Some Betting Exercises vs. Short Stacks

Part of my current viewpoint on poker is that understanding the betting decisions is key. Being good at putting your opponents on ranges is fairly useless if you can't make the right decision based on that decision. Here are a few exercises where I'll give you Villain's range in a situation and you decide what you think the best line is.

I've decided to make all of these exercises have to do with short-stacks since that's always a fun topic.

You will get the most out of these exercises if you complete them in three steps. The first step is to work out what you think the right play is without any tools or writing anything down. The second step is to work it out on pen/paper using whatever tools you deem necessary and try to figure out if the decision you came to in the first step was correct or not. The last step is to post all of your findings for each exercise here and let myself and others comment on your analysis.

Exercise 1: Preflop, it folds to the small blind who had 15bb before he posted the blind and you have him covered. He open shoves {22+, K2+, A2+, QT+, JT}. What hands can you call with profitably in the big blind?

Exercise 2: Preflop, a 20bb stack opens for 5x with {AQ+, 99+} UTG. You call on the button with A K and you have him covered. The flop pot is 11bb after the rake and you have 15bb behind. The flop comes AQTr. Villain open shoves 100% of his range. Can you call profitably?

Exercise 3: Preflop, it folds to you on the button. Both blinds had 20bb stacks before posting the blinds and you have them covered. You open raise to 4x, the SB shoves {AT+, 22+}, then the BB shoves {AQ+, 88}. What is your profitable calling range?

I look forward to your answers.

Preflop, it folds to the small blind who had 15bb before he posted the blind and you have him covered. He open shoves {22+, K2+, A2+, QT+, JT}. What hands can you call with profitably in the big blind?

We would need to call with hands that have close to 50% equity against this range, though its closer to like 45% due to the money already in the pot. So before stoving it, an initial guess would be 66+, KT+, A6+ which i think would be the upper half of his range.

The actual equity we need to be profitable i determined to be
EV=pw*gain - pl*loss
EV=pw*15-(1-pw)*13
EV=pw*28-13
if we expect to break even then this becomes
0=pw28 - 13, and then pw = 46.4%

So hands that have > 46.4% equity against villains range would be profitable to call with.

The results were somewhat surprising to me, 22 had 46.7% equity against villains range. I assumed that since it had only a slight edge vs the unpaired cards and a huge disadvantage vs the paired hands that this would be further behind. The reason for this is likely the shear magnitude of unpaired hands for villain (56) while there are only 13 paired hands. Thus, out of 69 hands, our ev with 22 is equal to 56/69* 55% + 13/69*20% =48%.

Then, 22+ is profitable. Similarly, i found that my KT guess was almost right on, KTo has 48% equity, but K9s has 47.6%. The A6 guess was off, A3o has 46.9% equity and A2s has 49% so the profitable calling range would then be
[22+, A2s+, A3o+, K9s+, KTo+]

Did some other hands quickly to make sure i didnt miss some, QJs only has 45% equity which makes sense since it isnt really a favorite over any hand but is only a huge underdog to the higher pairs. Things like T9s had about 40% equity as well. If the stack was smaller, these hands would probably merit a call


Preflop, a 20bb stack opens for 5x with {AQ+, 99+} UTG. You call on the button with A K and you have him covered. The flop pot is 11bb after the rake and you have 15bb behind. The flop comes AQTr. Villain open shoves 100% of his range. Can you call profitably?

My gut says eww here. We're only ahead of KK, JJ, and 99 while horribly behind AA, QQ, TT, AQ, and only tying with AK. Although, combination wise, its more likely he has kK, JJ or 99, then given the size of the pot and what we have behind, i think we can call profitably.

So, lets do a EV thing
EVcall = pw*gain - (1-pw)loss
Evcall= pw*26-(1-pw)*15
assume breakeven again
0=pw*41 - 15
so pw = 36.5%

So if AK is >36.5% to win, we should call.
Pokerstoving again, i get a shocking 55.4% equity. I was expecting around 40% or so, but i neglected our straight outs and i likely underestimated the combinations.
KK(3), JJ (6), 99 (6), = 15
AA(1), QQ(3), TT(3), AQ (6)=13
Since we are then huge favorites over the hands we're ahead of, and huge underdogs to AA,QQ,TT but have outs against AQ it makes sense to me that we would have an edge against this distribution.

Preflop, it folds to you on the button. Both blinds had 20bb stacks before posting the blinds and you have them covered. You open raise to 4x, the SB shoves {AT+, 22+}, then the BB shoves {AQ+, 88}. What is your profitable calling range?

Fuck, my guess would be to ignore the SB completely and just think about the BB's range, since we need to beat him to win and his range is way ahead of the SB's range.

So, to call,
0=pw*g - (1-pw)*l
0=pw*40 -(1-pw)*20
pw*60-20=0, so pw= 33%

The BB is tighter than that in example 1, but we need less equity to call profitably. Im thinking AQ+, 99+. AJ is only 25% to AQ, as are other aces and they are underdogs to 88+ so we need at least AQ. so that the effect of the pairs doesnt push our equity below 33%. Since there are alot of combos of AQ and AK, but less than that of 88+, im thinking we need a pair that is slightly better than 88 to be 33% ahead...but i wouldnt be suprised if it turned out to be less than this.

Stoving, and fuck. AJs is 35%, AQo is 37%, so AJs+, AQo+
99 was around 40%, 88 is 35.8%, but 77 is too low, so we get
[88+, AQo+, AJs+]. I think that i may have neglected some other broadways though, so im going to stove them to see what i get.
QJs is 35%, so i missed those too...QJo and KQo are like 31% though.

QJs, QTs, JTs, Kts, KJs, KQs, are all like 34%, with their unsuited counterparts being like 31%, ZOMG THEIR SOOTED AND IT MATTERS!
Things like 98s are like 31 too though, so an adjusted range is

[88+, AQo+, AJs+, QTs, QJs, JTs, KTs-KQs]

Im unsure if my assumption is valid though, is this the way you're supposed to do this spoon? Can i really just ignore the sb's range all together?

Originally Posted by JKDS

Can i really just ignore the sb's range all together?

Nope. Sorry but you can't.

Hint: If you call, you're risking x to win SB stack + BB stack + your original raise.

Originally Posted by spoonitnow

Exercise 1: Preflop, it folds to the small blind who had 15bb before he posted the blind and you have him covered. He open shoves {22+, K2+, A2+, QT+, JT}. What hands can you call with profitably in the big blind?

I'm going to solve a slightly different example to help those who are confused on how to do the actual solving part (the part that comes after you decide what you would do at the table).

Let's say that the guy's stack is 24bb and the range is {22+, Q2+, K2+, A2+} instead. After the SB shoves, we're calling 23bb to win 25bb. Our call is 23bb because we've already posted a big blind, and we're going to win 25bb because that's our opponent's entire stack that he's shoving plus our 1bb we've already posted into the pot. To break even, we need to have an equity of bet/(bet+pot) = 23/(23+25) = 0.479 = 47.9%. Now we just find what hands have 47.9% against {22+, Q2+, K2+, A2+} in PokerStove and we're done (you can do that part yourself).

ok, just using brain gumph.

I assume "open shoves" means all in.

1) I dont know about connectors. So if indoubt, leave them out.I think there are around 216 starting hands and I guess villian has 50% covered.Im out of my depth here.

All broadways and PP, 19 starting hands.and all Axs and Kxs.

2) If he has 99+ i think its 50/50. AQ+ , its either shared or 2 to him.
I never knew this. Its no profit.

3)I do not know.

Right , now for some research (time check 18:54).

-----------------------------------------------------------------

1) google said 169 starting hands.Poker stove said villians range is 37.3%

All broadways pairs and Axs Kxs. Im not sure how to disprove this range.

2)im sticking with that.

3)Non the wiser.I just dont know

19:45

EDIT: OMG my answers are bad.Im in the BC for a while then.

Originally Posted by spoonitnow

Hint: If you call, you're risking x to win SB stack + BB stack + your original raise.

shoot, forgot about our bet, then our equity would be
0=pw*g - (1-pw)*l
0=pw*40 -(1-pw)*16
pw*56-16=0, so pw= 28.5%

that 5% difference just blew my range to shit, lots of suited connectors and other hands just got included, ill redo my analysis as soon as i give the sb's distribution some more thought

Originally Posted by celtic123

ok, just using brain gumph.

I assume "open shoves" means all in.

1) I dont know about connectors. So if indoubt, leave them out.I think there are around 216 starting hands and I guess villian has 50% covered.Im out of my depth here.

All broadways and PP, 19 starting hands.and all Axs and Kxs.

2) If he has 99+ i think its 50/50. AQ+ , its either shared or 2 to him.
I never knew this. Its no profit.

3)I do not know.

Right , now for some research (time check 18:54).

-----------------------------------------------------------------

1) google said 169 starting hands.Poker stove said villians range is 37.3%

All broadways pairs and Axs Kxs. Im not sure how to disprove this range.

2)im sticking with that.

3)Non the wiser.I just dont know

19:45

EDIT: OMG my answers are bad.Im in the BC for a while then.

My suggestions:

1. Get this http://www.pokerstove.com/ (it's free)
2. Watch this http://www.spoonitnow.com/pokerstove.html

I have not read any other replys, since I wanted to think through this first. Let's see how I do.

Exercise 1: Preflop, it folds to the small blind who had 15bb before he posted the blind and you have him covered. He open shoves {22+, K2+, A2+, QT+, JT}. What hands can you call with profitably in the big blind?

With such a wide range, we could call with 22+, Ax, Kxs and it be profitable. Add in Kxo, and we're just better than a coin flip.

Exercise 2: Preflop, a 20bb stack opens for 5x with {AQ+, 99+} UTG. You call on the button with A K and you have him covered. The flop pot is 11bb after the rake and you have 15bb behind. The flop comes AQTr. Villain open shoves 100% of his range. Can you call profitably?

We have 55% equity against his range on this flop with TPTK. We're calling 15bb into a 26bb pot, which is giving us pot odds of 57%. We still have outs on the turn/river with any K. We can call profitably here.

Exercise 3: Preflop, it folds to you on the button. Both blinds had 20bb stacks before posting the blinds and you have them covered. You open raise to 4x, the SB shoves {AT+, 22+}, then the BB shoves {AQ+, 88}. What is your profitable calling range?

We have a nitty op2, but we can have a wider range and be profitable here since it's three way. Let's say 35% will get the job done. 55+, AJ+ should be profitable here.

Exercise 1: Preflop, it folds to the small blind who had 15bb before he posted the blind and you have him covered. He open shoves {22+, K2+, A2+, QT+, JT}. What hands can you call with profitably in the big blind?

Step 1 - I'm trying to figure this out in a logical way, but honestly don't know how. Let me see if I can figure something out. I will have to call 14bb to win a pot of 30bb. Thus the pot odds are roughly 2 to 1. If I understand this correctly, I need to win the hand at least 1 out of 3 to make 2bb (win 1 = 30 -lose twice (28)). So to accomplish that I need to be ahead of his range 33% of the time. His range is 22+, K2+, A2+, QT+, JT.... the top 1/3 of his range is probably any pair, AT+, KT+. Thus I think I would feel comfortable calling with 99+, AK, AQ, KQ to give myself a little extra headway...

Step 2 - I don't know if I'm figuring out the range I need to hit odds wise to be ahead enough, but since I'm hampered a bit at the moment, let me download and analyze with pokerstove. According to Pokerstove's estimate his range is about 37%. With me opening the top 10% of hands, the following results occur:

equity win tie pots won pots tied
Hand 0: 38.315% 36.78% 01.53% 35734063096 1491179408.00 { 22+, A2s+, K2s+, QTs+, JTs, A2o+, K2o+, QTo+, JTo }
Hand 1: 61.685% 60.15% 01.53% 58439707048 1491179408.00 { 77+, A9s+, KTs+, QTs+, AJo+, KQo }

Thus top 10% of hands does not give us a high enough win percentage to beat him on average to make the call profitable over time. If I run my range I guessed at above, I get the following results:

This gets us closer to our goal of winning 2/3 of the time, making us a favorite to win... but to be honest, I have gotten to the point that I think I'm doing the whole exercise wrong. It may be more correct to be searching for a point where I am at least a slight favorite, then beat it. If I need to win at least 1/3 of the time to make it a profitable call, I may only need to beat him 33% of the time also... I'm actually quite confused now.


Exercise 2: Preflop, a 20bb stack opens for 5x with {AQ+, 99+} UTG. You call on the button with A K and you have him covered. The flop pot is 11bb after the rake and you have 15bb behind. The flop comes AQTr. Villain open shoves 100% of his range. Can you call profitably?

Step 1 - The pot is now 20 bb from villian plus your 5 bb, for a total of 25bb in the pot. You have to call 9 bb to call. Thus the pot is offering you a little less than 3 to 1. You have top pair. You still have 9 outs to improve. Two cards left to come. Thus roughly you have a 36% chance to improve, though improving may chop the pot or still not win for you without improving to a straight. To cut it a little narrower let's say you have a 30% chance to improve. With pot odds of 3 to 1 you need to win one time in 4 at least, or 25%. You have a 30% chance to improve or are already ahead, call.

Step 2 - Let me try to confirm those numbers in pokerstove... Pokerstove puts you at
Board: As Qd Tc
Dead:

equity win tie pots won pots tied
Hand 0: 44.580% 34.63% 09.95% 11656 3349.50 { 99+, AQs+, AQo+ }
Hand 1: 55.420% 45.47% 09.95% 15305 3349.50 { AcKh }

A much higher percentage than I figured, making it a call.

Exercise 3: Preflop, it folds to you on the button. Both blinds had 20bb stacks before posting the blinds and you have them covered. You open raise to 4x, the SB shoves {AT+, 22+}, then the BB shoves {AQ+, 88}. What is your profitable calling range?

I look forward to your answers.

Step 1 - The SB range is looser than BB. Effectively you will be calling 44 bb with a bet of 16 bb. Thus you are getting a little less than 4 to 1 pot odds. Let's call it 3.75 to 1 (I did that in my head, yeah me!). To make the math easier, I am going to say 3.5 to 1. Thus I need to win more than 1 in 4.5 attempts to make this profitable. The BB range is the one I need to be beating as often as possible. 1 in 4.5 is about 22 % so I need to be ahead of 78% of his range. To do that I think I'm only calling here with AA, KK, AKs, maybe QQ.

Step 2 - Pokerstove confirms that this is close to the truth, IMO, with my QQ+, AKs range winning 54% of the time... I think I'm doing this wrong but that is still a good percentage of time ahead of the others, so even though my explanation in step 1 is not what I figure to be correct, the results might be...

Answer to Exercise 2:
PokerStove tells us that we have 55.3%. To break even, we need 15/(15+11) = 57.69% equity. We have less equity than that, so a call is -EV.

Originally Posted by spoonitnow

Answer to Exercise 2:
PokerStove tells us that we have 55.3%. To break even, we need 15/(15+11) = 57.69% equity. We have less equity than that, so a call is -EV.

Why is our equity not 15/(26+15) = 36.6%

Originally Posted by humanfugitive

Originally Posted by spoonitnow

Answer to Exercise 2:
PokerStove tells us that we have 55.3%. To break even, we need 15/(15+11) = 57.69% equity. We have less equity than that, so a call is -EV.

Why is our equity not 15/(26+15) = 36.6%

Your wording is off but your thought is correct. Our pot odds are somewhere around 2:1. Like Spoon said our equity is about 55%. Obviously a call. If we have 55% equity we can never fold in any spot in cash-games.

is it me or is the 2nd question being answered wrong? isn't the question whether or not we can profitably call the flop shove? if so, the preflop equity is meaningless. i think the term open shove might be throwing people off, as most people consider that a pre flop term.

Open shove: Go all-in when you are the first player on this betting street to put money in the pot. Go all-in as a first bet, rather than a raise or re-raise.

1. we risk 14 to win 30 so that's 46.(6)%
22+, A2s+, A3o+, K9s+, KTo+

2. we risk 15 to win 41 so that's 36.5%
stove says we have 55.31% so we can call profitably

3. call 16 to win 60, we need 26.(6)%
88+, AKo, AQs+
note that I used Monte Carlo trials because my PC can't handle this 3way
so if suited connectors are profitable (they are SUPER close) then I'm sorry, suited connectors showed up at around 26% but below the 26.6% mark

Alright, I'm fairly new at this so this is my look at this. I had to do this fast so I only did the first step i.e. what my gut tells me.


Ex 1. I call with A8+, TT+ Not much more, yes I'm nitty.

Ex 2. No I wouldn't call but Im pretty close. Since I didn't reraise he prob knows I dont have KK or AA. His early raise tells me he had something as does his shove. If he had 99, JJ or KK then I beat him. Shoving with 99 is kamikaze but possible. If he had AQ, TT, QQ, AA then I am lost.
If he had a set why the all-in? He could be afraid that I make a straight later. Or He has the str8 draw (AK) and wants me out (rare IMHO). I think 2 pair or bottom set and he wants the pot now...I fold.

Ex 3. I only call with JJ+ The pot odds are nice but the 2 raises behind me worry me.
I raised and had 2 raisers behind. The SB shoved without worry of the BB so I think he has something.

Those are my "gut feeling" answers. I don't have any method to work it out on paper yet or any calculation methods, I'm still having to learn that.

Vinland you completely missed the point of this exercise if you didn't download pokerstove and run the math.

Spoon, i think i understand my mistakes on the first two, but after thinking for awhile i'm still not sure on how to evaluate a range verses two opponents. Can you give me some insight on how to think about this in a different way?

Originally Posted by spoonitnow

Exercise 1: Preflop, it folds to the small blind who had 15bb before he posted the blind and you have him covered. He open shoves {22+, K2+, A2+, QT+, JT}. What hands can you call with profitably in the big blind?

My calling here is range is A8+ 66+ .

There is too many combinations I'll have to comeback to this one.
78 combos for PP
130 approx for Ax of which I beat about half
130 approx for Kx of which I beat
and I think 48 for QJ, QT AND JT.

I think there's room to open up my range in this situation

Originally Posted by spoonitnow

Exercise 2: Preflop, a 20bb stack opens for 5x with {AQ+, 99+} UTG. You call on the button with A K and you have him covered. The flop pot is 11bb after the rake and you have 15bb behind. The flop comes AQTr. Villain open shoves 100% of his range. Can you call profitably?

I think this is a fold. only 12 combintations you can beat. and tie with 6.

Originally Posted by spoonitnow

Exercise 3: Preflop, it folds to you on the button. Both blinds had 20bb stacks before posting the blinds and you have them covered. You open raise to 4x, the SB shoves {AT+, 22+}, then the BB shoves {AQ+, 88}. What is your profitable calling range?

I look forward to your answers.

AA, KK, QQ, AK. I may even fold AK or QQ... not always though.

I think the BB has about a total of about 74 possible combinations. With the top 4 hands I will beat about 32ish of those combinations. These are just my ballparks I did in my head. Also there's the added equity from the SB

Originally Posted by spoonitnow

I'm going to solve a slightly different example to help those who are confused on how to do the actual solving part (the part that comes after you decide what you would do at the table).

Let's say that the guy's stack is 24bb and the range is {22+, Q2+, K2+, A2+} instead. After the SB shoves, we're calling 23bb to win 25bb. Our call is 23bb because we've already posted a big blind, and we're going to win 25bb because that's our opponent's entire stack that he's shoving plus our 1bb we've already posted into the pot. To break even, we need to have an equity of bet/(bet+pot) = 23/(23+25) = 0.479 = 47.9%. Now we just find what hands have 47.9% against {22+, Q2+, K2+, A2+} in PokerStove and we're done (you can do that part yourself).

Hey, sorry to revive old threads, but I actually had a question on this. I understand why we need 47.9% equity, but my question here is how should we be designing our range to most effectively expolit this?

I was playing around with stove a bit, and if we just go range vs. range, it seems that we can build a whooole lot of different kinds of ranges that meet the 47.9% equity vs opp as a whole. eg, any broadway, any pair, any connector, and a couple mid 1-gappers for 49% equity, or a2+, k3+, q4+, j5+,22+ for ~49% equity again. if we wanted to, we could even throw in 27o into the latter range, and only have our equity drop to 48.7%

so my question is this, with this sort of info in mind, what kind of range should we be calling with? obviously on one hand, for the specific situation, it makes sense to play a bit tighter to increase our equity for the single hand, but would it also make sense to adjust our range according to the table dynamic, for example, adding some mediore/bad hands to our range in order to make our table image more fishy, and thus inspiring more action from other opps at table, while still maintaining a greater than 47.9% equity for the given hand?

and if so, how do we decide which bad/mediocre hands to add into our range in this situation?

or is this instead a case where we need to look at our equity by specific hand, and make sure that each one maintains the 47.9% we need, with less consideration given to our range as a whole?


sorry if this is somewhat donk logic, but im interested in hearing thoughts on this

Originally Posted by Zorkion

how should we be designing our range to most effectively expolit this?

You want to maximize your EV, not find a range that has 47.9% equity. If you call with a range that has 47.9% equity, then your long term EV will be 0 in that spot.

So knowing that you want to maximize EV, you simply create a range that includes all hands that have are +EV individually. That's it -- leave out all other hands that are not +EV.

Awesome bump, and it made me lol, so +rep ldo.

Of course you're looking for hands that have x% equity against HIS range and not a range that breaks even.
In spoons best interest I have to tell you that math exercises cannot be answered with questions. There is a right answer and a wrong one, and not much in between. So sit your ass down and work on this because it's awesome.

roger that, captain. i feel a bit like facepalming now though xD