Leader of the stack. Poker Player

Getting over the finishing line fast in a sit-and-go can make a big difference to your overall profit

Settling down for a bit of online poker, you fire up a nine-handed turbo sit-and-go and start off playing a tight, solid game. Gradually you accumulate chips with quality hands, and you make it to the bubble. With four players left, you make some tight folds against the chip leader, but manage to sustain your stack and take advantage of the other three players who fear finishing out of the money. After a long battle, the bubble bursts, and the blinds are high. The very next hand, the other two players clash, leaving you heads-up.

Now you might think your work is done, but the next step is incredibly important, because you’ll either eke out a small two buy-in profit for finishing second, or get a huge four buy-in profit for winning. That’s a big difference! Do you know how to handle this situation to maximise your profit?

WINNER TAKES IT ALL

Heads-up poker is winner-take-all as both players are guaranteed second-place money, so it’s the difference between first and second that’s up for grabs. At this point each hand should be played as though both players have the shortest stack in the game as that’s the most you can win or lose in one hand. If one player has 9000 chips, and the other has 4500, both players must play as though they have 4500. This is called the ‘effective stack’ and the biggest concern at this time is how deep the effective stack is, in terms of big blinds.

HAND VALUES

As you may already know, hand values go up as the number of players in a game goes down. Whereas a hand like A-2 offsuit is complete rags at the beginning of a sit-and-go, it becomes a reasonably big hand when you’re heads-up. For those of you who are used to playing at full tables, some of the hands that are correct to push all-in heads-up with, may come as a surprise. But it’s a fact that far too many players do not push enough hands or call often enough. After this lesson, you’ll be able to exploit those tendencies perfectly.

THE NASH EQUILIBRIUM

The Nash Equilibrium was named after Nobel Prize-winning genius, John Nash, who theorised that some games featured an unexploitable strategy; if however, one player deviates from the strategy, the player who sticks to the Nash Equilibrium strategy, benefits.

In poker, and in particular high-blind heads-up play, this theory can be applied to optimal push/fold strategy, where two opponents can play unexploitably.

In practice this means if you are the small blind/button, you should push your hand if the number on the chart is greater than the number of big blinds in the effective stack. For example, if the blinds are 200/400, and the stacks are 9500 and 4000, your stack effectively has 10 BBs in it. Consulting the chart you may correctly push J-3s (10.6), but not 10-7o (9.0). When you are the BB/caller, you should call if the number of big blinds in the effective stack is less than that. For example, with the above stacks and 10 BBs, you could call with J-8s (10.6), but not J-9o (9.5). This calling chart only works if you believe your opponent is pushing according to Nash, or wider. Of course, many opponents don’t play perfectly, so you can adjust the Nash strategy to make it exploitive rather than simply unexploitable. Turn over for three examples of how to do just that.

In case 1 (see right), because the hero has such a tiny stack, most villains are likely to call all or almost all of the time. The Nash range assigned to the villain accurately reflects this, so the pushing range given is very wide.

In case 2 (see right), most villains realise they’re committed to calling often, but many inexperienced villains play much tighter. As such it becomes profitable to push any two cards if the villain is calling only 48% of the time or less.

Unlike the first two cases, in case 3 (see right) the villain will call a lot less often here – probably less than 40% of the time. Also, most players won’t push often enough, so a good player will tighten up his calling range to adjust. Inexperienced players, however, don’t call as often as they should. In addition, as the hero, you can really dent the villain if he calls and you win, so he may play cautiously to keep the lead. In any event, unless you think that the villain will call with as wide as the range given here, you may push more hands than the equilibrium range (60%). If the villain is calling with less than 30% of hands, you may profitably push any two cards. pushing range given is very wide. 48% of the time or less.

Nevertheless, many players do not want to put their tournament life on the line with 2-3o, and may be hesitant to push all-in. For the doubters, here’s the maths comparing a push and a fold in case three:

If you fold you have 5100 chips left.
If you were to push 2-3o 100 times, when the villain is calling with a typical range (25% of all hands): 75 times the villain folds, you win the blinds, and your stack, after winning the blinds is 6000. Total gain is 75 x 900, which is 67,500.
Seven times the villain calls but you get lucky and win the hand! Your stack is 10,800 (+ 5700). Your total gain is 7 x 5700, which is 39,900.
18 times the villain calls and you lose (-5100). Your total loss is 18 x 5100, which is 91,800.
Over 100 pushes you win 15,600 chips (156 chips per shove) by pushing 2-3o, instead of folding.

ADJUSTMENTS

If you’re lost, your adjustments aren’t working, or
you think your opponent has a skill advantage, feel free to revert back
to the Nash Equilibrium at any time. If you play this way, the greatest
player in the world can only tie with you – at best! I hope this guide
gives you some insight into how to play not only unexploitably, but
perfectly. After all, four buy-ins profit, is much sweeter than two.

For this article Jennifear used the following: