Math!

[Saborion]

I really need to learn the basic math stuff once and for all, and I think this hand is pretty good for the basic stuff. I have three questions that I'll add after the hand.

NL 6-max
Random preflop action. Flop comes T92. I have QQ. Pot contains $49 after my opponent bets. I have $89 and my opponent covers.

Let's put my opponent on AK, AA-JJ. He will never fold to a push on the flop.
Combos:
AK (16)
AA (6)
KK (6)
JJ (6)
total (34)

Percentage that he has a certain combo:
AK ~47 %
AA ~18 %
KK ~18 %
JJ ~18 %

Question 1:
How do we calculate if a push is more +EV than folding? Do we set folding at zero EV, or do we set it -x since we have equity in the pot? I have this vague memory of using folding as zero EV.

If I push and he has AA, my equity is ~13 %. Do I just take the full pot size, $227, and multiply it with 0.13 to get my equity, in this case $227*0.13 = ~$30? Comparing this number to folding can't be right since folding had zero EV, meaning that my push is making me money, which I'm pretty sure it doesn't. I therefore assume that we have to compare it to my stack before I push, which shows that it is a -EV move. This means that the simple way to do this is to just compare out expected stack size if we push to our current stack size to see whether a play is profitable or not? But if that's true, aren't we using our stack size as "zero EV (whatever it is called)"?

Question 2:
How do we calculate our EV if we push vs his range?

Question 3:
How do we calculate our EV if we push and he folds JJ 10 % of the time?

[Vern]

After you learn how, you can use Poker Stove (http://www.pokerstove.com/) to do your math.

[Saborion]

[ QUOTE ]
After you learn how, you can use Poker Stove (http://www.pokerstove.com/) to do your math.

[/ QUOTE ]
Thanks for the tip, but Poker Stove won't really do the trick since you can assign probabilites to holdings and how often each of them will fold. What if I would like to use 20 % folding equity when he has JJ and 95 % when he has AKo, combined with 0 % folding equity when he has AA and KK. How do I put all of that into PS?

[Vern]

I guess you will have to use excel. I use Excel to do my EV stuff when I have multiple probability branches I want to balance. Sorry, I thought from reading your original post you wanted to be able to figure out the advantage of different ranges of holdings vs yours.

[EMc]

i usually and regrettably ask Pokey

[theblitz]

Try looking at this post by fimbulwinter: http://forumserver.twoplustwo.com/favlin...amp;postmarker= (http://forumserver.twoplustwo.com/favlinker.php?Cat=0&Entry=182744&F_Board=ssplnlpok er&Thread=3069765&partnumber=&postmarker=)

[Saborion]

[ QUOTE ]
Try looking at this post by fimbulwinter: http://forumserver.twoplustwo.com/favlin...amp;postmarker= (http://forumserver.twoplustwo.com/favlinker.php?Cat=0&Entry=182744&F_Board=ssplnlpok er&Thread=3069765&partnumber=&postmarker=)

[/ QUOTE ]
Thanks! A quick look in that thread and it seems to be what I'm looking for. I actually remember reading that a long time ago. Time to learn some math.

[eigenvalue]

Qu1: Folding is 0 EV. How the money went into that pot is of no interest any more. So if You fold, You loose nothing and You win nothing.

Qu2: Let n be the number of hands in his range , pc[1]...pc[n] be the percentage for any combo of his range and let wc[1]...wc[n] be the percentage You win against this combo. You need a poker calculator to determine that percentage for every hand.

Given these percentages, this is the calculation:
(1) (pc[1]*wc[1] + ... + pc[n]*wc[n])*$138
(2) (pc[1]*(1-wc[1]) + ... + pc[n]*(1-wc[n]))*$89.

Your EV is equal to (1)-(2). So, if (1)-(2) is positive, You have to push, if it is negative, You have to fold.

Be aware of the amount of the money in the equations: You gain the pot size + an additional $89 if You win, because You assume that Your opponent never folds, and You loose only $89 if You loose. The money already beeing in the pot is not part of Your loss.

Qu3: The equation will be more complex now, but all I told You about the EV after You calculate Your equation remains the same:

Let JJ be hand n:

(1) (pc[1]*wc[1] + ... + pc(n-1]*wc[n-1] + pc[n]*wc[n]*0.9)*$138 + 0.1*$49
(2) (pc[1]*(1-wc[1]) + ... + pc[n-1]*(1-wc[n-1]) + pc[n]*(1-wc[n]*0.9)*$89.

The amount of 0.1*$49 in (1) represents Your fold equity.

[Saborion]

Thanks eigenvalue. With your post, as well as fimbul's, I'm sure I'll be able to do my calculations. =)

[munkey]

This thread and fims already posted here helped me sort out EV AI calcs once and for all:

tks to jskinn and jouster FR -NL50 -AKs flushdraw (http://forumserver.twoplustwo.com/showflat.php?Cat=0&Number=7551020&page=0&fpart=1&v c=1)

[Pokey]

[ QUOTE ]
i usually and regrettably ask Pokey

[/ QUOTE ]

Speak the devil's name and he appears.

The easiest way to do this is to plug all the information into PokerStove and see what it spits out:
<font class="small">Code:</font><hr /><pre>
Text results appended to pokerstove.txt

207,900 games 0.063 secs 3,300,000 games/sec

Board: Tc 9d 2h
Dead:

equity (%) win (%) tie (%)
Hand 1: 55.1804 % 53.75% 01.43% { QQ }
Hand 2: 44.8196 % 43.39% 01.43% { JJ+, AKs, AKo }
</pre><hr />
See where it says that QQ has 55.18% equity against villain's range? That means that for every dollar that enters the pot, hero will, on average, collect 55.2 cents. Since any called wager in a heads-up pot involves putting in 50 cents to build the pot $1, this means hero increases his profits by pushing this flop and getting called.

Specifically, after pushing the pot will have $49 + $89 + $89 = $227, of which hero will win (on average) $125.26. Since hero must put $89 into the pot to build this, hero's pot equity after the flop push is $125.26 - $89 = $36.26 more than his flop investment.

If hero does NOT push, the pot remains at $49, and hero wins 55.18% of that money, meaning hero's pot equity after checking the flop is $27.04. In other words, pushing gains hero an extra $9.22. (Note that this is 5.18% of the $178 that goes into the pot on the flop bet -- hero's profit margin on the heads-up bet is 5.18%, since hero wins the pot 55.18% of the time, and 50% would be a break-even situation.)

Things get more complicated when you include the possibility that villain folds to a push, when you include turn and river betting rounds, etc., but for the basic problem presented, this works nicely.

In general, if you have more than 50% pot equity and zero folding equity, betting is +EV heads-up. If you have more than 33.3% pot equity and zero folding equity, betting is +EV in a two-way pot. Etc.

[Dennisa]

Does JJ and AK really call 100% of the time a push from you? Also can you really rule out tt and 99 in your assumption?

Text results appended to pokerstove.txt

243,540 games 0.094 secs 2,590,851 games/sec

Board: Tc 9d 2h
Dead:

equity (%) win (%) tie (%)
Hand 1: 51.1431 % 49.92% 01.22% { 99+, AKs, AKo }
Hand 2: 48.8569 % 47.64% 01.22% { QQ }

[Saborion]

[ QUOTE ]
Does JJ and AK really call 100% of the time a push from you? Also can you really rule out tt and 99 in your assumption?

[/ QUOTE ]
That's irrelevant. I wasn't interested in whether they always call or not, I was interested in how to do EV calculations. The answer to Question 3 , where he folds JJ a certain percent of the time, shows me how to do those kind of calculations as well, which was all I needed for now.

[Saborion]

Pokey, I know I'm +EV if he always call with AK and JJ, but given that he rarely will call with AK, and that he sometimes, although rarely, will fold JJ, I can't use Stove. That's the reason for my intial post; I need to learn how to adjust for those percentages where he folds. Using Stove to find out what kind of equity I have vs a certain hand in his range if very nice, but I do need to do some manual calculations after that.