 72o. Opinions?

thanks for your reply rvrr, but you have to explain it a little better. I dont understand your point.

Couple of things:

- why do you use 375 instead of 750 chips for a bounty?

- I dont understand your ev calculation for the 22s situation.

Ev(push with 22s) = Ev(villain calls we win) - Ev(villains calls we loose) + ev(villain folds)

Ev(push) = 1970*0.58*0.47 - 850*0.58*0.53 + 0.42 * (150 + 90) = 537 - 261 + 100 = 376

Now if we take the bounty into effect it becomes:

Ev(PSKO push) = 740 -261 + 100 = 579

Difference of: 203 chips.


- we are not looking at a single hand that we shove. but a range of hands. 22s is part of that range, but AA and T9s as well. So i think if you want to make an ev calculation. You will have to take the win odds our range has against villains calling range.

Or am i mising something?

lol, disregard OP. Totally forgot that now when everyone folds we also get the bounty chips. So its useless.

Bounty tournaments are unsolvable because of the effect of your stack over later hands - i.e. your chips also represent the opportunity to take someone else's bounties.

One interesting thought experiment:

In $5+$5 3-man tournament 50% of the prize pool is ordinary bounties, 50% to the tournament winner, BTN folds and SB and BB have collusively agreed they go all in blind against each other given the opportunity - so they do.

Ignoring the possibility they chop, is this collusive strategy good for them? What are the new dollar values of the situations of winner of the flip and the player who did not flip?

WOF: 5$ (bounty) + 16.66$ = 21.6$
( because of his 2:1 chip lead HU for the 15$+10$ prizepool+2bounties)

LOF: 0$

Other: 8.33$ (1:2 behind in chip HU, for 25$)

(21.6 + 0 )/ 2 = 10.8$. So i think the flipping players are better of.

Yes, so there's kind of an inverse ICM at work.

I'm wondering if a Nash equilibrium in these might just be for everyone to jam all in on the first hand

yeah reverse icm indeed. Whats your opinion on the 3 models i have described to represent bounties in a different thread?

@ Leia Amidala

what kinda roi would you like to achieve at $5 90 sngs ?

IMO nash charts are outdated because they tell you what to push without considering your opponent's calling range , in ko tourneys they'll call lighter which affects your shoving range.

I've grinded these games for a long time and what helped me most was running spots in icmizer . went from 5.5-6bb/100 to 8.5-9bb/100 over a large sample.

I'm not sure it can be captured by models at all.