The effect of bounty on $EV

I haven't seen much discussion on this topic even though I think it deserves some attention.

Nearly everyone realises that your calling range to a shove in a bounty tournament should widen if you have villain covered and you're not likely to be reshoved on. The question is -- by how much?

I've developed a formula for this, but I want to test the water first against the CC community's intuition. There are players on this forum with excellent feels for the game.

Let's take a situation. It's midway through a $6 bounty tourney and you're in the BB w AQo. The blinds are 100/200 and you have 3000 chips after posting (your starting stack). A player with 1500 chips shoves from MP2 and everyone folds to you.

Assume his range is 88+ AQ+ KQs KJs (6.2%)

Do you call?

If there's a $1 bounty on his head, do you call?

To save you time, pokerstove puts your equity at 39.7% against his range.

Assuming you have villain covered (if you don't you can't win his bounty and then normal cEV applies), the preflop equity you need for a call is

Pw > (beta - alpha) / (2beta + delta + S0/(6*S) )

where
beta = the fraction of villain's stack to yours (0 < beta <= 1)
delta = the dead money in the pot as a fraction of your stack
alpha = the fraction of your stack you've commited to the pot already
S0/S = your starting stack over your current stack

So taking the above example,

beta = 0.5
alpha = 0
delta = 0.1
S0/S = 1

So you need 39.5% equity to call. Since villains range gives you more than this with AQo, it is a call.

Without the bounty you need 45.5% equity to justify a call, so it is a clear fold.

it's a clear call, bounty or no. If yo uthink it is a fold then you have a horrible feel for proper shoving ranges. MP2 with 7.5BB (and presumably there should be antes in play here at this point as well...)

I'm shoving more like 31% of my range, not 6%. 22+,A2ss, A3o+, K6s+, KTo+, Q9s+, QTo+, J8s+, JTo, T8s+, 98s+, 97s+, 76s+.

That's the nash range assuming antes. OK I might tighten it a bit if i see a bounty hunter with a big stack, but not by much.

Regardless, your formula is bunk. Why? The money to be made is in going deep. Making a decision for an extra buck is terribly negative $EV assuming it is a standard $10+1 where it's $1 or $2 for a bounty. You will always be better off making a fold where it's on the margin for a bounty unless it's for a complete pittance of chips.

Would you rather get 5 $2 bounties or ship a tourney for $2,000? And if you go deep, the bounties will come on their own.

The only exception I might make to this is if the bounty is 50% or more of the buyin. (or if it is in a live casino where a $100 + $100 +$20 structure might exist, where it's $100 buyin + $100 bounty...) IN that case, *maybe* you might widen your range, but then I still think the relative stack sizes will impact this and it's a minor factor at most.

p.s. Apart from just knowing that you should never let a bounty influence you here, you wrote out a formula that there is no way for someone to evaluate because you just plunked these factors down without even a rudimentary explanation of why you chose those terms and the construction of the formula.

In the end, you are re-inventing the wheel. It's simple ICM/nash that describes the ranges (and in a non $EV affecting situation you plug in no payouts to the ICM formula, and you can get ranges.)

So if you know that someone is shoving too loose or too tight, you just adjust your calling range appropriately.

I didn't ask what the shoving range might be. I asked, given the shoving range, how does the bounty change your calling range?

loopmeister said:

I didn't ask what the shoving range might be. I asked, given the shoving range, how does the bounty change your calling range?

Click to expand...

It doesn't change my range 1 bit. (exception like I said for a slight adjustment in a $100 + $100 casino tourny. And if then, it's a tiny adjustment at most)

Way more money for going deep then collecting a bounty. Plus in going deep you inevitably will collect plenty of bounties anyways.

Too many people fundamentally call wider which is a mistake, since people should be shoving tighter knowing that bounty wanna-bes call light.

And regardless, you presented a formula that is gobble-dy-gook and comes from thin air, without you even presenting the non-mathematical thinking behind it.

Of course if you have his range beaten which you say you do in your example then its a no brainer to call regardless of if there is a bounty. You have him beaten.

loopmeister said:

Assuming you have villain covered (if you don't you can't win his bounty and then normal cEV applies), the preflop equity you need for a call is

password > (beta - alpha) / (2beta + delta + S0/(6*S) )

where
beta = the fraction of villain's stack to yours (0 < beta <= 1)
delta = the dead money in the pot as a fraction of your stack
alpha = the fraction of your stack you've commited to the pot already
S0/S = your starting stack over your current stack

So taking the above example,

beta = 0.5
alpha = 0
delta = 0.1
S0/S = 1

So you need 39.5% equity to call. Since villains range gives you more than this with AQo, it is a call.

Without the bounty you need 45.5% equity to justify a call, so it is a clear fold.

Click to expand...

Wait a minute. This formula is cockamamy for reasons I missed the first time around. You gave the stove equity as ~39%.

Then yo say that if there is a bounty, you need MORE equity to call? That is completely impossible! Personally like I said, it's the same equity as stove would give you, but if the $$ value of the bounty got factored in at all then if anything you would call slightly wider (even though I wouldn't as I don't feel the marginal bounty is the right move to go after.)

Regardless though, if you really think there is $EV value to the bounty then your formula cannot be right as calling ranges would always and I mean always be WIDER as the $ value of the bounty grew in relation to the prizepool.

Wat?

Has anybody been able to come up with a better formula for calling an all-in with a substantial bounty? For example, if it's breakeven EV to call with a 15% range against a short-stack who jams with 1/3 or 33% of hands in a $300 tournament, how much does a $100 bounty widen your calling range (1/3 is bounty and only 2/3 goes to the prize pool)?

loopmeister said:

I haven't seen much discussion on this topic even though I think it deserves some attention.

Nearly everyone realises that your calling range to a shove in a bounty tournament should widen if you have villain covered and you're not likely to be reshoved on. The question is -- by how much?

I've developed a formula for this, but I want to test the water first against the CC community's intuition.

Click to expand...