Thinking about ranges and combinations.

Here's an excercise to help you think about ranges and combinations. If your thinking wtf, I dont know how to do this and go next thread, then you really need to start putting more time into thinking about this kind of stuff. It'll really help your game.


PLEASE POST ANSWERS HIDDEN (IN WHITE TXT), SO NOT TO SPOIL THE FUN!

Hand 1
We have :Kd: :Ks:, we open 4bbs and get repopped by a 10/8 nit to 12bbs. We know his 3bet range is AK/QQ+. How often does he have the following hands?

1.1 AA
1.2 KK
1.3 QQ
1.4 AKs
1.5 AKo


Hand 2
150bbs+ vs nit. Again we open with :Ts: :Td: to 4bbs, get threebet to 12bbs by same neet. We call...

Flop comes AhKsTc

How often does he have
2.1 two pair
2.2 a higher set
2.3 a gutshot


Hand 3
100bb deep. We open :Ad: :Kh: MP 4bbs and get flatted by one villain in LP. We put him on 22-TT, ATs-AQs, KQs, QJs, JTs, T9s.

Flop comes Kd9h3d, we cbet 7bbs

3.1 How many hands are in his range?
3.2 What % of his range are we ahead on flop?
3.3 Villain raises the flop to 20bbs, what should we do if we know he would only raise FD's and sets?

Fuck me. I really need a coach.

I'd also like to know how often a guy will go to the death with Ax in hand 2 and K10 in hand 3. Whenever I've looked at 10 - 25NL, it happens all the time.

This is a good place to start if you have no idea how to go about answering:

http://www.flopturnriver.com/phpBB2/...metric%20range

or this:

http://www.flopturnriver.com/phpBB2/...tc-t75711.html

Both by spoonitnow, ldo

Nice post muzz. I'll wait before answering, let some others take a crack at it. I'll just add this comment, about WHY the first two questions are great for folks to think about.

Preflop, we estimate the probability of Villain holding AA and QQ as EQUAL.

Postflop, however, we correct our estimates. Villain is TWICE AS LIKELY to be holding QQ (pair + gutshot) than a set of Aces.

The mathematical term is "conditional probability," reworking the estimates of probabilities based on additional information or conditions. And tons of good poker players have trouble with it. Heck, most of us get surprised sometimes with how the flop can change the ranges and equity.

Interesting post. Thx muzz.

I just woke up, so there is a very good chance that I fucked some of this shit up. But I tried nonetheless... Anyways, very nice thread muzz. Nice work. It's in white below.

1.1 AA - 6 combos - 28.5%
1.2 KK - 1 combo - 4.7%
1.3 QQ - 6 combos - 28.5%
1.4 AKs - 2 combos - 9.5%
1.5 AKo - 6 combos - 28.5%

2.1 two pair - 9 combos - 42.6%
2.2 a higher set - 6 combos - 28.6%
2.3 a gutshot - 6 combos - 28.6%

3.1 How many hands are in his range? 70 combos
3.2 What % of his range are we ahead on flop? All but sets (6 of 70 combos), so 91.4%
3.3 Villain raises the flop to 20bbs, what should we do if we know he would only raise FD's and sets? There are 6 set combos (33/99) and 3 flush draw combos (QdJd, JdTd, Td9d) so we are ahead here only 33% of the time. Since we have little equity when behind, and he has ~36%+ equity when he's behind we should let this go. THe main "problem" here is us having the Ad, which effectively takes out numerous FD combos that our villain could have.

Giving it a try here...


1.1 AA 28.5%
1.2 KK 4.7%
1.3 QQ 28.5%
1.4 AKs 9.5%
1.5 AKo 28.5.3%

2.1 two pair 25%
2.2 a higher set 25%
2.3 a gutshot 50%
(Edit Note - I messed up on this one and had it in my head we had KK)

3.1 How many hands are in his range? (70 Hands)
3.2 What % of his range are we ahead on flop? (91.4%)
3.3 Villain raises the flop to 20bbs, what should we do if we know he would only raise FD's and sets? (We're well behind his range so I'd fold here)

Originally Posted by Muzzard

Here's an excercise to help you think about ranges and combinations. If your thinking wtf, I dont know how to do this and go next thread, then you really need to start putting more time into thinking about this kind of stuff. It'll really help your game.


PLEASE POST ANSWERS HIDDEN (IN WHITE TXT), SO NOT TO SPOIL THE FUN!

Hand 1
We have :Kd: :Ks:, we open 4bbs and get repopped by a 10/8 nit to 12bbs. We know his 3bet range is AK/QQ+. How often does he have the following hands?

1.1 AA = 6/29
1.2 KK = 1/29
1.3 QQ = 6/29
1.4 AKs = 4/29
1.5 AKo = 12/29


Hand 2
150bbs+ vs nit. Again we open with :Ts: :Td: to 4bbs, get threebet to 12bbs by same neet. We call...

Flop comes AhKsTc

How often does he have
2.1 two pair = 9/21
2.2 a higher set = 6/21
2.3 a gutshot = 6/21


Hand 3
100bb deep. We open :Ad: :Kh: MP 4bbs and get flatted by one villain in LP. We put him on 22-TT, ATs-AQs, KQs, QJs, JTs, T9s.

Flop comes Kd9h3d, we cbet 7bbs

3.1 How many hands are in his range? 74
3.2 What % of his range are we ahead on flop? 91.9%
3.3 Villain raises the flop to 20bbs, what should we do if we know he would only raise FD's and sets? We are 57.4% to win over his betting range. This is very interesting because half of his range here is semi bluffs, so you want to raise, but the other half is sets which have you crushed. Call and reevaluate on the turn, might be the best.

Edit: Stacks is right, I didn't see that we had the Ad. Fold is best now.

After reading spoonitnow thread of blockers and ranges,i manage to solve Hand 1 properly and 2 i think,which is great in terms of my knowledge using 6310 function.Hand 3 is kinda hard for me as im still reading about it.

Hand 1:

AA:6 combos
KK:1 combo
QQ:6 combos
AKs:4 combos
AKo:8 combos

Hand 2:

2.1: (AK: 16 combos)(AT: 8 combos)(KT:8 combos)
32 combos
2.2: 6 combos(3 of each)
2.3: 12 combos of AQ,12 combos of AJ,12 combos of KQ,12 combos of KJ,8 combos of TQ,8 combos of TJ
Total:64 combos

nice post, but you should probably include what position hero and villain are in for each example because that can change ranges quite a bit.

Originally Posted by bode

nice post, but you should probably include what position hero and villain are in for each example because that can change ranges quite a bit.

The ranges aren't in debate. The thread is about how boards/our holding affect the likely hood of villain holing a certain hand.

Conditional probability.

Hand 1:


3 Bet range of AK/QQ+ is a total of 34 hands (6xQQ/KK/AA, 16xAK) With KsKd, we hold a total of 13 blockers against his range.
This means he has 21 possible hands:


1) AA = 6 times, 28.5%
2) KK = 1 time, 5% (we hold 5 blockers)
3) QQ = 6 times, 28.5%
4) AKs = 2 times, 9.5% (we hold 2 blockers)
5) AKo = 6 times, 28.5% (we hold 6 blockers)



Hand 2: EDIT (I can't count!!!)


On an AhKsTc flop we have 21 hands in villans range:

1) Two pair (AK is only hand in range) a total of 9 times, 43%
2) Higher set (AA and KK) a total of 6 times (3x for each AA and KK), 28.5%
3) Gut shot (QQ is only hand in range) 6 times, 28.5%


Hand 3: EDIT - I completely read this wrong the first time. I'm still a little confused, but I think I figured out how the board affects his range. Here's another shot.


1) We hold AdKh, which blocks part of villans range. This leaves him with 70 hands. 42 non-set pairs, 6 set pairs, 22 SC combos.
2) We're behind 33 and 99, so we're ahead 64/70 for 91.5%
3) He has 6 set hands. We're blocking his ATs-AQs range since we hold Ad. The board also kills his KQs. This leaves him with 3 FD hands (QJ/JT/T9). Of the 9 hands he would raise, we're behind 6 of them. With 33% equity facing 71% pot odds to call, we have to fold here.


EDIT: Alright Muzz, how'd I do this time?

NP Muzz.

I just wanted to mention that it's important after you do this math not to just run to the forum, double check your answers, and then high five yourself and move on to the next post. When you start getting into the math it's easy to forget that while this is a math question, it's more importantly a poker question. So learn the math, get good at it, but also don't forget to step back and look at what this math is telling us about these situations.

For example, the math in #2 will tell you that even though you hit your set:

42% of the time, villain has 4 outs. Of the 42%, villain will hit one of his outs 16%, for a total of .42 * .16% = ~7%.

29% of the time, we have 2 outs. Of that 29%, we'll hit one of our outs 4%, for a total of .29 * .04 = 1%, which means villain will win ~28% of the time.

29% of the time, villain has 6 outs. Of that 29%, villain will hit one of his outs 24%, for a total of .29 * .24 = ~7%.

So in total, villain will win this pot ~7 + ~7 + ~28 = ~42%, and pokerstove confirms this with 41.051%.


The only reason I thought of commenting here is because I did the first problem, and then started to move on to #2 and realized that if I got up from the computer and walked away, I wouldn't have actually learned anything from the problem, because all I did was a quick math problem without looking at the implications of my solution.

Remember to take a step back and think about what we're actually figuring out.

Hand 1:
1.1- 28.6%
1.2- 4.7%
1.3- 28.5%
1.4- 9.5%
1.5- 28.6%

Hand 2:
2.1- 50%
2.2- 25%
2.3- 25%

Hand 3:
3.1- 70 hands
3.2- 91%
3.3- Fold, because he is twice as likely to have a set as a flush draw and even when he does have a flush draw he can still make it to beat us.

Good to see ppl having a go, I'll leave it another day or so then post results.

Part 3.3 is a pretty interesting spot.

Originally Posted by Muzzard

Good to see ppl having a go, I'll leave it another day or so then post results.

Part 3.3 is a pretty interesting spot.

Did you make this up, Muzz? Or find it somewhere?

Here's my crack at it. Rounded some off but hopefully I'm close.
#1
1.1 AA 28%
1.2 KK 5%
1.3 QQ 28%
1.4 AKs 9.5%
1.5 AKo 28%

How often does he have
2.1 two pair
2.2 a higher set
2.3 a gutshot
2 pair - 42%
High set 28%
Gutshot 29%

#3 I will have to leave for now. I dont know how and I am at work so I need to figure that out when I have lots of time. Nice questions though....fun stuff!

I need all of the help I can get in this area, so here goes... answers in White below... [quote="Muzzard"]
Hand 1
We have :Kd: :Ks:, we open 4bbs and get repopped by a 10/8 nit to 12bbs. We know his 3bet range is AK/QQ+. How often does he have the following hands?

Ok, so the total number of possible hands in his range is AA (6), KK (1), QQ (6), AK (8) for a total possibility of 21 hand combinations.
Right so far?

1.1 AA 6/21 = 28.6%
1.2 KK 1/21 = 4.7 %
1.3 QQ 6/21 = 28.6%
1.4 AKs 2/21 = 9.4%
1.5 AKo 6/21 = 28.6%

Ok, how am I doing? If the above is right (and I think it is) we are currently ahead or equal to roughly 70% of his range. (Pre-flop only)

Hand 2
150bbs+ vs nit. Again we open with :Ts: :Td: to 4bbs, get threebet to 12bbs by same neet. We call...

Flop comes AhKsTc

Well this one is a little more interesting... Let's see... based on the above figures...

How often does he have
[color=green]2.1 two pair He has two pair any time he holds AK, thus 8/21 combinations for 38%
2.2 a higher set He holds a higher set with AA or KK, thus since there are 7 combos of that he could hold, he hits this 33% of the time.
2.3 a gutshot Hmm... he only has a gutshot with QQ, which is 6/21 for 28% of the time.

If I figured this right, we are currently ahead 66% of the time, right?

[b] ran out of time on lunch, will have to try hand 3 tonight... sorry for disjointed answer.. but would appreciate response on how I'm doing so far...

Great post btw. I had fun doing this and I feel it was very helpful to me.

I'd like to see these types of posts and the posts spoon has been doing around the BC more.

I'm not posting results just yet, but I'll give feedback to those who posted.

Stax:
Well done! Not suprised a 200nl reg got them all right

JR9477:
You got hand 2 wrong, but you edited it and said you know you got it wrong. Other than that all is fine!

Animal Chin :
You got parts of 1 right, I think you kinda missed the fact we have KK on the AKs and AKo hands for villain. This has messed up your total combinations and therefore your fractions are wrong.

Question 2 correct!

Question 3, I think you need to look at again! NOt sure where u went wrong, got a few too many combinations in there.

hangchiong:
Hand 1 is correct apart from your AKo and AKs combinations, we have KK remember.

I think you misunderstood Hand 2, we are giving villain same 3betting range QQ+/AK.

kb coolman:
Hand 1 correct! Look at 2.2 and 2.3 again. Hand 3 I gave his range already (We put him on 22-TT, ATs-AQs, KQs, QJs, JTs, T9s). You need Re-evaluate your answer.

kfaess:
All correct, assuming you rounded up/down in Hand 2!

Vinland:
Correct on 1 and 2, why not give 3 a go!

Monty:
Hand 1 correct! Have a look at 2.1 and 2.2 again.

Well done to everyone who attempted, still open to others if you want a go. Post any questions in the thread if you have them. Also 3.3 is an interesting spot even though his range is more sets than FD's. If anyone wants to look at that in a bit more detail I'd advise you range it up in POKERSTOVE

Thunder: I think you are hurting your growth by not at least attempting this problem. If you are clueless on where to start I hope you read the threads muzz posted and are at least attempting it. These problems can be solved rather easily if you know how to calculate combos. You simply take the number of combos for a given hand, and divide that by the total combos in villains range. That give you the % of the time he has that hand.

Example: villain raises on AA, KK, AK preflop (don't worry about how likely this is). Well there is 6 combos of AA, 6 combos of KK, and 16 combos of AK. Therefore, villain is raising a total of 28 combos. Therefore, villain has AA 21.4% of the time (6/28), KK 21.4% of the time (6/28), and AK 57.1% (16/28).

Above is basically what you need to do. However, you must know how to calculate combos and work with blockers (example if you have an Ace in your hand the chances of villain having AA is cut in half).

Originally Posted by RML604

I just wanted to mention that it's important after you do this math not to just run to the forum, double check your answers, and then high five yourself and move on to the next post. When you start getting into the math it's easy to forget that while this is a math question, it's more importantly a poker question. So learn the math, get good at it, but also don't forget to step back and look at what this math is telling us about these situations.

I absolutely agree with this.. Understanding the math is great and all. But if you don't understand what it actually means, and how you should apply this stuff to your common poker situations then you are missing out on the most helpful part of knowing how to do this. Learn it, but then make sure you apply it.

Vinland: I'll let you attempt 3 on your own, but if you need help on how to do it then you can either post here or shoot me a pm and I'll see if we can't get it worked out for you.

Monty: Question 1 is correct. Good job.. On 2.1 and 2.2 you are only off by a small margin. Look back at the number of combos for AK and AA/KK in relation to the flop. 2.3 is correct.

To everyone that didn't get the correct answers I highly suggest going back and trying to find your errors before looking at someone else's work or just giving up. It will help you loads to find your own errors. And remember if you don't know how to do it, don't be ashamed to ask for fear of sounding like a donk/noob/whatever. If you are afraid to admit you need help, then you will never get that help.

Originally Posted by RML604

I just wanted to mention that it's important after you do this math not to just run to the forum, double check your answers, and then high five yourself and move on to the next post. When you start getting into the math it's easy to forget that while this is a math question, it's more importantly a poker question. So learn the math, get good at it, but also don't forget to step back and look at what this math is telling us about these situations.

+2

[quote="Monty3038"]I need all of the help I can get in this area, so here goes... answers in White below...

Originally Posted by Muzzard

Hand 1
We have :Kd: :Ks:, we open 4bbs and get repopped by a 10/8 nit to 12bbs. We know his 3bet range is AK/QQ+. How often does he have the following hands?

Ok, so the total number of possible hands in his range is AA (6), KK (1), QQ (6), AK (8) for a total possibility of 21 hand combinations.
Right so far?

I see my mistake now... didn't add the KK back in... oops...

Let me re-do 2 and 3 in a seperate post... since I haven't tried 3 yet.

1.1 AA 6/21 = 28.6%
1.2 KK 1/21 = 4.7 %
1.3 QQ 6/21 = 28.6%
1.4 AKs 2/21 = 9.4%
1.5 AKo 6/21 = 28.6%

Ok, how am I doing? If the above is right (and I think it is) we are currently ahead or equal to roughly 70% of his range. (Pre-flop only)

Hand 2
150bbs+ vs nit. Again we open with :Ts: :Td: to 4bbs, get threebet to 12bbs by same neet. We call...

Flop comes AhKsTc

Well this one is a little more interesting... Let's see... based on the above figures...

How often does he have
[color=green]2.1 two pair He has two pair any time he holds AK, thus 8/21 combinations for 38%
2.2 a higher set He holds a higher set with AA or KK, thus since there are 7 combos of that he could hold, he hits this 33% of the time.
2.3 a gutshot Hmm... he only has a gutshot with QQ, which is 6/21 for 28% of the time.

If I figured this right, we are currently ahead 66% of the time, right?

[b] ran out of time on lunch, will have to try hand 3 tonight... sorry for disjointed answer.. but would appreciate response on how I'm doing so far...

Originally Posted by Muzzard

Hand 2
150bbs+ vs nit. Again we open with :Ts: :Td: to 4bbs, get threebet to 12bbs by same neet. We call...

We don't have KK any longer, now that changes the numbers a bit, 6 combinations of AA, 6 combinations of KK, 6 combinations of QQ and 16 combos of AK, of which 4 combos are suited, for a total of 32 hands) - THIS IS PRE-FLOP
Flop comes AhKsTc
Now that changes things again... He now cannot have any AA with the Ace of Hearts, making AA combos = 3, Same for K of Spades, thus KK = 3. AK combos drops to 9, with two suited. Still are 6 QQ combos also. Total possible hands is now 21
How often does he have
2.1 two pair Ok, 9 Combos of AK, thus we can say he hits this 9/21 times or 43%
2.2 a higher set Ok, for sets he could use any combo of AA or KK, thus he has 6 possibles out of 21, or 29%
2.3 a gutshot Hmm... Now this one involves the Queens, he could have them 6 ways out of 21 hands, or 29%

Thus, with our set, we are ahead still of all hands but the higher sets, which account for 29% of hands he could have, making us 71% favorite
[/color]

Hand 3
100bb deep. We open :Ad: :Kh: MP 4bbs and get flatted by one villain in LP. We put him on 22-TT, ATs-AQs, KQs, QJs, JTs, T9s.

Ok, home now and can do this, I know I can...
22 = 6 combos, same for 33, 44, 55, 66, 77, 88, 99 and TT for a total of 54 combos so far.
ATs = 3 possible, AJs = 3, AQs=3
KQs = 3, QJs = 4, JTs = 4, T9s = 4
Total hands possible so far: 78 Hands

Flop comes Kd9h3d, we cbet 7bbs

Now, we have to take out some combos. I'm doing this on paper and I come up with that taking out some hands and making total possible hands 70 (I think)
3.1 How many hands are in his range? 70
3.2 What % of his range are we ahead on flop? I already forgot what we had... just a sec... Oh yeah... let's see We have a pair of Kings. We are ahead of all of his pairs except 3s and 9s (set) We beat all of his other hands for a total of 64 hands that we are beating.
3.3 Villain raises the flop to 20bbs, what should we do if we know he would only raise FD's and sets? [/color]
Ok, we are ahead of flush draws, though he has outs, and we are behind sets. So we are mostly worried about sets 6 of his hands. Flush draws are only possible with the QJs, JTs and T9s hands, making 11 combos. Sets are possible with 6 hands. that makes 17 hands. If he only raises sets and flush draws, we are ahead of 11/17 possible hands, roughly 64%, let's call it 2/3. We are thus ahead 2/3 times and the bet is for 20 bbs into a pot of 15 bbs. It costs us 13 bbs to call a bet of 20. That is roughly the same percentage we are ahead, I make it a call.

Am I even close? My logic feels a bit screwy but I honestly did this by my self with only a calculator for percentages

PS I edited this like 9 times to get the color right darnit.

Originally Posted by Muzzard

kb coolman:
Hand 1 correct! Look at 2.2 and 2.3 again. Hand 3 I gave his range already (We put him on 22-TT, ATs-AQs, KQs, QJs, JTs, T9s). You need Re-evaluate your answer.

Ok, I re-evalutated and I think I know where I went wrong. Edited original post. How'd I do?

kb - Nice edit your spot on this time. There is only one error that I think is present. On the flop, the pot should be 9.5bb (our 4 + villains 4 + bbs 1 + sbs 0.5). We are cbetting 7 bb and getting raised to 20bb total. This makes the pot 36.5bb and we must call 13bb. Therefore we are getting 2.8:1 odds. Therefore, we need 1/(2.8 +1) = 26% equity to make this call.

It's true that we are ahead 33% of the time (because of the 9 combos in his raising range, we are ahead of the 3 flush draws); however, we only have 22% equity in the pot (pokerstoved). This is because when we are behind of villains sets we have very little equity. However, when villain is behind and has his flushdraws he still has 36% equity. So he's in much better shape.

Now lets say for instance that we did have the 26% equity needed, and we were still getting the pot odds to make the call. Well I believe a call would still be inappropriate. Mainly for the fact that we would be OOP and likely be forced to put more money in the pot when behind, but he would be able to get off the hook when he misses his flush. I think this is a clear fold given villain's raising range in this example. However, against a real villain it obviously isn't always going to be this clear cut because villain should/would be bluffing in some instances here, and raising other marginal hands.

Stacks - you're right. I missed the 7bb turn bet and how it would apply to 3.3. The end result is the same, but my reasoning was flawed. Great explaination on our play here. You just helped me out a ton.

And FWIW, working through these excercises gave me a HUGE epiphany in regards to ranges. I've been getting good at defining opening ranges (I think), but have been very weak understanding how the villan's betting patterns clue me in to his hand. For example, he only 3bets with xx vs flatting with yy, etc. I need to work on defining villan's opening range vs. 3bet/4bet/AI range.

Hand 1:

3bet range is QQ+,AK which means there are 34 combinations. Our two kings act as blockers and leave us with 21 combinations of hands. (There is only one combo for KK left, and only half as many AK combos are now possible leaving us with 13 less combinations)

Thus, in decreasing order probabilities are:
AK - 6/21
AA - 6/21
QQ - 6/21
AKs - 2/21
KK - 1/21

Hand 2:

3bet range is the same here. The flop is rainbowed so there aren't any flush draws (save backdoors). Since our TT doesn't affect opposing hand likelihoods, we are up against 34 hands before the flop. Flop comes and changes everything, however. It removes 3 combinations of AA and KK, six combinations of AKo, and two combinations of AKs for a total 14 removed.

Now we're up against 20 hands, in order of likelihood (we'll count AKo the same as AKs here since their postflop value in this example is roughly the same, unless villain holds AcKc ).

Two pair (AK): 8/20
Gutshots (QQ): 6/20
Higher sets (AA/KK): 6/20

Hand 3:

We put villain on 22-TT, ATs-AQs, KQs, QJs, JTs, T9s. This represents 82 combinations of hands that we could be up against, however we hold blockers in our hand, and the flop contains some more. Our Ad removes 3 combinations from ATs-AQs, our Kh removes a combination from KQs, the Kd on the flop removes another combination, and the 9h and 3d on the flop remove three combinations of 99 and three from 33. All in all, we've removed 11 combinations, leaving us facing 71 hands.

We hold TPTK on this flop, and we're only really lagging behind sets in our opponents range. We see 6 combinations of these, in a total 71. Here we consider ourselves to be ahead of 65/71 of our opponent's range, i.e: 91% of it.

Here we hold TPTK and we know villain only raises FDs and sets (and I take it in this example we're allowed to assume that our villain doesn't know that we know this). Since we hold the Ad, we know he isn't raising us with the nut flush draw - the Kd is on the flop so we're not getting raised by KdQd. This leaves 99,33,QdJd,JdTd,and Td9d.

This range has us beat, unfortunately, since sets have us crushed completely and all of his flush draw hands either have a pair in them also or a gutshot so we're almost flipping against those. In this case I'd probably call his range and on the turn, bet any blank card. Our villain is unlikely to raise us again with a draw and our equity against all of his flush draw hands increases dramatically here. However he is likely to raise us again with a set so we should fold to any more agression on the turn, in my opinion.

How did I do?

Monty - take another look at 3.3. Remember that he can only be on a diamond flush draw.

Hand 1
1.1 AA - 6 hand combinations (28.6%)
1.2 KK - 1 hand combination (4.8%)
1.3 QQ - 6 hand combinations (28.6%)
1.4 AKs - 2 hand combinations (9.5%)
1.5 AKo - 6 hand combinations (28.6%)
Total of 21 hand combinations

Hand 2
How often does he have
2.1 two pair - 9 hand combinations (42.9%)
2.2 a higher set - 6 hand combinations (28.6%)
2.3 a gutshot - 6 hand combinations (28.6%)
Total of 21 hand combinations

Hand 3
3.1 How many hands are in his range?
70 hand combinations
Sets: 33, 99 (6 hand combinations)
Paired kings: KQs (2 hand combinations)
Paired nines: T9s (3 hand combinations - of which one is a diamond flush draw)
Pocket pairs: 22, 44-88, TT (7 * 6 = 42 hand combinations)
Suited aces: ATs-AQs (3 * 3 = 9 hand combinations - no flush draws as we have the ace of diamonds)
Other suited cards: QJs, JTs (2 * 4 = 8 hand combinations - two diamond flush draws)
3.2 What % of his range are we ahead on flop?
Behind sets (6 hand combinations 8.6% - 5.4% equity)
Ahead of pairs (46 hand combinations excluding the one that is also a flush draw with 90.8% equity)
Ahead of unpaired, suited cards (15 hand combinations excluding the ones that are flush draws with 90.5% equity)
Ahead of flush draws (3 hand combinations with 56.8% equity)
Total ahead of 64 hand combinations (91.4%) with 89.1% equity.
3.3 Villain raises the flop to 20bbs, what should we do if we know he would only raise FD's and sets?
Fold - there are 6 hand combinations against which we have 5.4% equity and 3 hand combinations against which we have 56.8% equity. Against this total range our equity is 28.1%
Interestingly the ATs-AQs part of the range could have given him 3 more flush draws in his range if we didn't have the ace of diamonds - with the ace of spades he has 3 more hand combinations as draws with a total equity of the range at 33%. Funnily, this is not enough of a change really - flush draws have really solid equity against our hand on the flop and doubling up the flush draws in his range is still unprofitable for us to continue - we still fold.
This is especially exacerbated by us being out of position in the hand - we can either get eaten by a better hand (a set) or by reverse implied odds.

Originally Posted by kb coolman

Monty - take another look at 3.3. Remember that he can only be on a diamond flush draw.

I understand it can only be diamonds, but I've re-read it twice... I don't see it.

You are correct with the sets, but you're off on the draws. You've defined the proper hand in villans range he could draw with, but your count is way off. This is affecting the total outcome of the exercise.

Originally Posted by Monty3038

Flush draws are only possible with the QJs, JTs and T9s hands, making 11 combos.

And only ... if they are diamonds
QsJs, QhJh, QcJc, JsTs, JhTh, JcTc: Gutshot
QdJd, JdTd: Flush draw and gutshot
Ts9s, Tc9c: Made pair
Td9d: Flush draw and made pair
That makes 3 combos that are flush draws.

Originally Posted by Monty3038

Originally Posted by Muzzard

3.3 Villain raises the flop to 20bbs, what should we do if we know he would only raise FD's and sets? [/color]
Ok, we are ahead of flush draws, though he has outs, and we are behind sets. So we are mostly worried about sets 6 of his hands. Flush draws are only possible with the QJs, JTs and T9s hands, making 11 combos. Sets are possible with 6 hands. that makes 17 hands. If he only raises sets and flush draws, we are ahead of 11/17 possible hands, roughly 64%, let's call it 2/3. We are thus ahead 2/3 times and the bet is for 20 bbs into a pot of 15 bbs. It costs us 13 bbs to call a bet of 20. That is roughly the same percentage we are ahead, I make it a call.

Am I even close? My logic feels a bit screwy but I honestly did this by my self with only a calculator for percentages

PS I edited this like 9 times to get the color right darnit.

Ok, I see it now, thanks, for some reason that just wouldn't click no matter how much I read it.

1.1 AA 6/24=25%
1.2 KK 1/24=4.2%
1.3 QQ 6/24=25%
1.4 AKs 3/24=12.5%
1.5 AKo 8/24=33%

2.1 two pair: 11/29=37.9%
2.2 a higher set: 6/29=20.7%
2.3 a gutshot: 20.7%


3.1 How many hands are in his range?: preflop there are 78 hands in his range, but after we see the board that number is reduced to 70.
3.2 What % of his range are we ahead on flop? we are ahead of everything but trip 9s and trip 3s. That leaves 64 of the 70 hands in his range that we are currently ahead. so that means we are ahead on the flop vs 91.4% of villain's range.
3.3 Villain raises the flop to 20bbs, what should we do if we know he would only raise FD's and sets? Since we have the Ad, this severely limits villain's range for flush draws leaving him 3 flush draw hands in his range. So we are only ahead of 87% of his range given this raise. However, we are a huge dog to any of the hands within his range. Conlusion: throw this into the muck.

bump for value

I'll attempt this being its important for MTT players to know as well. This was bumped back in feb so I think its ok to post none in white?

Hand 1
1.1 28.5%
1.2 4.7%
1.3 28.5%
1.4 9.5%
1.5 28.5%

Hand 2
2.1 42.8%
2.2 28.5%
2.3 28.5%

Hand 3
3.1 70 combos
3.2 91.5%
3.3 Villain will have a set 66% of the time and will fold his FD to a 4-bet ship 33%. Based on the pot odds, we need villain folding 69/(4+4+7+20+69)=66.3%. So this is a fold.

Great post - Are there others some could link me to like this one?

Great post I had to look back at the other posts to get the math down, but would love to see more examples like this just for more practice.