Math help needed! 5bet jamming
Posted by UpUpAndAway
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UpUpAndAway
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Mid Stakes
Math help needed! 5bet jamming
So I've encountered a few regs who open and 4bet quite exploitatively from the button versus the blinds. Many of them are opening about 50% OTB and 4betting 20% of the time.
I've started to get the ball rolling with math and ranges with what little I know about theory but would appreciate some advice on how to find the 'equity theshhold' so that I can crosscheck individual hands in my 3bet range to this 'equity theshhold' and, if they have equal or higher equity than needed I can 5bet jam them. I'm at a bit of a stand still at the moment but here's what I have so far....
Villain opens OTB 50% of hands.
Villain 4bets 20% of time.
Villain calls the 5bet jam with 4% of hands [AA-TT,AK] or 12.5% of opening range.
Since villain 4bets 20% of the time and 4% of his hands are for value, villain is 4bet bluffing 16% of the time
or a 4:1 bluff:value ratio. So villain will fold to a jam 80% of the time he 4bets and call 20%.
2/4 game:
Opens OTB to $8, hero 3bets to $32 from SB, BB folds, vilain 4bets to $78.
Assuming hero plays a 5bet/fold strategy OOP, villain risks $70 to win $32+8+4+70 with his bluffs.
$70/114=61%.
Villain breaks even 4betting ATC if hero folds 61% of the time and loses money if hero jams more than 39% of the time.
Assume hero 3bets 15% from the SB vs villain's button open 77+, A2s+, KTs+, QTs+, J9s+, T8s+, 97s+, 87s, ATo+, KQo].
In a vaacuum without villain adjusting yet, what range can hero profitably 5bet jam vs villain's 4bets?
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I would say if he is calling with a 12.5% range, then a 7% range should be profitable to jam.
Apart from this you need to remember that he is in position and will make every street to play extremely difficult.
But if hero is playing a 5bet/fold strategy, position shouldn't matter too much. How did you to your 7% range figure?
I think you chose a 4bet sizing that is slightly bigger than what is typical for a 4bet. Maybe more like $68 or $72. Doesn't change much but that means you have to be defending slightly more.
I'll definitely keep that in mind. You're right, my 4bet sizing example might be a bit too big.
Can anyone show the math for what % of my value hands (bonus: which value hands) I should be 5bet jamming? I think seeing how we got to the figure is more important than the figure itself since different ranges and %'s can be plugged into it depending on future villains.
I think you have some mistaskes in your calculation.
If Button opens 50% and 4bets 20%, then it is a 10% Range.
If he 4bet/call TT+,AK(3,47%), then he will bluff with a 6,53% range. Therfore he folds around 65% of the time to a shove.
If he folds so much (you need a big sample) then you could shove ATC.
Below is a cardrunnersEv calc.
Thanks Butcher, this looks great. But is the only way to figure out the math behind it through CREV or are there any math formulas we could do without the program?
I know my example's answer is shove ATC but I'de like to know how to do the math if many of the hands were closer....
Butcher is right. You could shove ATC against that strategy.
When you jam and he folds you win $78+32+4 = $114.
When you jam and he calls you have x% equity in a pot of $804 (assuming 100bb stacks and no rake, adjust accordingly).
If he's folding f%, then your EV is:
EV = (f)(114) + (1-f)(x*804 - 368) where $368 is the amount you're jamming
Then it's just plug in numbers and see. Using butcher's 3.5% 4b/c and 6.5% 4b/f, for f = 65% and using Excel to solve, you find that you can 5b jam any hand that has >19.5% equity vs his 4b/c range. So you can't quite jam any two cards - T3o-, 94o-, 83o-, 72o are -EV 5b jams - but you can certainly jam every hand you 3bet.
Awesome Steve, this is exactly what I was trying to figure out (with the shown math). I appreciate it!
Hey Steve Paul/others.
Dont we need 22,98%? Or where is the missing link? :)
EV = F * EVc + (1-F) * EVf (EVc = EV, when villain calls our jam, EVf = EV, when villain folds, F is the % of the time he calls)
We got some of the values:
EVf = 8 + 1 + 19,5 = 28,5
F = 46/133,2 = 34,53%
1 - F = 65,47 %
We can plug those in:
EV = 0,3453 * EVc + 0,6547 * 28,5 =>
0 = 0,3453 * EVc + 0,6547 * 28,5 =>
0 = 0,3453 * EVc + 18,66 =>
-18,66/0,3453 = EVc =>
EVc = -54,04
Which means, that we can jam hands, that we lose less than 54,04 big blinds.
We therefore need to win:
W = 45,96/201 = 22,87% (where W is the time we need to win).
PS. When we know that we need X% vs a given range, is there a smart program, that can show us, which range we can jam, since Equilab cant?
You have a mistake near the end:
We've already 3bet to 8bb so if we fold we'll have 92bb left. If we call any hand that loses less than 54.04bb, then we need to call any hand where W>(92-54.04)/201 or W>18.9%, with the small difference here probably being you using more accurate #s (I used 6.5%/3.5%).
Also, I found your method somewhat convoluted but maybe that's just personal preference.
If he's this weak, then calling will always have +EV too, and shoving should be measured against calling. Not that it matters really if he's this bad, just don't fold.
I have a hard time believing anyone plays this badly over a large sample and fails to adjust if you begin to jam a very high frequency. Seems like this is probably variance, since it will take a long time to accumulate a significant sample of positional 4b stats unless you play huge volume with this player.
Good points Ben. Believe it or not, the player in question is actually a winning reg with a 4k hand sample. 4bets 21% from the button vs blinds. 4k hands might not nearly be enough for a stat like this but I'm sure its definitely super high compared to the field.
And I think he will definitely adjust and since he's a good player, he'll likely adjust fairly quickly but I just wanted to see the math of shoving certain parts of my range so I can readjust accordingly to his adjustments.
sick thread here imo
i would guess that while the 4k hand sample isnt like completely significant it definitely shows some ideas in his strategy that we need to try to play well against?
This stat on 4k hands is the same as nothing.
Can you check how big the sample of button 4b hands is? 4k hands, so 666 buttons, say it's folded to you around 50% of the time (utg/hj/co open 15/20/25%), 333 raise opportunities. Raise ~50%, get 3bet around 25% of the time, so raise and face 3bet around 40 times. So it's probably something like he 4b 8/39 or 9/43 or something. Seems better than nothing but I wouldn't go using it to make huge adjustments.
I'll double check next time one of those players is on but IIRC it was indeed in the 40-50 sample range for that particular stat.
You can also check the sample size against anecdotal evidence: for instance a) his fold to 5b freq (if he folds very often to 5b, this supports a high freq of 4b bluffs), b) his showdown hands in 3b pots (if he shows down AQ/TT/JJ in 3b pots you can more heavily weight his 4b range to bluffs) and c) his showdown hands in 5b pots (if he shows down AQ/99-JJ in 5b pots then you can be more confident he's expanding his "value" range rather than bluffing too much d) you can just think about the player psychologically and guess at what sort of stuff he might be capable.
I've seen players with 4bet stats like this on the button as well. It could of course still be variance but if anything my guess is that it's a player adjusting explosively vs what he perceives to be a high 3bet% from us. So it's just up to us to counter adjust explosively and start 5bet jamming too much for a while. Then he will probably adjust back and so it goes on until we get to an eventual Nash equilibrium.
i guess id start by cutting out the bottomest parts of my sb v btn 3b range.. and then just start loling and piling over his 4bs a bunch more guessing it wont take that many 4b/folds for him to take a note and regress to a more standard strategy with his button opens
I've made an EV Calculation tab in Flop Inspector that lets you play around with each parameter of the calc and see how each part in the equation is affected as villains use different 4bet strategies. You can play around with it to find combinations of "equity threshold", "fold equity threshold" and 4bet sizings to see which 5bets are profitable. In your example you have a clear proceed with any two, and as Ben points out you should compare your EV shoving with your EV calling.
As it happens you can also find the EV of calling by estimating your realized equity for different types of flops using this brilliant software ;) In my example under I put in 77 vs 10% 4b range. You need to realize a total of 96% or more of your hand vs range equity to prefer calling the 4bet.
I play pretty much the percentages of villain and i'm not bluffing nearly as much as you have villain bluffing. Vs me you can shove roughly the same range I am calling so that means you can't shove to light. What ever your standard 5b ranges are I don't think you should change them but probably just call some 4bets instead.
Guys who 4b so frequently have typical 4b/calling range of AQo+, AJs+, 99 - and some guys go even wider and add AJo, ATs, 88.
Yeah his 4b/c range is definitely gonna be wider then TT+,AK.Like Sauce mentioned, no one is that stupid to not be aware of his image and adjust his ranges accordingly, especially a winning reg.Maybe not as wide as ^, but something like 99+,AQo+,AJs+.
From my experience regs adjust by 5b jamming very light/too light for it not to be okay to open up my 4b/c range. If you go atc or even axs and all pairs I think you will be spewing vs this player. I don't know what you 5bj jj+AK maybe but perhaps make it a bit wider and call some 4b with some ajs kqs hands as when you flop equity it will usually be very good equity vs this players range.
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