• Bronze
Joined: 15.07.2011
How exactly can you commonly calculate the expected value (EV) during a hand? I have read different answers on numerous websites but I just can't seem to get my head round it.

Would anybody be kind enough to explain it in dummy terms please?

Thanks.
• 11 replies
Joined: 19.04.2006
he ytsoP,

unfortunately there won't be an easy solution to calculate the EV.
Why? Let's assume you hold AA, your opponent holds KK and the board is AA8. You will win 100% of a time, so your EV (expected value) is 100% (of the Pot ). This should be somehow obvious since your opponent can not beat you.

But in reality we usually face two problems:
• we do not know what hand our opponent has
• we thus usually do not know if we are ahead or behind, do not know exactly what cards are good for us on turn and river

What does a good poker player do now ?
• He learns a lot about how certain hands perform. For example do you know how many outs an open ended straight draw has, or a flushdraw? You should therefore read and understand Mathematics of Poker: Odds and Outs . This will enable you to calculate how often your hand will improve if on a draw.
• He learns to assume what hands his oponent could possibly have. The combination of all hands is called a 'range' and determines your course of actions.

Explaining with an Example:
Let us go trough the following hand to demonstrate how you can define an opponents range. I played this hand in my yesterday's german coaching, I got rid of all unimportend information:

[quote]
NL \$0.02/\$0.05
Hero (\$7.07)
BB (\$2.07)
UTG+1 (\$4)

Dealt to Hero K A

UTG calls \$0.05, UTG+1 raises to \$0.20, fold, fold, fold, Hero raises to \$0.60, fold, fold, UTG+1 calls \$0.40

[COLOR=green][b]I head no specific read on this oponent, so we have to go with general assumptions. According to our Starting hand chart AK is a reraise here because we think better hands could fold (pocket pairs who indeed are in front =>they have a pair,we don't) but also worse hands like AJs, KQs could call.
We now have to consider what type of hand UTG+1 raises preflop = define his range. I assumed that he openraises every pocket pair bigger then 77, means 88+. Also he will openraise any Ace with a kicker better then 9 = means AT+. In addition he will raise some other hands like KQ,KJ,76s+.
[/color][COLOR=blue]His raisingrange is: 88+,KQ,KJ,76s,AT+[/color][COLOR=green]
But the situation changes: I reraise. I assume that his range changes now because he will go allin with AA,KK. However he will fold a lot of hands: let's say he folds 88,76s+,KJ,AT. His range is now narrowed down to 99+,AJ+ and KQ.
[/color][COLOR=blue]His callingrange to our reraise is: 99-QQ,KQ,AJ+[/color]
We are ahead of his range with 60% to 40%. How did I calculate that? Have a look at what our great software, the PokerStrategy.com Equilab does for me:[/b]

FLOP (\$1.30) K 9 A

[COLOR=green][b]Now I hit a great flop. Just bet out big and hope you get a call? NO! We now have to take the very same range that we made up before: QQ-99,AJs+,KQs,AJo+,KQo and see how our opponent performs now: we are ahead 85%. But it also means that our opponent did not hit that big. He will have no flushdraws in his range (AJs+ and KQs can not have a Flushdraw since they the A and K for the Flushdraw are already on the board), a lot of Ax with top pair but also hands like TT,JJ and QQ that would probably fold. I could now bet pretty small to get calls out of all hands of his range, which I actually decided to do - so his range does not change.
[/color][COLOR=blue]His range stays: 99+,KQ,AJ+[/color] [/b]

Hero bets \$0.75, UTG+1 calls \$0.75

TURN (\$2.80) K 9 A 2

[COLOR=green][b]The turn card let's the Flushdraw arrive, but hey, we are sure he did not had one. But a fourth club could certainly hit on the river and we now have to commit us, bring in most of the money. Unfortunately this means that hands like TT,JJ,QQ will fold to our bet, even KQ will be likely to fold. Therefore if we bet the hands that will continue are now only: 99,AJ+.
[/color][COLOR=blue]His calling- and maybe Allin-range is: 99, AJ+[/color]
Good news, we still have 76% against this range. If we knew our oponent had only 99 we would only have 9%, but again: he plays a lot of hands like seen to this point so we should always assume a reasonable range. We bet and our oponent goes allin, we just have to bring another 79cent and think that he will do it with any ace,too - so 'easy call'
[/b]

Hero bets \$1.86, UTG+1 raises to \$2.65 (AI), Hero calls \$0.79

RIVER (\$8.10) K 9 A 2 8

UTG+1 shows Q A
(Pre 25%, Flop 2.2%, Turn 0.0%)

Hero shows K A
(Pre 75%, Flop 97.8%, Turn 100.0%)

Hero wins \$7.71
[COLOR=green]We see here that we in fact had the oponent crushed troughout the hand. However I am pretty certain that he would have played 99 or AK similar to the actual hand. The hand he showed was indeed included in our calculations![/COLOR]
[/quote]Now what is your course of action?

• try the PokerStrategy.com Equilab, try the hand analysis with ranges
• confirm your ranges => you can do it by two courses of action:
• a) have a look if the hands that show up at showdown are included in your calculations
• b) use our hand evaluation forum to confirm with our hand judges if your assumptions are right
• read our articles and make odds&outs your 2nd nature. You should and will know as a good poker player that an Open ended Straight and Flush draw has 9(for the flush)+6(for the straight,2 outs already counted for the flush)=15 outs
• ask in the forum if you are unsure about anything poker related. There are no stupid questions, just stupid answers.
• use the equity trainer, it is part of the Equilab
• Bronze
Joined: 11.07.2010
Awesome post SvenBe thanks
• Bronze
Joined: 31.12.2010
Really great explanation !! thankyou for posting this

Roo
• Bronze
Joined: 06.10.2008
Originally posted by matel17
Awesome post SvenBe thanks
+1

Added to favorites so we can direct others to it in future.
• Bronze
Joined: 30.01.2010
• Bronze
Joined: 06.12.2009
great post, thanks
• Bronze
Joined: 02.03.2011
wow! amazing post Sven! Thank you for helping out!
• Bronze
Joined: 06.12.2009
I re- read it again this morning and learnt so much from it, it should be turned into an article
• Bronze
Joined: 01.06.2011
Great post SvenBe.

This should be made sticky or as Fishlock says turned into an article.

Its too good to get lost amongst all the other posts.

SvenBe can we request that you post more of these little treasures soon???????

If so look forward to reading them.

Great work and hope I dont see you at the tables LOL
Joined: 19.04.2006
he guys - guess what - I am just playing NL25 myself. It is not a rocket science to review your game - just use the free tools you have at PokerStrategy.com.
If you don't have a clue about equity 'n stuff - participate in the Beginner Course and you will learn it all.
Also Articles, Hand evaluations, coachings and videos will surely help you to understand all those topics.

Maybe I have a task for YOU guys!
Try to analyse a hand the way I did it - and post it in the hand evaluation forum (+crosslink it here) - veriz and all other hand judges will surely help you in finding out the proper ranges.
I'll promise I'll care about a news to publish the best evaluations once we gathered a decent amount of evaluations here...Deal?
• Bronze
Joined: 25.03.2011
yeah,i guess you can say it's a good post,but that's explaining only a part of the whole equation,namely your equity.

it's a wee bit more complicated.

I guess range assumptions are ok-ish for NL 10,but you assume villain is never calling a 3bet with a speculative hand OOP (remember that fishes love SC type hands).Since you assume he is a fish,because no SS reg or even wSS will call 3bet OOP with that wide of a range and will never open to min in UTG with the same range.

SO, WHAT YOU WANT TO DO IS:

determine a range for the opponent.remember,you must take into account all information available and also,if you make a wrong assumption about his range,you must fix this as fast as you can or it will lead to disastrous decisions from your part.

NOW you can calculate the equity of your hand against a specific part of your opponents range (bluffs,semibluffs,mediums,monsters).

then make a decision based on the sum of all possibilities.

Formula:

EV = Pfold * Pot + ( 1 – Pfold ) * ( Equity * ( Pot + Bet ) - ( 1- Equity ) * Bet )

where

- Pfold is the likelihood of your opponent folding,
- Pot,the potsize WITHOUT your input,
- equity,your share of the pot

to estimate profitability,EV=0

Pfold,in a rough,general sense is Bet/Pot+Bet or in percentages Bet%(Bet% +1) with Bet%=Bet/Pot

there are situations where will your equity will be zero or Pfold will be zero.

using zeroes as general values are good for exercising

any further discussions generated will be appreciated.any corrections and feedback also.