If you had two bots that posted a sb and bb each as per usual but constantly went all in vs each other using a 100% jam range and auto refilled their stack each round then you’d have to estimate that long term this would be a neutral outcome due to the zero sum game nature of poker but what I’m wondering is if you tightened one bots range 1% so it now jams 99% of hands, would this bot eventually be the profiteer over a long enough time span?

2nd question, if you tighten his range to only 20% then would it profit?

All thoughts welcome

You've had an account since 2013, you should be able to think this one through.

How deep are the effective stacks?

If 100bb,

1) yes
2) yes

Yeah 100bb. So you don’t think the forfeiting of the blinds would penalise the tighter player in any significant enough way to make him be less profitable?

I say this cos nits get destroyed heads up when they don’t expand their vpip

Nits would not be destroyed if their opponents just jammed 100bb preflop with 100% range!

Less profitable than a player openjamming 100% at 100bb? No.

You should be able to math this out yourself. Use equilab and you might learn something.

A 99% range is basically everything except 32o, so you don't get a very big equity advantage from this tiny difference in range. (It's about 50.09% vs 49.91%). That said, the small equity edge adds up over time.

I did some EV calculations, based on the following assumptions:

* Prior to each hand, there is 1.5bb of dead money in the middle (which has been taken from the SB and BB).
* When the "tight" bot is in the SB, it jams 99% of the time and gives a walk when it has 32o.
* When the "tight" bot is in the BB, it calls 99% of the time and folds when it has 32o.
* There is no rake.

Based on these assumptions, I calculated that the approximate long term result is that the "tight" bot collects an average of 1.83bb of the 3bb of dead money after playing each position once (and contributed 1.5bb in forced bets). If my numbers are right, this means he wins about 0.165 bb per hand, which translates to a rather nice 16.5bb/100. The swings would be pretty crazy with all those 200bb pots flying back and forth though!

P.S. FWIW, at 100bb deep, the best exploitative strategy vs a bot jamming 100% of hands would be to only call with 51.43% of hands, since - if I've done the maths right - it's only hands in the range [22+,A2s+,K2s+,Q2s+,J5s+,T7s+,98s,A2o+,K2o+,Q5o+,J7 o+,T8o+] that would be getting the right pot odds to make profitable calls. If the bot never adapted, you could punish him to the max by only calling with +EV hands, and just print money with your huge equity advantage.
Tightish is rightish.

If Player 1 open shoves 100% of the time and Player 2 open shoves <100% then Player 2 is a very, very rich man.

Awesome. Could you replicate this against a player who only played aces and see what the bb/100 rate is? I’m curious to see if he can make more than the blinds he lost folding

And to mr attitude dunce equilab is good for range vs range analysis which is only half of what we are looking at here

Maybe you could ask him how he did it instead so you can do it yourself. Knowing how to do EV calculations is important.

It annoys me a bit that you posted all this, not because it's incorrect but because I think it's important OP develop the skills to be able to do this math himself.

Why don't you math it out yourself and report back?

Yes, equilab is good for range vs range analysis. Take your equilab result, multiply by the frequency with which allin pots happen, and then add in the fold results multiplied by the frequency those happen.

I don't have attitude here really. This is just math I expect someone who's been around for the better part of a decade to be able to do, and I don't really think it's appropriate to do the work for you and post the answers. This is a pretty simple poker math problem.

Follow Arty's example and give it a shot.

I agree with this.

I could, but I won't. It was quite a fun exercise for me to dig out Equilab and a calculator for an isolated case, but it took me ages to do and I don't want to do it again right now. I saved my workings, but didn't want to spell it all out.

When doing similar EV calculations, you have to list out all the possibilities and multiply them by their frequencies, then sum the whole thing.

e.g. To find out a player's EV in the SB, you need to plug in variables for:
How often he shoves, how often he folds
How often he gets called when he shoves.
How much money he can win when called (multiply this by his equity).
How much money he can lose when called (multiply this by villain's equity).
How often villain folds (multiply this by the size of the pot, usually 1.5bb)

So for the guy jamming 99% of the time in the SB, always getting called, and having 50.09% equity when called, with a possible profit of 100.5bb and a possible loss of 99.5bb, the equation looked like:

EV = [Jamming frequency * {(equity * potential profit) - (villain's equity * potential losses)}] + [Folding frequency * loss of small blind]
EV = [99% * {(50.09% * 100.5) - (49.91% * 99.5)}] + [1% * 0.5]

i.e. 99% of the time, he basically wins or loses a flip for a stack (with the former being slightly more likely), and 1% of the time he loses his SB.

Things get a bit more complicated when the calling frequency isn't 100%, since the blinds picked up via fold equity get added, so you have to multiply the above equation by villain's calling frequency, and then add [Villain's folding frequency * pot].

With someone that only plays aces, you should be able to work out how much he wins or loses on the 1/221 times he has the nuts, and how much he's losing 0.5bb by folding pre on the 220/221 times he doesn't have aces. If the [profits * frequency of aces] are less than the [small blinds lost * frequency of all other hands], it's just a flat out losing proposition.

So in a nutshell, if we can vaguely apply these ideas to real life then tighter is righter up until a certain point then a shift takes place where wide beats too tight due to the sunk costs of the blinds. It never made much sense to me to try and out tight someone who is as tight as possible. At some point the counter strategy must be to go much wider and run him over.