# FINISHING AN OPPONENT HEADS-UP: SAGE, NASH AND CHUBUKOV

Stuff in advance:

If you have t2700 and villain t300 and blinds are 15/30, you are indeed the chipleader but this shouldn’t adjust your play AT ALL. You’re still only 10bb’s and should treat it like you both have t300 in chips. Obviously if you make an ev- shove or call here you’re going to lose less \$\$\$ in ev than if stacks would be t2000 and t1000 and blinds 50/100 but you’re still 10bb’s deep and ev- decisions stay ev-! Don’t think about “I can gamble, if he doubles up, I’m still big chipleader!” make sure your moves are ev+.

Maybe I’ve been a bit to harsh about “it shouldn’t affect your play” because sometimes it can. However, this will not be because of your play, but because of villain’s play. Some people will shove ATC when they have the chiplead with the 2.7k in chips because they indeed want to finish you quickly, so your callingrange should get wider by a decent percentage. Also if you just won a big pot from villain one way or another this will affect metagame and he may be tilted so you should try and add these into the equation when you calculate ranges and odds and stuff. Just keep in mind that in the end you should only look at the amount of bb’s you have.

Even if you play a big mtt, there won’t come any ICM into play. Suppose first prize is €2k and second prize is €1k, then you already have won the €1k and can just look at the end-game as being a €500 hu sng. Doesn’t matter how big the difference between first and second place is really.

Sage:

Most people have probably heard about this already, you can find a lot of links about it if you google for a bit.

Sage works with a chart and a power-index which is really easy to memorize. You just have to know how shallow effective stacks are and calculate the power index for your hand and see whether you push or fold. Power index is easy to calculate, just take the value of your highest card (ace is 15, not 14, face cards are 11,12,13 obv) and double it; add the value of the other card to it and if it’s suited add an additional 2. If you have a pocket pair you add 22 to the number. Then you look in the chart and see if you can push/fold from your button and if you can call if villain openshoves.

Note that this becomes slightly ev- for the sb to push starting from 7bb’s. Small negative ev, but still ev-. So you should only adapt this when really shallow imo.

Also note that this is far from optimal play. If you think villain shoves tight your calling range should be a little tighter but you can shove wider. Basically (since it only works for 6bb’s or shallower) this is just a crapshoot and it’s almost a “push any two cards” and hope villain folds. 6bb’s is really nothing, and you barely need fold equity preflop to make shoving ATC ev+ because there’s already 1.5bb’s in the pot. Some higher stakes winning players actually DO shove ATC in these spots because villain will often have a way too tight callingrange.

Nash equilibrum:

Something a little more worked out and interesting is the nash equilibrum.

problem is you just see a chart there and while the chart itself is still pretty easy to figure out, you still need some info to go with it to know what you’re doing. Why are we shoving 54s for 20+bb’s for example, but not J8o?

Let’s just say we’re playing headsup, we’re 100bb’s deep and I’m on the button. You know 100% sure I only openshove AA on the button. If I openshove what’s your callingrange? Obv only the

other two aces. When I openshove KK+ what’s your callingrange? Still, only AA. When I openshove QQ+ your callingrange is KK+ (although KK only has 49.995% equity vs QQ+ it’s still an ev+ call due to the sb + bb in the pot).
Okay that’s for strong hands, now let’s look at a range of {AA,54s}. What’s your callingrange now? You call with KK?

equity win tie pots won pots tied
Hand 0: 58.174% 57.94% 00.23% 59530656 236778.00 { AA, 54s }
Hand 1: 41.826% 41.60% 00.23% 42734028 236778.00 { KK }

Appearantly calling with KK will lose you money in the long run. A lot of people think that in the nash pushing chart shoving a hand like 54s is 20bb’s+ and 54o for 2.1bb’s is because 54s has more equity because of the possibility to hit a flush. This BARELY has anything to do with it. In the small example I gave here the only reason why KK is not an ev+ call is because there’s 6 combo’s of AA and only 4 combo’s of 54s. There’s 12 combo’s of 54o, so…

equity win tie pots won pots tied
Hand 0: 39.788% 39.56% 00.23% 73162224 417762.00 { AA, 54o }
Hand 1: 60.212% 59.99% 00.23% 110931084 417762.00 { KK }

this makes KK a snapcall if your range would be {AA,54o}.

So they started like this and in the end they came up with an entire chart of all hands you can openshove which is unexploitable for 20bb’s or shallower. There’s a decent amount of hands which say 20bb’s+ but the maker of the chart just assumed that you shouldn’t play push/fold deeper. Openshoving A2o for 200bb’s would be very likely ev- if villain has a different callingrange than the “nash equilibrum” calling chart.

So this is an equilibrum, which means a stalemate position: if both hero and villain use the pushing and callingrange you’re gonna be ev0 against each other. If one of the two deviates from one of the charts, he’s gonna be ev- against the other. What does this mean? Do NOT use the CALLING chart against a random opponent. Actually, it’s better not to use it vs ANY opponent unless you know 100% sure he uses the nash pushing chart, which is a really rare occassion. Just forget about the callingrange and you’ll be better off imo. It only is ev0 if villain uses the pushing chart and will be ev- in pretty much all other cases.

Another important thing you have to remember: don’t deviate from it if you want to use it. Suppose you’re 11bb’s shallow and you have Q7o. Nash says you can openshove this and it will be ev0 at worst. HOWEVER, what would you do with QQ+ in this spot? Would you also openshove it? Or limp or minraise in order to induce a shove from villain? If you would also openshove these hands, you can indeed openshove the Q7o as well. If you would play any other hand differently from the chart it becomes totally worthless and would have to be recalculated entirely before the equilibrum can be reached. Can you still openshove this? Hard to determine a new equilibrum so you should go to Chubukov instead.

I wouldn’t really recommend using this above 12bb’s, where there’s still room to manoeuvre a bit preflop. Usually 10-12bb’s is the part where I start openshoving a lot of my buttons, because minraise/folding becomes too expensive and you need some specific gameflow for your opponent to allow limping (however, if villain allows you to limp, do it as much as possible and try to just stab at it postflop; i sometimes limp some hands which i could shove ev+ for sure but i just don’t want to change the dynamics of the match and let villain see some flops because it keeps him passive and happy).

One last thing is that you have to take the bb and sb posted with the effective stacks in the chart (so looking for push/fold BEFORE blinds are posted actually).

Chubukov:

Okay, let’s just say you’re in a spot now with K3s, there’s an aggro push/fold dynamic already and you are on the button with 12bb’s effective stacks. Nash says this is a push, but let’s just face it, you’re probably not gonna openshove QQ+ vs this aggrotard who has attacked all your limps preflop already and will just limp in most of the time. Can you still openshove the K3s?

What is this? This is a chart which says how deep you can be EXPRESSED IN SMALL BLINDS to openshove a hand and be still ev0 at worst when villain has a perfect callingrange due to flipping over your cards (the amount of small blinds is shown in the right column, so just cut in half for bb’s obv). Obv AA you can shove for infinite bb’s as you chop in worst case. KK will only get called by KK+ so that’s a tiny fraction of a random hand and you still have equity when called (like you always do). So you look up K3s and see that you can openshove it for 14.2bb’s! That’s a whole lot, even though nash gives us almost 20bb’s, we can still openshove a ton here without openshoving the top of our range. Basically his callingrange will be any pocket pair, any Ax and K3s+/K4o+ hands.

What are the important things to remember from this chart? The fact you can openshove K2o for 10bb’s preflop imo. So shoving a pocket pair, Ax or Kx hand for 10bb’s or less is always gonna be ev0 at worst, irregardless of villain’s callingrange. Again, don’t overdo this, even with aggro dynamics there’s a lot of play left from 12-20bb’s and you can limp/openshove/minraise/fold instead of just openshoving. Given, this will take some time to master because it depends a lot on villain and gameflow but if you get some experience in it it shouldn’t be THAT hard to quickly see how villain plays and adapt to it.

Cliffnotes:
1) Sage is a bit outdated. Just use nash for 6bb’s or shallower because you will probably openshove QQ+ anyway with these stacksizes.
2) Use nash only if you use it correctly, and preferably 12bb’s or shallower.
3) Use Chubukov if you dislike minraise/calling a shove, or limp/folding, or folding in general, but openshoving is appearantly ev+, also don’t use it over – say – 14bb’s imo. Openshoving 33 or K3s for 13bb’s is something I do from time to time, against certain opponents it’s going to be the easiest way to play these hands.
4) When your opponent openshoves his button for x bb’s, don’t use any chart, but estimate a shovingrange and see if you have odds to call with the dead money in the pot.

– Spamz