Preflop stacking ranges

[StoicSage]

I can not replicate the math

A quick worked example:
100BB deep
CO opens to 3.5BB
BTN 3bets to 12BB
BTN 3bets from BTN 4.7% (TT+,AQ+)(62 combos)

EV of 4bet and call of BTN shove:
Assume BTN shoves 1.4% (QQ+)(18 combos)

BTN folds 62-18 = 44 combos (71% of the time). CO net when BTN folds:
0.71 * (12BB + 3.5BB + 1.5BB) = 11.72BB

BTN shoves 18 combos (29% of the time). CO net when BTN shoves and CO calls
CO equity (QQ vs QQ+) is 21%
201.5BB * 0.21 = 42.32BB
CO invested 96.5BB to 4bet+shove, so CO net:
(42.32 - 96.5) * 0.29 = -15.71BB

Combining the two cases:
EV = 11.72BB -15.71BB = -3.99BB

This is worst than folding to the BTN 3bet (EV = -3.5BB).

I interpret the above to say that it is not EV positive to 4bet and call a shove against a 4.7% 3betting BTN with QQ. The table at the top of this thread says it's EV positive if BTN 3bets greater than 3%.

Where did my math/analysis/framing go wrong??

Thank you

 

[WVHillbilly]

A quick worked example:
100BB deep
CO opens to 3.5BB
BTN 3bets to 12BB
BTN 3bets from BTN 4.7% (TT+,AQ+)(62 combos)

EV of 4bet and call of BTN shove:
Assume BTN shoves 1.4% (QQ+)(18 combos)

BTN folds 62-18 = 44 combos (71% of the time). CO net when BTN folds:
0.71 * (12BB + 3.5BB + 1.5BB) = 11.72BB

BTN shoves 18 combos (29% of the time). CO net when BTN shoves and CO calls
CO equity (QQ vs QQ+) is 21%
201.5BB * 0.21 = 42.32BB
CO invested 96.5BB to 4bet+shove, so CO net:
(42.32 - 96.5) * 0.29 = -15.71BB

Combining the two cases:
EV = 11.72BB -15.71BB = -3.99BB

This is worst than folding to the BTN 3bet (EV = -3.5BB).

I interpret the above to say that it is not EV positive to 4bet and call a shove against a 4.7% 3betting BTN with QQ. The table at the top of this thread says it's EV positive if BTN 3bets greater than 3%.

Where did my math/analysis/framing go wrong??

Thank you

The error is bolded. You shouldn't be using 96.5 bb there. It should be whatever is left in the CO's stack after his 4bet (you didn't specify 4bet size so I can't complete the math).

 

[StoicSage]

Very different table then....

As I understand it....

If we include our 4bet in the dead money (sunk cost), then it's true that we've priced ourselves into calling, and that the call (of the shove) will be +EV.

However; the title of the table says we can show a profit by "4betting and calling" -- this (I think) is NOT correct. Assuming the 4bet is sunk means the table shows where we can "call a shove AFTER 4betting" (based on villain's 3betting rate) and be better off than folding (i.e., lose less than 20BB (our 23.5BB 4 bet less the sunk 3.5BB opening raise). Our 4bet can be terrible, yet once it's done we're priced in to a call (based on the table).

As my worked exampled showed, 4Betting QQ into a 4.7% 3better and stacking-off when they 5bet/shove is an -EV strategy if the 3 better is 5betting tight (e.g., QQ+).

Net, (my current understanding) is that the table tells you when you can stack-off (call 5bet shove) -- not when you can profitably 4bet (and shove)

 

[WVHillbilly]

You're wrong because of the folds you get when you 4bet.

 

[vinylspiros]

i just came across this thread, and in all honesty, i cant understand one word.

can someone be profitable at poker and not be able to do this kind of complex mathematical analysis?

I mean i understand what the chart says is best .But do i follow this chart religiously?

 

[tenbob]

i just came across this thread, and in all honesty, i cant understand one word.

can someone be profitable at poker and not be able to do this kind of complex mathematical analysis?

I mean i understand what the chart says is best .But do i follow this chart religiously?

IF you dont understand the maths of it then yes. If i remember it correctly you are not using any sort of tracking software, so it really wont apply to you if you dont understand the concept first.

 

[vinylspiros]

IF you dont understand the maths of it then yes. If i remember it correctly you are not using any sort of tracking software, so it really wont apply to you if you dont understand the concept first.

i understand what you mean bob. yes you remember correctly. I got to get that software in order to start understanding these concepts is basically what you mean right? I know that the normal 3 betting range is somewhere around 6% but i dont know what that would translate to in ranges. This chart is basically getting into 3 betting and 4 betting ranges, if im not mistaken but do you actually refer to this chart when making decisions always or is it just good to have next to your pc monitor for emergency situations was what i was trying to figure out.

 

[tenbob]

I use it all the time , especially against regs in btn vs blind raising wars. I mean if you open AQs standard on the button and a reg that has a 3bet % of 10, decides to 3 bet from the bb. Then 4 bet call off is standard, if that stat is 7, then just fold.

If you dont have tracking software and are relying on notes, then the chart will not make much sense to you, mainly because as you can see 1-2% makes the difference between shoving and folding in lots of spots.

 

[vinylspiros]

I use it all the time , especially against regs in btn vs blind raising wars. I mean if you open AQs standard on the button and a reg that has a 3bet % of 10, decides to 3 bet from the bb. Then 4 bet call off is standard, if that stat is 7, then just fold.

If you dont have tracking software and are relying on notes, then the chart will not make much sense to you, mainly because as you can see 1-2% makes the difference between shoving and folding in lots of spots.

Ok man, thanks for the help. I understand exactly what your saying. Ok enough said. Im going to focus on getting myself a tracker before getting into any further details on this. excellent thread chuckk and thnks alot bob.

 

[Aces2w1n]

Thanks for that graph... It's already helped me so much

 

[StoicSage]

Since the original table comes from an unknown source....

The table is clearly wrong. If you stack off with QQ vs a 3% 3Better that only shoves with QQ+ you will lose EV big time (QQ+ is 1.4% ...so it's just about 50% of his 3bet range. On 50% of his 3bet range you win the 3bet (13.5BB) and on 50% of his 3bet range you're playing for stacks with 21% equity (which is going to cost you way more than the 13.5BB you win when he folds).

Below is my effort at a table that assumes:
100BB deep
RFI of 3BB
3Bet of 9BB
(Note: Also assumes neither player is in the blinds. Also ignores rake)

This table only tells you if 4betting + calling a shove is mathematically +EV.

*AA: Any range
*KK: >3.7%
*AKs: >5.0%
*QQ: >5.9%
*AKo: >6.2%
*JJ: >7.3%
*TT: >9.5%
*AQs: >11.2%
*99: >11.8%
*AQo: >13.5%
*88: >14.2%


If you use 3.5BB and 12BB the values go down:

*AA: Any range
*KK: >3.2%
*AKs: >4.5%
*QQ: >5.0%
*AKo: >5.6%
*JJ: >6.4%
*TT: >8.3%
*AQs: >10.0%
*99: >10.4%
*AQo: >11.8%
*88: >12.5%


If we want to discuss this, lets examine a single case where there is a large difference between my tables and the original -- AQs.

Example math (3BB / 9BB case):

Villain 3bet 11.3% (148 combos).
Villain folds 50% (74 combos), so we win pot (1.5 + 3 + 9 = 13.5) 50% of the time.
Villain shoves with (88+, AQ+) (74 combos) , and our AQs has 40% equity against this range. We get back our equity in the whole pot (201.5 * 40% = 80.6) for a loss of 19.4.

Combining the two case we net (13.5 * .50) + (-19. 4 * .5) = -3BB

Since the initial raise of 3BB is sunk (dead money), -3BB net is our breakeven.

 

[WVHillbilly]

Bunch of wrong stuff

NO. Everything you have said above is wrong and OP is 100% correct.

You're considering the 4bet as money that's not already in the pot. That is incorrect and makes ALL of your math worthless. Anyone who reads it needs to know it's completely and totally wrong.

 

[vinylspiros]

NO. Everything you have said above is wrong and OP is 100% correct.

You're considering the 4bet as money that's not already in the pot. That is incorrect and makes ALL of your math worthless. Anyone who reads it needs to know it's completely and totally wrong.

someone is having bad day.

 

[WVHillbilly]

No, my day is going good actually. Just don't want anyone to use bad math to make their decisions.

 

[vinylspiros]

No, my day is going good actually. Just don't want anyone to use bad math to make their decisions.

i hear you WV. just joking around. If it is wrong than its definitely good that you cleared that out. I am the last person that would know if it was wrong or right.

 

[StoicSage]

THe question is what to use the table for

Dear WVHillBilly - thank you for the engagement.

I am looking to understand what you use the table for - and I think that is the source of our debate.

If you use it to decide if you should call a 5 bet shove after 4 betting, then the OP table is correct, and the 4 bet is dead money. It is then a table of "when you've priced yourself into calling the shove." This is useful. This also really does assume a particular size for the 4 bet (i.e., if you 4 bet to 60BB then you're priced into calling with 72o vs a 2.6% 3bet)

If it's a table for when it's +EV to 4 bet (with intent to call a shove), then the 4bet money is not dead - it's part of your decision. If you're 4 betting and always calling (when 5 bet), then the situation is 100% identical (from an outcomes perspective) to the case when you 4 bet shove and villain calls with the same range he would have shoved with. In this identical (outcomes) case it should be clear the 4 bet is not sunk.

Referring back to the example at the bottom of the tables I posted. If you 4 bet and call a shove with AQs vs a 10% 3 better 100 times in a row you'll end up with less than -300BB (since your 3BB raise is dead money).

Lets just count chips.....

Villain will fold 44 times. You will win the 13.5BB pot 44 times. Your stack when you win is 97 (100 less your 3BB raise). So after the 50 folds you'll have (13.5-3)*44 + 100 = 562BB

Villain will also shove (and you'll call) 56 times. You will have 40% equity vs. his stack off range (88+, AQ+). The pot has 201.5, so you get back 80.6BB. You have therefore lost (-19.4 * 56) = -1086BB

Your stack after 100 4 bets is 562BB - 1086BB = -524BB. If you just folded to the 3 bet 100% of the time you would have -300BB. So 4 betting AQs with the intent to always call a shove when 3 bet by a 10% 3 better is -EV.

I think the simplest way forward is for someone to correct the math above (if it's not correct) -- that is, answer the question how many chips will I have after 100 times of 4 betting and calling a shove with AQs vs a 10% 3 better.

 

[WVHillbilly]

The table simply refers to how wide a villain has to 3bet before we can profitably 4bet certain hands and then call if he shoves. That's it. Your mathematical error is in considering the 4bet like it's part of your stack when figuring the EV. It's not and using it in the EV equation is an error.

 

[StoicSage]

Now we understand...

Now we're reached the point where you (WVHillbilly) need to provide math as opposed to repeating something that is (likely) incorrect.

Chips are all that matter.

If you raise you have 97 chips left.

If you are 3bet by a 10% 3 better and hold AQs suited the OP table says you can 4 bet and call a shove profitably (which means you'll have more than 97 chips after doing so). I have shown above, this is not the case. You will have 94.76BB (on average) after doing so.

(Please also re-read my prior post where I show how supper -EV 4 betting QQ and then calling it off is to a 3 better that has 3% 3 betting range and a 1.4% stack-off range (QQ+). (EV is ~ -16BB!!!! Not positive like the OP table says)

 

[WVHillbilly]

Again your math is wrong because you're using the wrong number. Plug in the remaining stack AFTER the 4bet and you'll get it. Until then you're just doing it wrong.

 

[benevg]

i believe StS has a point there. there are two decision points in our hypothetical situation:
- when we decide if it is worth calling the 5bet shove after we 4bet;
- when we decide whether to 4bet/call;

in the first one, it is obviously +EV, and this is the point where WV seems to think we are.
but before we do the 4bet, that 19bb is still in our stack so it has to be included somehow in the decision we are about to make.

where he is wrong is in the math. i need to work a bit on this and i have no time right now, but just let me say that when we have AQ, the range {88+, AQ+} reads to me like about... 57 combos, not 74 (because of card removal). so all the math he posted is quite a bit off.

 

[StoicSage]

Card Removal...oh my...

Dear benevg,

Thank you -- you are totally correct that my analysis does not take into account card removal when determining the expected ratio (worst case ratio) of folds to shoves (it is taken into account in the equity calculation).

Of course, now the actual content of the villain's 3 betting range matters, since cards are removed from both his stack-off range (88+, AQ+) which goes from 74 to 57 combos, and from his 3bet/fold range . If his 3 bet fold range has the same proportion of combos removed, then the net result will be unchanged.

In my worked example of the breakeven point for AQs being a 3 bet of 11.3% things do change -- a little -- to 10.6%.

Redone math
Villain 3 bets 10.6% (141 combos)

vs AQs he stacks of on (88+, AQs+) which is 74 combos which become 57 combos after card removal.

vs AQs he folds with AJs-A9s,AJo,KTs+,KQo (only 7 combos),QTs+JTs,77-66 which is 72 combos which become 55 combos after card removal

Villain folds 49.1% (55/(55+57) and we win the pot of 13.5.
Villain shoves and we call 50.9% and we "win" 40% *201.5 - 100 = -19.7.

Net is .491 * 13.5 - .509 * 19.7 = -3.0

This is our EV breakeven since we had sunk 3BB (our initial raise).

So, my takeaways:

1) The OP table shows when you are priced into calling a 5bet shove (after you have already 4 bet -- NOT when you can 4 bet and then call 100% of villain's shoves. (I've checked this for a few cases, so I'm assuming it's correct for all of them.)

2) The tables I produced (prior post) are wrong because they do not account for card removal. In the specific case of AQs, the correct answer for when you can 4 bet and then call 100% of villain's shoves is 10.6% (vs. the 11.3% in my table above -- and vs. 8% in the OP table).

3) Producing the "correct" version of the table for when you can 4 bet and call 100% of villain's shoves is dependent on the content of villain's 3 bet / fold range. This range can vary a lot (Broadway, Axs, SC, ...) and will effect the net effect of the card removal adjustment.

4) I will try to create correct versions of the OP table for villain's that 3bet polarized -- as polarized as one can be 3 betting 10% ;-) and merged ranges. I think this will highlight the sensitivity (how ever great or small it is) to changes in villain's 3bet/fold range.

Again, thank you benevg for the helpful comment/correction.

 

[dj11]

A rather esoteric discussion that I almost understand. I love it tho. Very few members here will understand half of what I almost understand, which suggests that it will mostly be used wrongly. Certainly by me.

As for StoicSage, all 6 of his/your total post count (as of this moment) is ITT. Hell of a great way to start and introduce yourself SS.

And for the other great minds ITT, try to remember that the vast majority of members are going to look at this thread and scratch their head. References might help, or even just a few fewer abbreviations.

 

[Cafeman]

1) The OP table shows when you are priced into calling a 5bet shove (after you have already 4 bet -- NOT when you can 4 bet and then call 100% of villain's shoves. (I've checked this for a few cases, so I'm assuming it's correct for all of them.)

Yeah, I think this is key. I've not had time to work it out, but OP looks like the GTO of the 3bet/4bet/5bet game, you know, when you work out how not to lose according to optimal strategy pairs.

So busy with diverting an over flowing septic tank (I know, you're envious right) that I haven't got time to check out all the math, so I'm hoping you're all happy by the time I get back.

 

[vinylspiros]

Stoic stage should be working over at N.A.S.A in my opinion. im not even exagerating. I am just going to pretend this thread and all the posts i read in it do not exist because it makes me feel SLOW.

 

[StoicSage]

Final post -- Final table (I hope)

Assuming:

• Stacks 100BB deep
• Raiser and 3 better not in blinds
• Worst case 3 better's 5 bet shoving range
• 3bet range (hands in order that they're 3 bet):
  AA KK QQ JJ AKs TT AKo 99 AQs AQo 88 KQs ATs QJs KJs KTs AJs JTs QTs 77 66 AJo A9s KQo 55 K9s T9s J9s Q9s 44 A8s ATo 33 A7s A5s KJo 98s 22 A6s A9o A4s A3s T8s QJo (this is the shoving hand ranking from "Kill Everyone" by Lee Nelson et al.)

Taking into account:

• Card removal

Initial raiser can 4 bet and call a shove with +EV whenever villain's positional 3bet frequency exceeds that shown in the below table

Min villain 3bet %​

4bet hand 9BB 3bet 12BB 3bet

• AA......0.5%........0.5%
• KK......3.5%........2.6%
• QQ......5.1%........4.2%
• AKs.....5.9%........5.6%
• JJ........7.1%........5.9%
• AKo.....7.1%........6.5%
• TT........9.8%.......8.4%
• AQs....11.0%.......9.8%
• 99......11.5%.....10.1%
• AQo.. 12.7%.......11.5%
• AJs... 13.4%.......12.7%
• 88.... 15.1%.......13.4%
• 77.... 16.3%.......14.8%

Note: Percentages are approximate because I did not allow ranges with partial hands (e.g., 3 betting only 7 of the 12 KQo combos)
Note: Standard deviation of 3 bet percentage is approximately equal to 0.3/sqrt(N)….so if your HUD has data on 100 3 bet opportunities (from a given position) the standard deviation is .03 (i.e., +/-3%)

I really think this table replaces the table in OP. Please let me know if you find any errors