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StrategyNo Limit

Mathematical Concepts for No-Limit Holdem (1) - EV & Ranges


In this article
  • Why mathematics is important in poker
  • What "equity" means
  • How to calculate your expected value
In this series you will learn about basic and advanced mathematical concepts in No Limit Hold'em. You will learn to understand mathematical relationships and find out about their possible application to online poker. Here the main focus will be on the precise calculation of, or the estimating of results from various possible decisions in a hand.

You will frequently see the statement "That's +EV"  in videos, the hand evaluation forums, and even articles. This will be explained in more detail later on, but for now it is clear that it means that the decision might be the right one i.e. it will create profit.

So far so good. A problem arises, however, when players have differing opinions. What if player A says "It's +EV" but player B says "No way, it's -EV or +-0 EV at best"? How do we proceed?

In many situations, there is no mathematical concept to clear things up. It is often possible though, to come to a clear conclusion or at least have the basis for an informed discussion. Those cases in particular will be the focus of Mathematical Concepts of No Limit Hold'em.

That's not the entire article...

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Comments (25)

#1 ronekinky, 04 Mar 10 14:37

this i will never understand..

#2 ReyPeon, 04 Mar 10 18:13

Thanks hasenbraten, very nice and helpful article!

#3 Firehoper, 08 Mar 10 21:36

I don't know, maybe I am too stupid, but even now this looks really complicated to me. This article will be red a huge amount of times by me till I get the idea. Hopefully I ever will.

#4 Gabinr1, 25 Jul 10 20:26

Nice article.

#5 Scarabeus, 04 Aug 10 19:47

Really brain indeed

#6 BigAl123456, 19 Aug 10 06:11

My Brain hurts. I wish there was a video that might help ease the pain.

#7 mrkaktus, 08 Oct 10 11:50

love it :)

#8 flopraiser, 27 Oct 10 22:08

Wow, think i'd better read that again!
Has the potential 2 be a very useful article.

#9 RottPete, 06 Dec 10 12:28

Not easy to digest that one :(

A video might be helpful?

#10 JohnDoe1313, 17 Mar 11 15:49

Really appreciate this article. Thanks a lot.

#11 Reaching4Zen, 17 Jun 11 22:39

Hi there. I think you've made an error in one of your calculations. I've been scratching my head over it for the past 20 mins and I eventually asked my dad about it aswell. We've both come to the same answer 3 times so it appears you made a mistake.

On the first tree diagram your answer for the EV was 0.694. The answer that I've tripple checked is 0.6724.
( 0.5*0 + 0.33*1 + 0.16 * 0.16 * 3 + 0.16 * 0.83 * 2 )

#12 pokwoot, 12 Jul 11 11:01

Great stuff. Thanks for the article indeed!

#13 Harnas31, 24 Jul 11 13:12

"using mathematical simulations based on realistic standard deviations it becomes clear that for a NL BSS player, swings of up to 60 stacks are very possible, and do indeed occur even for a player with a win rate of 4BB/100 hands."
- this is pretty sad.

#14 David, 25 Jul 11 08:15

@11: Will will look into it, thanks for your hint.

#15 Pouserly2, 12 Aug 11 11:03

AnaKe Sitthisak

#16 daftbet, 27 Aug 11 11:07


#17 joeldowey123, 24 Oct 11 17:07

my head is wrecked after reading that! gonna need a re read at some point!!!

#18 luckyme44, 18 Sep 12 10:45

Excellent article. Want to hear about Gbucks!

#19 Festfingre, 11 Jan 13 23:25

Perhaps a good idea to go through my hand history and calculate equity in previous decisions, both for practice and too see where i make good\bad calls.

#20 milbos, 23 Mar 13 01:45

much better explained than video :)

#21 AtrociousNightmare, 02 Apr 14 07:06

@#11,#13: The result differs because they used the "real" (non-rounded) numbers when calculating it. E.g. 1/6 (.1666666...) instead of .16.

#22 AtrociousNightmare, 02 Apr 14 07:07

sorry #14 not #13

#23 ferrye, 07 May 15 09:43

This article I find not so important. Even though it contains some good theory of poker, you don't need this kind of information to be a winning player.

#24 TommyMcRock, 26 Sep 15 18:17

How the hell is anyone supposed to process this quantity of mental arithmetic accurately at a table without looking like they're having a stroke for two minutes?!!?!

#25 Avskum, 02 Aug 17 03:11

@#24 why do you think phil ivy and tom dwan always looks like they have a stroke for 2 minutes when they face a hard decision? ;D