# The Nash Equilibrium

• Bronze
Joined: 19.01.2011
A little background to start, I'm a decent heads-up player, I can turn a profit from heads-up sitngos and do reasonably well in the heads up phase of tournaments when I get there. I don't play heads up cash as I haven't got the roll to deal with the variance swings entailed in heads up play when playing for stakes that make heads up worth playing.

I have only just heard of the Nash Equilibrium in an article I read elsewhere, ive never came across it before and I've never used it.

People who are familiar with it what are your thoughts on it? Just from a quick read over the article it seems too simplistic to work, and the theory only truly works if opponent is familiar with it also. In practice has anyone any experience if using it and what have you found when using it?

• 5 replies
• Bronze
Joined: 12.01.2011
A Nash Equilibrium is a balance whereby it is impossible for either side of the equilibrium to improve their lot unilaterally. It has its upsides and downsides, e.g. if you're heads up at the end of a sitngo and have way more chips than the other guy, but the other guy is a heads up pro and you're not, you can use Nash to help your lead in chips win the day. Using Nash if you're behind isn't a great idea, though.

Nash is the tip of the iceberg in balance as far as poker is concerned really. We're able to work out Nash equilibriums for certain situations but elsewhere we're just able to estimate what perfect balance is.
• Bronze
Joined: 19.01.2011
Thanks for your reply, that makes it sound like there is more than one. I didn't know this. The one I'm looking at assumes your heads up with relatively high blinds (eg end of a STT or MTT).

It is a table with every starting hand combination, each hand has been assigned a number. If that number is equal to or greater than the amount of big blinds in the effective stack (ie short) at the table, then you shove from the small blind. It also has a calling table on the same principle.

What I read didn't imply there a number of them, it said this table is the theory devised by mathematics John Nash. I was interested to see if anyone uses it and had any thoughts on it?
• Super Moderator
Super Moderator
Joined: 02.09.2010
Moved to the Sit-N-Go board since the topic applies there.

This site:
http://www.holdemresources.net/h/web-calculators/nashicm.html

has some good resources for Nash calculations
• Bronze
Joined: 19.01.2011
Thanks Vorpal, had a quick look at Thayer link looks good. Think that's my next theory session sorted, and then try and it to my game in practice. Already +\$ consistently over last couple of months on full tilt and stars, hopefully this will improve figures further.

Thanks
• Bronze
Joined: 12.01.2011
The concept of a Nash equilibrium was indeed "discovered" by John Nash, but there isn't just one, there are equilibriums everywhere - anywhere where 2 or more parties are trying to achieve something really. Sometimes they're desirable (like when you're playing hu against Phil Ivey with a chip lead) and some aren't.

As you mention, the known Nash equilibrium points in push-shove poker change based on stack size. Similarly, there is a no doubt a Nash equilibrium for (n)bb multi-street poker, we just don't know it, yet.