What's the calculation for figuring out what your shove range should be SB on BB?

Let's say for example, you're SB, (to keep things simple, there are no antes) and the BB has 10bb's, what's our shoving range looking like here?

I've heard shoving any 2 is +EV, but is this true, do we have to factor in that it's an MTT and losing a flip will hurt our stack etc.

Can someone show me the maths? Thanks

Do you know the BB calling range?

you can profitably shove any 2 blind vs blind for up to 45 bb's, I will show the maths later

When ICM not involved the push range prolly somewhere between 50-60%, calling range close to 40%. For 10 bb stack.
The math is not so easy cos your EV comes both from FE and equity when called, it needs iterations to find correct strategy for both blinds. Use tools to learn correct ranges for these important situations.
Antes widen your pushing range but not too much. Ofc you win more when V folds but you also get more calls.
If pushing atc is profitable it must be only due to bad BB defend.

Yup all that plus if the big blind covers and calls too wide, this will hurt both of the blinds' tourney equity. If the big blind folds too much, this benefits the small blind at the big blinds detriment.

If you're using a strict push/fold strategy (no limps, no minraises), there are no antes, and you're completely ignoring ICM factors, the optimal shoving and calling ranges for 11bb and less are something like the following chart:



(Top half is jamming ranges at various stack sizes, bottom half are the calling ranges).

Google "Nash push fold" or something like that for more info. The math is fairly complex to a beginner (your EV comes from a mix of fold equity + hand equity when called), as mentioned above.

Ahh ok, this makes a lot more sense. My SB on BB shove and vice versa used to be fairly nitty, but once I started reading posts saying how wide you should be shoving, (literally any 2), I thought it felt wrong. I tried opening my shove range dramatically but I feel it's proving a hinder to my game s opposed to an improvement.

I think I took this concept way too far and will go back to much closer to my original shove / call range, which looks fairly similar to what is outlined above

The (approximate) math works like this. (Apologies in advance for any schoolboy errors).

Assume 10bb deep before the blinds.

Hero puts in 0.5bb in the SB, leaving 9.5bb behind.
BB puts in 1bb, leaving 9bb.

Hero has T5s. The chart says this is a jam, so hero jams for 10bb total.

Villain calls with [22+,A2s+,K2s+,Q7s+,J8s+,T9s,A2o+,K6o+,Q9o+,JTo] (37%), which means he folds 63%.

So, 63% of the time, hero picks up 1.5bb uncontested, and 39% of the time he's racing for his life.

When villain calls, hero's equity is around 36% vs villain's optimal range, which means hero wins 10.5bb 36% of the time, and loses 9.5bb 64% of the time.
EV when called is (10.5 * 0.36)-(9.5bb * 0.64) = 3.78 - 6.08 = minus 2.3bb.

So hero either wins 1.5bb, which happens 63% of the time (villain folds), or he loses 2.3bb on average, which happens 39% of the time (villain calls). The total EV of the jam is therefore (1.5 * 0.63) + (-2.3 * 0.39) = 0.945 - 0.897 = 0.048bb.
i.e. the jam is slightly profitable, netting 5% of a big blind on average.

With stronger hands in hero's shoving range, he'll have a higher EV since they get a lot of their EV from being called by worse, but with the worst shoving hands much more EV comes from fold equity. The nut worst hand in the jamming range should at least break even, however. If it doesn't it's a fold pre. If you really wanted to, you could calculate the EV of T4s (not on the chart). It's probably extremely close to zero, but slightly negative.

Very nice explanation Arty!

Yeah, thanks for the explaination Arty, very concise and easy to understand mathmatically... going to start using these nash GTO charts in future, it's a shame it doesn't go up to 15/20bb's, is there a reason for this? Is the maths much more complex the higher the number of bb's?

Generally speaking, once the effective stack is more than 15-20 bb's, then a push-fold strategy is no longer optimal. You have enough "room" to make a standard raise and, possibly, fold to a shove. (Same for your opponent.)

Ok, this kind of makes sense but what about the 10-15bb range? Surely you're not min raise / folding every hand until you're @10bb's or left? You've got very little playability at that stack size?

I don't understand your question. There are two aspects of this.

(1) Optimal push/fold ranges can be calculated for any number of bb's if you assume that those are your (and your opponent's) only options.

(2) Determining when push and fold are your only viable options is a more complicated question and not easily "solved". Most people believe that other options are viable once the effective stacks become larger than 15-20 bbs.

I have no idea if that helps or not.

To someone that grew up in the "shove or fold" era, optimal sub-15bb stack play can look very odd, because it apparently features a mix of raising, limping and shoving, and many combos use mixed strats. e.g. for hand XX, the optimal strategy might be to minraise it 42%, jam 12%, limp 46%, while hand YY is jammed 80% and minraised 20%, and hand ZZ is always jammed. I think HUSNG players learned first that you are not into strictly into "push or fold" territory until you're much shorter than most tourney newbs realise (maybe the cutoff point is 7bb or something like that). There's a surprising amount of playability with 12bb, for example, and if minraising or limping a hand nets more than open-shoving it, as part of a balanced strategy, then those options are preferred.

I would agree with Arty it can be better to min-raise fold some hands 8 or 9bb deep SB vs BB (you really need to know some ranges though).

If the opponent re-shoves the same hands as (s)he calls shoves with, lets say 35%, it can be better to r/f 9bb deep with antes. If the opponent is the type that punishes weak looking SB bets by opening up and re-shoving wide then this r/f line with a 23o hand would be a terrible play, but a great play with a monster.

Sometimes some advise never to r/f with less than 10,12 or 15... and I think this is too simple, try to find optimal plays. The default shove can be a great fall back line though. And again like Arty I think the 7bb would be about the limit with any semi-sensible ranges in play.

I like where the discussion has gone. I think that the small blind is the exact position where good play really looks different provided that players have >7bb. Without antes, I'm limping in with hands that are just too good to fold, and the occasional monster. I'm raising 2.5x with a lot of hands and I'm folding the rest when I have >12 bb. I have a raise fold range with >12 big blinds in the small blind vs the big blind. I play shove/limp/fold poker with sub 12 bb.

With >30bb and no antes, I start raising 3x from the small blind and folding everthing else.

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If antes are introduced, you'll need to think about how big these antes are relative to the blinds. Some sites have huge antes, others have small antes.

With big antes that increase the potsize by >50%, I loosen up a lot with my preflop raising requirements, and as such I need a bigger stack that allows me to invest 10-15% of my stack for the necessary 3x preflop raise. It's necessary because minraising, and 2.5x raise sizing just allows the big blind to play a ton of pots in position, which I think is bad for the small blind. With big ante's I size my raises so that I'm not investing >15% of my stack; if a 3x raise with antes is >15% of my stack, I shove/fold/limp. If a 3x raise is <15% of my stack, I raise call/raise fold/fold and I cut out limping.

That's my default vs unknowns and good players.

whats your screen name?

This is just one of my many internet aliases. Any matching screen name is an impostor for any of my screen names, including this one.

I've been poker for 4 years or so - is this the shove or fold era? I've always employed the stratergy of just shoving with 15bbs or under, I had no idea that it was optimal to play differently. There were periods where I saw people open limping / min raising w/under 15bbs, which usually indicated a premium PP and people will play cautiously knowing this.

I may start experimenting with different stratergies as a SS after reading this, I remember reading in books and stuff that it's not optimal because after you c-bet the flop, a significant portion of your stack is at risk, leaving you in very tricky spots, as you're "pot commited" to some extent.

All the posts thus far are equilibrium play. You can exploit people a lot if you know what they are calling with/how they are reacting.

Answer post #2 you can extrapolate from there.

About 5 years ago, I was taught that "If you have <15bb, you only have two options: shove or fold" and I just kind of believed it for two or three years (I rarely played tourneys). It was only when I did a bit of reading, studying, and watching better players, that I learned that there are other options*.
That said, there are still a lot of 'old skool' players that haven't adapted to changing game dynamics. (Witness Johnny Chan's 20bb spewjam with 85o in the WSOP Main Event last year or the year before.)

* In a similar vein, cashgame tutorials would say things like "Always open for 3bb, and c-bet between half and full pot", and then solvers came out and now I'm minraising pre, and betting anything from 1/4 pot to 3x pot.

In a similar vein for a long time I believed that in limit poker if you started a hand with, say, 2bb and had to face a decision for 0.5bb or so where you were almost sure you were beat, you had to call. And I always did even when I was pretty sure and it cost me a lot of tournaments. Finally once I said "**** it" and folded. I was drawing dead in that hand, I went on to win the tournament (with quite a bit of luck, obviously, I had to go all in very soon after that and a few more times just to get enough BB to play a hand)

^ Same. I think a fair amount of supposed "call any two" spots (because you're very short in the blinds, or are facing a very small jam so the pot odds are crazy) are not actually 'max-profitable', due to factors related to ICM and "future game" possibilities. e.g. You fold with 2bb in the SB and survive a whole orbit and ladder up to a pay jump, or you triple up when you get a much better hand on the button, or whatever.

Yeah I tend to think of these as "strategies that are not wrong", i.e. a good thing to tell someone who is relatively new. Arm them with a list of things that can't be losing propositions, as opposed to bogging them down with figuring out the best thing for any given case.

this this is TL, DR, but just use the jenifear chart for your pushing range and use hrc to brush up on what you should call. you can widen up your push range if you dont think the bb will call correct, the jenifear chart assumes bb knows what the **** is going on.