# Micro Stakes Online NL Poker Forums

## Check my Maths

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#### dcart

319 posts
Joined 01/2011

Calculating a shove:

For the sake of the example, ignore UTG. When SB donks, there is 2.70 in the pot effective stack is 5.45. Again for the example say i know he has Th8c and 50% of the time he calls, 50% he folds. My equity is 53% against his hand, so if the money goes in the middle, i win 53% of the final pot. But say i want to factor in fold equity:

Our fold equity is the amount of times he gives up his equity share (0.5x0.46x100) 23%

50% time he folds we win the existing pot of 2.70. 50% of the time we get called and win 53% of a 16.30 pot, but if we add our 23% fold equity, we win 76% of that pot? So we win \$12.23 every time we shove in this spot?

Is it that simple? Did i miss something out? When i watched MNLH by WoT there was a huge algebra equation involved that i couldnt solve so i just tried to figure it out myself.

Party Poker \$10 No Limit Hold'em - 6 players - View hand 1854022
DeucesCracked Poker Videos Hand History Converter

BB: \$13.83
UTG: \$10.09
Hero (MP): \$10.00
CO: \$27.43
BTN: \$10.00
SB: \$6.95

Pre Flop: (\$0.15) Hero is MP with J A
UTG raises to \$0.40, Hero calls \$0.40, 2 folds, SB calls \$0.35, BB calls \$0.30

Flop: (\$1.60) 2 9 T (4 players)
SB bets \$1.10, BB folds, UTG calls \$1.10, Hero raises to \$9.60 all in, SB folds, UTG folds

Final Pot: \$4.90
Hero mucks J A
Hero wins \$4.66
(Rake: \$0.24)

#### dcart

319 posts
Joined 01/2011

Wait do i have to deduct my \$10 stack from \$12.23 to give the actual EV of the shove?

#### mwildjack

50 posts
Joined 01/2012

% FOLD * EV(FOLD) + % CALL * EV (CALL)
% when he folds * Current POT + % when he calls * (Our Equity * Total Pot when called - Cost)
= 0.5% * 3,80 + 0.5% * (.53 * 15.8 - 6.55) = 1.6 + 0.5 * 1,824
= 1.6 + 0,912 = 2,512

#### dcart

319 posts
Joined 01/2011

Ok so using % FOLD * EV(FOLD) + % CALL * EV (CALL) to work out my flop raise:

Assume 50% fold equity again for simplicity, we hold 51% equity vs his 20% c betting range.

(0.5 x 1.55) + 0.5 x (0.51 x 4.55 - 1.80)

= 0.78 + (0.5 x 0.52)

= + \$1.04

Party Poker \$10 No Limit Hold'em - 5 players - View hand 1854871
DeucesCracked Poker Videos Hand History Converter

UTG: \$12.32
CO: \$6.32
Hero (BTN): \$10.81
SB: \$10.00
BB: \$10.00

Pre Flop: (\$0.15) Hero is BTN with A K
UTG raises to \$0.40, 1 fold, Hero calls \$0.40, 2 folds

Flop: (\$0.95) Q 4 7 (2 players)
UTG bets \$0.60, Hero raises to \$1.80, UTG folds

Final Pot: \$2.15
Hero mucks A K
Hero wins \$2.05
(Rake: \$0.10)

50 posts
Joined 01/2012

Looks good to me

#### dcart

319 posts
Joined 01/2011

Sweet, cheers for the help.

#### Entity

8040 posts
Joined 11/2006

Assume 50% fold equity again for simplicity, we hold 51% equity vs his 20% c betting range.

(0.5 x 1.55) + 0.5 x (0.51 x 4.55 - 1.80)

= 0.78 + (0.5 x 0.52)

= + \$1.04

Your equity needs to be against his calling range, not against his betting range.

Rather than assume your FE, actually figure it out. Take his range for betting the flop, then figure out what % of that range is getting it in, and what % of it is folding. Then calculate your equity against the % that gets it in vs you. Tools like Odds Oracle and Combonator help a lot with this.

Rob

#### dcart

319 posts
Joined 01/2011

Thanks for the reply. Not sure i follow. So his betting range includes a narrow range which will shove over me for value which i will fold to. A calling range which is ahead of me in equity, and an air range which will fold.

But rather than calculate the EV of my raise against his ENTIRE betting range, i have to do it only against the range which calls my raise? Why we cant include his air range which he bets, since his is what i want to attack right?

Also are there any mental short cuts i can use at the table to give me an idea of fold equity and adding it to my overall equity?

I downloaded Combonator, but not sure how to use it yet, where do you enter villains cards is that feature only available in the full version?

Thanks.

#### Entity

8040 posts
Joined 11/2006

Thanks for the reply. Not sure i follow. So his betting range includes a narrow range which will shove over me for value which i will fold to. A calling range which is ahead of me in equity, and an air range which will fold.

But rather than calculate the EV of my raise against his ENTIRE betting range, i have to do it only against the range which calls my raise? Why we cant include his air range which he bets, since his is what i want to attack right?

When you're calculating EV, you're summing the value of all of the possible outcomes. In this case, what we're looking at is:

EV = (pot size * % chance he folds) - (amount risked * % of time he shoves) - (amount risked * % of times he calls * his equity % in the pot)

This is because we don't actualize any of our equity when he folds or when he raises - only when he calls.

Also are there any mental short cuts i can use at the table to give me an idea of fold equity and adding it to my overall equity?

I downloaded Combonator, but not sure how to use it yet, where do you enter villains cards is that feature only available in the full version?

Thanks.

Practicing this away from the table is pretty much the best you can do. The more you practice it, the more you can understand how board textures and our opponent's hand ranges mesh, which will lead to you understanding how to exploit people's tendencies on certain board textures. EV calcs are a great way to tune your intuition so you become better at spotting the obvious spots to bluff/semibluff.

Here's what we need to run the full calculation:

1) His range for betting the flop given his PFR.
2) His portion of that range that will call your raise.
3) His portion of that range that will shove over your raise.
4) His portion of that range that will fold to your raise.
5) Your equity vs his calling range.

Let's walk through these step by step, then you can run the full calculation. I'm using Combonator Pro to run some of the calcs, so sorry if it's a pro-only feature (I'm not sure which are available in the free version). Answer these questions:

1) What's his range (in your opinion) for betting this flop, given that he PFR'd and you flatted?
2) Which hands does he shove when we raise?
3) What hands does he call when we raise?

#### dcart

319 posts
Joined 01/2011

Ok so his PFR is 20% in that position, his c bet stat is 100%

His value shoving range is 44 77 QQ KK AA AdKd (2.3%)

His calling range is 88-TT, AQ,KQ,JQ,QT (6.3%)

Folds the rest.

We have 25% equity when called.

#### Entity

8040 posts
Joined 11/2006

Ok so his PFR is 20% in that position, his c bet stat is 100%

His value shoving range is 44 77 QQ KK AA AdKd (2.3%)

His calling range is 88-TT, AQ,KQ,JQ,QT (6.3%)

Folds the rest.

We have 25% equity when called.

Ok. Here's what I was able to break that down into:

Preflop, a 20% range is: 66+, A4s+, ATo+, K8s+, KTo+, Q9s+, QTo+, J9s+, T9s

On the flop, that means he's shoving with: Ace and King high flush draws, sets, and pairs with a flush draw. That's 13.6% of his hands.

He's calling with: Qx, JJ-88, lower flush draws. Your equity against those hands is 25.86%, and those make up 40.7% of his hands.

He's folding the rest of his hands, about 45% of the time.

So with that info, we can show that our EV is:

(1.55 * .45) - (1.80 * .407 * .75) - (180 * .136) = -.09675

You can play around with your assumptions to tweak things. Here were mine:

Combonator Output combonator.com
Board: Qd 4d 7s
Vs Hero Cards: As Ks

Combinations in complete range: 179 [Hero Eq: 48.52%]

Grouped: 177 combos, 98.9% [Hero Eq: 48.86%]
Ungrouped: 2 combos, 1.1% [Hero Eq: 19.1%]

Group 1: 24 combos, 13.6% (13.4% total) [Hero Eq: 28.40%]
Group 2: 72 combos, 40.7% (40.2% total) [Hero Eq: 25.86%]
Group 3: 81 combos, 45.8% (45.3% total) [Hero Eq: 75.36%]

Group 1: Set / trips, pair with flush draw, ace-high exactly with flush draw, pair of kings or better, king-high or better with flush draw

QQ+, 77, AKs, AJs-A5s, KJs-K8s

Group 2: Pair of queens or better, added JJ-88, queen-high or better with flush draw, queen-high or better with flush draw

JJ-88, AQs, AQo, KQs, KQo, Q9s+, QTo+, J9s+, T9s

Group 3: Ace-high or worse with no fd and no sd, ace-high or worse with no fd, added 66, A4s, ace-high or worse with 3-flush

66, AKs, AJs-A8s, A6s-A4s, AKo, AJo-ATo, KJs-K8s, KJo-KTo, J9s+, T9s

#### Luke00016

1113 posts
Joined 11/2009

Here's what we need to run the full calculation:

1) His range for betting the flop given his PFR.
2) His portion of that range that will call your raise.
3) His portion of that range that will shove over your raise.
4) His portion of that range that will fold to your raise.
5) Your equity vs his calling range.

Let's walk through these step by step, then you can run the full calculation. I'm using Combonator Pro to run some of the calcs, so sorry if it's a pro-only feature (I'm not sure which are available in the free version). Answer these questions:

1) What's his range (in your opinion) for betting this flop, given that he PFR'd and you flatted?
2) Which hands does he shove when we raise?
3) What hands does he call when we raise?

Entity - has DC ever put together a video on this specifically? I know there are a lot of math vids, but a topic like this could be cool to do in a DC Short. Just a quick step by step 'here's how to do this, now go do it at home a bunch' video. Or maybe WoT or Bellatrix or someone already covered this substantially enough that it doesn't need another vid?

#### Entity

8040 posts
Joined 11/2006

Entity - has DC ever put together a video on this specifically? I know there are a lot of math vids, but a topic like this could be cool to do in a DC Short. Just a quick step by step 'here's how to do this, now go do it at home a bunch' video. Or maybe WoT or Bellatrix or someone already covered this substantially enough that it doesn't need another vid?

I've been working on some stuff specifically on this (hence my interest in responding here). It'll be a while before it gets released - still has a lot of work to go - but it very much discusses things like this.

Rob

#### dcart

319 posts
Joined 01/2011

Ok so our equation for EV has changed.

(current pot x %he folds) - (cost of our raise x % he calls x his equity) - (cost of our raise x % he shoves)

= EV

Correct?

Now i just need to work through loads of different situations, seems i have been over estimating my fold equity

#### StackHunter

2649 posts
Joined 09/2010

Party Poker \$10 No Limit Hold'em - 6 players - View hand 1854022
DeucesCracked Poker Videos Hand History Converter

BB: \$13.83
UTG: \$10.09
Hero (MP): \$10.00
CO: \$27.43
BTN: \$10.00
SB: \$6.95

Pre Flop: (\$0.15) Hero is MP with J A
UTG raises to \$0.40, Hero calls \$0.40, 2 folds, SB calls \$0.35, BB calls \$0.30

Flop: (\$1.60) 2 9 T (4 players)
SB bets \$1.10, BB folds, UTG calls \$1.10, Hero raises to \$9.60 all in, SB folds, UTG folds

Final Pot: \$4.90
Hero mucks J A
Hero wins \$4.66
(Rake: \$0.24)

I have Excel spreadsheet, which calculates EV in such spots pretty fast.

Assumptions:
B1: Fold Equity: 50%
B2: Equity: 53%
B3: Pot Size: \$2.70 (\$1.30 main pot + \$1.10 UTG's call)
B4: Villain's Bet: \$1.10
B5: Our Raise/Bet Size: \$5.50

Expected Value: =B1*(B3+B4)+(1-B1)*((B2*(B3+B5)-(1-B2)*B5))
Expected Value: \$2.8

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