Big THANK YOU 4 doing this.

thx a lot
im a endgame fish
just beginning at SNGHU

Issue1: I find Nash > Chubukov.
Chubukov assumes we play against god who knows our hole cards. Bacause of that it tells us to not push with 86s untill we have below 4.5BB (Chubukov number for 86s is 8.99), because our opponent will call our shove (even if it will be for ~10BB or whatever) with things like T2o, 94o, T6o, etc which is never gonna happen. Chubukov has a big leak here. Because of that I use (for pushing, not for calling) Nash with little adjustments. This leads to...


Issue 2: I think you can make changes in Nash.
I disagree. NO WAY Nash become worhless. Lets say my opp is aggresive and there is 50% chance that he will push to my SBC with any2 (such opp happen in mid stakes, especially when they are angered with you wide pushing). So I play almost exact Nash, but I call SB with {AJ+, 99+}. I moved a bit from Nash to best strategy and lost nothing.
In other words: I play the hands that are not QQ+ exactly with Nash (so no losing ev here) and I play my QQ+ hands with better expectation (so gaining ev here). Summing it up, let me say it again, I lose nowhere. And even if I miss sth here, the chart isn't becoming worhless, possibly less acurate, but still very close.


So...
So I pick the adjustments (some other plays, like minraise or call if I think they will work good), but I don't switch from Nash to Chubukov, because I think Nash is better even with the adjustments. I use a bit more complex strategy than the obvious one (some SB calls with ~T9s hands / whatever). I assume my opponent does not know what I am doing. So I get at_lease_0ev Nash for the standard hands I push according to the chart and some extra ev for non-standard hands (unless I get outplayed in those)


Feel free to discuss my post =)

he doesnt even have to know exactly what you're doing, your strategy is so obvious any semi-decent player would crush you in endgame
you just pointed out that you are exploitable, and nash isn't, thx

i dont think you get the point of this thread tbh, where did i say i ever talked about max ev or something? obv if you can do some things vs your opponent because he's really bad, go ahead, do them
this thread was only to explain all posibilities, and in what ways you can and can not use them

and you're so very very wrong
if your opponent calls according to the nash chart, and you jam according to the nash chart except for AJ+ 99+ which you limp because he will shove a decent amount; there's SO much more hands in the nashchart which you will openshove with a negative ev because you fail to understand that you need to openshove nuthands to balance your range; AJ+ 99+ is only 6.3% of hands but those are the ones with best all-in equity obv and will REALLY hurt your nash range which you can openjam and i'm quite sure there's more than 6.3% of hands you will be openshoving wrong then

Imo, Nash is computed as a whole and works like one mechanism. If you take one part away it will not work properly.
Chubukov numbers are computed seperatelly that's why you can do whatever you want with your nuthands (limp, minraise etc) and still push some lower hands.
There are some hands that u can push according to Chubukov and cannot following Nash.

can you guys like make a chubukov appreciation thread somewhere so i can try to convince him to come back to poker? while i like playing bridge i never got in to it as much as him, and between that and grad school he totally retired from poker =( i tell him that there's still a lot of people out there to whom he is like a poker demi-god, but he doesn't believe me.

That is the thing I dare to disagree with. I know it is computed as a whole, but it doesn't crash that much if you take one or two small parts. If done properly it stops being exact equilibrium but stays really close to it.


That QQ+ or {AJ+, 99+} only was just an example to show that you CAN take one part away and it will still work properly (or even better) under certain circumstances.

Later on in my post I pointed out that this is just an example. Let's say I use Nash except {AJ+, 99+, mid connectors and one-gappers} or sth like that (***this is still an example, not the way I want to play exactly***). Now I may loose/win some extra equity with {AJ+, 99+, mid connectors and one-gappers} but I still am very close to nash equilibrium with the rest of hands.


And to maybe more clearly put out what I mean - I think it is big +ev to push 86s with 8BB (or 6BB or 10BB). And Chubukov chart would tell me not to unless I have less than 4.5BB.

BTW I apriciate the topic, the first post deep analysis and Chubukov table.

I just happen to disagree with some points in the discussion how to use it in practice (Nash vs Chubukov).

That's exactly the point. If you are taking out upper part of the range you need to do the same with lower part to balance it. So Nash should be than computed once again to make it perfectly balanced. Of course you can try to do it.

you are exactly what i wanted to prevent by posting this: people thinking they can openjam bottom of the range but can do something else with the top of their range

will this be ev+ vs a bad player? meh, depends a bit in what way(s) he is bad, could be right yeah
will this be ev+ vs a (semi-)good player? lol, not at all, definitly not the way you're playing it

Believe me I am not that kind of a player and I have winning volume to back it up (I woulnd't be winning if I was playing like that). But are you even trying to see my point???

Did you see my another example? To call SB with top but also with (suited or unsuited) mid connector range? I give you another example - I push top range always, but call SB with mid/low suited connectors to see flop. You wrongly put me on top 5% when I call SB and I get some nice draw hands. Its an edge. So you start to push my SBC? You yourself said that it is obvious that I have a monster... See where I am going?



In reality , to be exact, I tend to sometimes (lets say 40%) call SB with top range and with some lower mid-range (I rather always push "almost top" range and "bottom" range). I do it to maybe a bit more for meta game, so as you said at some moment in the topic, that the pace of the HU shall stay slow. I will still most of the time push KK or 98o (Im talking ~10BB). But sometimes I call with them. I guess I find not pushing KK and not pushing 98o (*sometimes*, not always) evens itself, maybe not exactly but enough.
Here, I told you how I play. Do you feel like you can totally crush me? And normally my opponents wouldn't know what I want to do. And BTW maybe I will call only with 98o and push KK, or and maybe I will call 80% of time with both, I decide it upon the pace of the game and how I read my opponent. I decide it upon if I folded or pushed last 3 hands. Really that bad approach? But for the most time I use Nash. I derive from it for meta game slowing the pace or if I see that I can exploit my opponent (doing calls/sth with both top and lower range). And I truely believe that adjusting Nash like that, "taking few pieces out of it", is the right +ev thing to do. Please prove me wrong, if I'm wrong. And this is not the figure of speech to argue, but if I am missing something I would like to know it to eliminate a leak.


PS - one thing about you saying "versus good player (...)". Versus realy good player you better play exact Nash (and that is what I do if I find myself against better opponent). I expect we are discussing versus semi-good players, breakeven reg rakebackwhores, someone you tilted with badbeat, whatever, who you think you can outplay ldo

this is wrong. every individual hand in the nash shoving range is a +eV shove (relative to folding) if villain calls according to the nash equilibrium. promise.

example: T7o, openjam for 9bb's right?
callingrange for 9bb's is:
{ 22+, A2s+, K2s+, Q6s+, J8s+, T8s+, A2o+, K4o+, Q8o+, J9o+ }
which is 40.6% of hands

so villain will fold 59.4% of the time, which will result in us picking up 1.5bb's right?

okay, so he will call 40.6% of the time, and we're going to be in an 18bb pot with 35.365% equity; which means we'll get on avg back 6.3657bb's and we invested 9bb's so we lose 2.6343bb's every time opponent calls

okay, so add that up: 0.594*1.5-0.406*2.6343 = -0.1785258bb's
so each time we openshove T7o for 9bb's we lose around 1/6th of a bb

or am i missing something?

Cards do not have memory or consciousness. I get K9s I push it, and it chages nothig if I pushed/called/folded AJ in the previous hand or if I plan to push/call/fold AJ in the next hand.

The only way to exploit my push here, if you know I do not have AJ+ 99+, is to start calling me *wider* than Nash call chart and nobody does that in real game. And again there is the factor that when I push my opponent won't know that I have less than AJ/99+

and grasiu: yes, i know understand what you mean; and yes, this is how a lot of my games end as well, though this doesn't have a lot to do with nash anymore imo (especially how you worded your first post could be VERY misleading for a beginning player)

a lot of what you just posted has a ton to do with gameflow, previous hands and villain tendencies in general, which was not the point of this thread tbh (i just wanted to give a clear answer to the questions about sage/nash which were posted multiple times each week by a new forummember/player)

extreme example: opponent is very loose but weak/tight as hell when it comes to all-in preflop; you have 10bb's on button, what do you do?
well, you can just openjam ANY two cards here literally, since his callingrange will be way too tight to make up for it; do you HAVE to openjam ATC? not at all... just minraise hands like KQ, ATs, JJ and everything else which flops good as long as he defends vs them or will try to make a stand for once preflop figuring he might have fold equity... you can also limp a bunch of hands, whether they're nuthands or garbagehands, doesnt really matter, vs an opponent like this you can't do much wrong on button (except for folding i guess)

mixing it up vs a lot of players is indeed the best way to play endgame, however this is really hard to put into words or write something about, therefor i only gave the explanation of the 3 different things which are used to play it mathematically

I guess some split pot or wrong equity?
SnG Power Tools says you get called 41.2% times, if called you win 35.4% times (almost same as your numbers), and the push is +0.0%/+$0.01 if playing a $100 HU

EDIT:
OMG simple missread by both of us By folding you lose half the big blind, so:
pushing -0.1785258bb's > folding -0.50bb's

BTW nice discussion
poker flame wars >> other flame wars - i pasted one or two posts to my non poker friend (with all the percentages and numbers) and told him it is a poker players flame war =)

I guess we both get each other's point. I simply think, if you decide not to play a hand tricky, just simple push/fold, it is better to use Nash than Chubukov. Even if you play some other hands tricky (as it doesn't matter, because cards have no memory and noone calls wider than Nash call chart).

Ok so, I didn't actually check your math, but I think I know what's going on. The chart says that 9BB is the bare maximum stacks such that shoving the T7o will be ok. So if the chart were perfect, I would expect it to be exactly a 0 eV move at 9BB (when villain also calls Nash). However, the chart can't express an arbitrary strategy, and I'm pretty sure it's not quite an accurate representation of the equilibrium, in a way you'd only note by picking a more-or-less exactly borderline case. In particular, it can't represent hands which have broken strategies (that is, situations where the exact equilibrium involves shoving a particular hand a non-0 but non-100 percent of the time). The chart from Chen/Ankenman notes some hands (63,53,43) that have particularly notable broken strategies, but I'm pretty sure most all hands do right around the stacksize where they become 0eV. I actually don't know if the standard chart notes where hands should always be shoved, where they should ever be shoved, where they should be shoved half the time, or what.

I'll look into quantifying this this evening for the T7 example. But anyway, I don't know why there's any confusion since my claim follows immediately from the definition of Nash equilibrium (the strategy such that neither player can improve his eV by unilaterally deviating from it). If T7o is in the Nash shoving range at 9BB (or w/e) but dropping it while villain's calling range stayed the same would improve SB's eV, that would contradict the definition of Nash equilibrium.

I think this is really the most important thing to take from this discussion. Edges are almost always going to be v small if you turn your endgame into a preflop shovefest. I think I've been way too quick lately to setup minraise/3bet shove dynamic against a lot of guys who would be willing to keep playing poker (poorly) with me if I'd let them, and I'm going to try to get out of that habit.

The equilibrium is calculated on a range vs range bases. I don't think you are suposed to calculate it for a specific hand like your T7o example.

I have lended the book to someone but I seem to remember that to calculate the chart, Chen/Ankenman start by the stack size and calculate the equity requirement for the "shover" if the caller calls with any 2 cards. Then they calculate the "caller" equity requirement vs that new shoving range of the "shover". the "shover" then has to change his equity requirement vs the "caller"'s new range and so on till the equilibrium. But this is a Range as a whole vs a range as a whole calc and not for a specific hand.

I think

this appears to not be right.

this is still right

fwiw table appears to be a bit flaky. for example, at 9BB, BB call range is:

22+, A2s+, K2s+, Q6s+, J8s+, T8s+, A2o+, K4o+, Q8o+, J9o+

and SB shove range is:

22+, A2s+, K2s+, Q2s+, J3s+, T4s+, 95s+, 84s+, 74s+, 63s+, 53s+, 43s, A2o+, K2o+, Q6o+, J8o+, T7o+, 97o+, 86o+, 76o

giving a total EV of game for SB: -0.02229495380930757

however, if SB changes his shove range slightly to:

22+, A2s+, K2s+, Q2s+, J2s+, T3s+, 95s+, 84s+, 74s+, 63s+, 53s+, 43s, A2o+, K2o+, Q5o+, J8o+, T7o+, 97o+, 86o+, 76o, 65o

he can unilaterally increase his total EV of game to -0.02193787441347439

implying that the table's equilibrium is off a bit. but i guess it's close.

as for T7o (i see grasiu did this already, but slightly more explicitly: ), it has 35.365% equity against the BB call range which is 40.6% of hands.

so with T7o:
total eV of fold = 9-0.5 = 8.5bb
total eV of shove = (9+1)*(1-0.406) + (2*10*0.35365*0.406) = 8.81
so it's a shove in a vacuum against the nash call range

Pardon my ignorance but it is just beyond my understanding why a hand like 54s and 54 are treated so differently. And if SAGE is a rough approximation of nash why does it give 54s a slightly better power index and not a huge one? I do understand that pushing some hands like 54s that are -EV is more than made up for when you get called with one of your strong hands. However just because its suited and there are fewer combos treating 54s so differently than 54o... I use SAGE for up to 7BB and the SC ranks for 7-15BB... I just never fully understood that part of nash.... Can someone clarify this point?


P.S. really nice post

Hey i think spamz will prolly weigh in on this,

but as far as i can tell the difference of 45s to 45o as given in the OP's example is that by having LESS combos of 45 in your range, then you have MORE AA in your range, which is the reason for the large difference in %.

Someone smarter might be able to explain that better than i did, but i think thats the general idea.

i just call when i think they're bluffing. and shove weak preflop with 8bb when i think they're ready to make a big laydown. is that bad?