I’ve never been sold on the GTO hype but you make it make a lot of sense with your explanations. You grasp the “why” part of it and explain so most players can understand. Thanks for posting these.
That was very interesting. I didn't believe it that on a board like K74r you Xed most of the time with completely misses. Then I ran it myself in Flopzilla. It's right considering how players are calling today. I included all pairs and draws + Ace high + 2 card with BD draw. And it was absolutely right. They would be calling ~84-93% of the time depending on how loose they were. Really interesting. I was betting any 2 on a dry board 100% of the time. Even K72r doesn't change these numbers by much. WOW! 10 years ago players would fold a lot more. I learned something new.
I thought I would watch the video and hopefully pick up something new that I could easily implement in my game. Amazing information! I'm very happy with the simplified rules your provided. I never could figure out why certain hands were a bet out of position on various flops. That was until now. You've shed light on something I was lacking in my game. Thank you very much! I'm off to play at the casino and plan on practicing your recommendations.
Mr. Alvin thank you so much for making these videos. You are a beast & an incredibly efficient conveyor of dense information in an easy to digest manner.
This is amazing and indeed very useful. But this is just the first action on the flop, and the calculations are run for the entire tree. If you're unable to follow up on your bet/check correctly you might still end up ruining the entire strategy. By the way, have you tried to test some really weird looking c-bet strategies and see if the solver can still get close to equilibrium? Given that a lot of those hands should be mixed checks/bets on the flop, I wouldn't be surprised if you could do pretty much anything and "get away with it" as long as you play the rest of the tree perfectly.
about the rules number 2, we just proceed betting turns that we improve? or should we also bet on blanks? how about turn sizes? could you make a video with some clarification in capped ranges (atack/defense) spots? omg, sry i have asked too much.... =p u are awesome...
More or less, bet when the backdoors come in and check when they don't, yet. "Some clarification in capped ranges" is extremely vague and I don't really know what you mean?
It seems the strategy you put in while nodelocking was a mix of your heuristics and the optimal strat - not purely the stategy you wanted. Its because you selected fixed in both bet and check. I think you need to leave the check range set to proportional. This changes frequencies and EVs a bit.
No it doesnt, if you look at 7:46 timestamp for example 44/88/KK should be bet at the same percentage (75%) according to your strategy and they are not KK is at 69%, 88 at 81% and 44 at 77% - there is no card removal that would explain this. When you compare it to the 5:22 timestamp which shows the original strat, the strategy is different.
@@yegonsk oooouu good catch! I ran these the night before with "fixed" during prep, I probably forgot to during the real run. Fortunately, I didn't even notice the difference in EV change.
@@AlvinTeachesPoker Definately. But, I feel you missed the option of pointing that out in the video. People might leave thinking a flop simplification is all it takes. Good luck Alvin. Greatly enjoy your content.
God these videos show me that even if I'm currently a winning player results-wise, I'm really a massive fish because I'm not studying or labbing ANYTHING nearly this detailed or in depth. Gotta be intentional if I really wanna eventually be a high stakes crusher :/
Yeah, but hopefully the path is now clearer, I hope? Some people don't even know this work exists. My friends get told "solvers don't work" all the time.
Hahaha yeah this is the baseline. It's like asking how to play the first THREE moves of the Sicilian defense--you still need to study way more deeply if you want to be competitive.
I see pio likes to check QQ-99 a lot on this K-8-4 board,but some people say it is better to bet the lower pairs like 99-10 here rather than the QQ to deny equity to the over cards to those pairs.But i think these overcard type hands in the button would have 3 bet preflop anyway(AQ,AJ,QK etc) so we arent that afraid of them when button just flats. I would presume that when in position(say button v BB) we can bet more of the K-weaker kickers KJ-K9 and the middle pairs?As we can check back rivers or maybe check back turns to induce bluffs on the river.
Not sure how I found your channel but I'm glad I did :) The hardest and most subjective part of these simulations is selecting an appropriate range for villain. For example, you mention the first 13% range is a "GTO type range". Where do that come from since PIO does not solve for multi-way? Is this coming from a more abstracted software like Snowie or Monker? Are those other 13% bad-reg and 18% fish range your basic estimations of the field? I feel like if you don't get those inputs correct then all bets are off (no pun intended). I also remember you mentioning either a forum or discord channel. Can you remind me of that? Keep up the good vids!
wait did i get that right? you bet 100% of hands 1/3pot in position, no checking back range? whats the EV difference between a balanced checking strategy vs 100% bet?
This is a great video, thanks for that first of all! I am an MTT player, can this strategy be used for different stack sizes? What would be the adjustments?
Alvin, could you do a video on river calls/folds? If you could look at some basic rules on the river when you are OOP and face a bet 1/3, 1/2, Pot...from an opponent on paired boards with a straight run out like 3d9c9dKhTc. Thanks.
Wow, that's great strategy. Do you have similar strategy for wet boards? BTW, watched and liked every single video of yours. Waiting for more videos to watch and like.
Would it make sense to include some amount of BDFD+BDSD hands in our check-calling range on rainbow flops to ensure that we have enough check-raises versus IP double barrels on various turn cards? For me, my most frequent turn check-raise semi-bluffs are turned combo draws (FD+SD), but if I automatically C-bet all of my BDFD+BDSD hands on rainbow flops then I won't have any combo draws in my range heading into the turn. Hence I won't be able to find enough high equity bluffs and my turn check-raises will be heavily imbalanced towards value (usually turned two pair+) in these spots. Curious as to your thoughts on this!
Hey Alvin, very nice video. Is it possible to apply this rules to many OOP cbet scenarios? For example EP/MP opens where we have much tighter ranges. Also i loved your course keep it up.
This Cbet strat is for dry board. But for drawy board, do you play similarly as when you are IP ? Sorry if it's a stupid question, i play micro LOL ^^'
The conclusion that I'm drawing from your video is to split your range into: -bet value range(75% of the total 3 street hands) -bet bluff range( bdfd+bdsd/gu) -bet random hands(10%) xr range(some of the hands that aren't in the 75%,) xc range(hands that aren't 3 street worthy ex tpmk,some that aren t in the 75% ) Also I see we have no xr bluff range(although that is very V and board specific,so we take exploitative route there mostly). Is my undestanding correct?
Calculating the loss in EV from implimenting the simple strategy should be made using the 32 EV (optimal EV) and not the 65 (size of pot) right? so its like 1,25% and not 0,6% EV loss....right?
Does this also work on boards where there is a flushdraw or an openender? What do I do with my flushdraws or openender then? And: Does that also work on super wet boards?
Hey Alvin, Did you check the ev of 100% check? For example, on a K95 rainbow the ev of 100% check is greater than the strategy you've outlined. Or am I missing something?
Against various villains I'm sure depol check is very close or better! I just wanted to offer an alternative equilibria strategy to show there are multiple ways to approach the same spot that are both GTO and very reasonable to approximate in practice.
@@AlvinTeachesPoker Baron have ~20% cbet SRP vs CC free positions. Could you tell exact non-intuitive board where range check is really bad(considering that we are playing vs good reg)?
Ranges are much wider so both player’s ranges would be comprised of a higher % of ‘nothing’, that said SB has a pretty significant range adv. on A and K high card dry boards for which it can bet full range at 1/3 pot. From what ive studied SB favours the small cbet size vs BB on dry boards
Great video and thank you for the content. However i still do have 2 questions: -What sizing did you use as your cbet? (i am guessing it is 2/3 but i don't am sure) -Did you give the solver the option to use multiple sizes? For simplification purposes that may not be useful but we still need to look how much EV the solver can generate when he can choose his betsizes more freely. Shouldn't we try to get close to that number instead of the EV of 1 betsize that might not even be preferred by the solver? Keep up the work!
Look at about 2:35 and you can see how he’s setting up the bet sizes. Regarding multiple bet sizes, fwiw (seeing the issue discussed elsewhere) I’d guess the ev difference is less than 1%.
These are different lines with similar evs when applied in the correct spot. And oop I recommend mixing in quite a few spots, so this isn't different than what I recommend in say "adjustments for morons" so maybe you need to study the course up more?
Sorry, I wasn't trying to come off aggro, I literally thought you were familiar with the course material and was suggesting that I don't say to big size / check in oop, I certainly do! But I also want to be honest about my material: it's mostly a library of my existing work and is currently imperfect, and after looking at many preflop high rake solutions I'm going to have to recommend new, unorthodox ideas and admit where I was wrong or less accurate than before. It IS my hope, however, that because my work is a breathing document- obviously the side study group is "living" lololol--that I'll be able to update it with my best, top of line theory as my own knowledge improves. Even over the course of making this uh course, I leveled up dramatically. But I do really like this simplification as a baseline is common mix spots, yes. I also think depol check, as someone points out, is a very close or slightly "better" simplification, which I certainly recommend in, as I said above, the section "adjustments for morons" in my course. Wasn't calling YOU a moron, sorry if that was confusing!!!
@@AlvinTeachesPoker Cheers for the reply. I agree with the vast majority of content you put out and think you approach the game very intelligently. Look forward to seeing more :)
Hi Alvin, just came across your channel after struggling immensely to interpret some solver strategies... can I ask, how did you come up with these simplifications? Was it just through observation and trial and error?
Thousands of hours in piosolver by myself, because there wasn't good information at the time, and then watching nosebleed players to understand their best practices and trying to justify them in piosolver. I watched a lot of sauce123 two years ago returning to poker after years away, but 99% of coaches hold back their really secret sauce so you have to go digging for gold your own. Even in my own pay walled material, I can't possibly cover even the basics of exploitative play, it's so deep and theoretical while simultaneously being heavily flow related. That's what she said.
I just like to not flat a single raise preflop in live games at all, except in the blinds. The games I play has $1 preflop rake and flat 6$ postflop rake ($5 $10 blinds). Do you agree with my decision?
AlvinTeachesPoker thanks. I deal in ________ at a prominent casino. Just found your channel. I guess I am playing a bit of catch up. You have a wonderful channel. I plan on watching nearly all of your vids. And I wish u all the success.
Looking at the watch to pick what line you take sounds like a compulsive gambling maniac: "What time is it? It's BLUFF O'CLOCK BABY!" Nice video btw
Hahaha
I’ve never been sold on the GTO hype but you make it make a lot of sense with your explanations. You grasp the “why” part of it and explain so most players can understand. Thanks for posting these.
You're so welcome! Thanks for support across multiple videos!
Oh! You're LozGod on 2+2 as well lol. I randomly saw your avatar on a thread about blind defense.
That was very interesting. I didn't believe it that on a board like K74r you Xed most of the time with completely misses. Then I ran it myself in Flopzilla. It's right considering how players are calling today. I included all pairs and draws + Ace high + 2 card with BD draw. And it was absolutely right. They would be calling ~84-93% of the time depending on how loose they were.
Really interesting.
I was betting any 2 on a dry board 100% of the time. Even K72r doesn't change these numbers by much. WOW!
10 years ago players would fold a lot more.
I learned something new.
Insane analysis. This information is very valuable for you to start winning at poker, and you giving up for free. Very generous of you, God bless you.
I thought I would watch the video and hopefully pick up something new that I could easily implement in my game. Amazing information! I'm very happy with the simplified rules your provided. I never could figure out why certain hands were a bet out of position on various flops. That was until now. You've shed light on something I was lacking in my game. Thank you very much! I'm off to play at the casino and plan on practicing your recommendations.
Mr. Alvin thank you so much for making these videos. You are a beast & an incredibly efficient conveyor of dense information in an easy to digest manner.
This is amazing and indeed very useful. But this is just the first action on the flop, and the calculations are run for the entire tree. If you're unable to follow up on your bet/check correctly you might still end up ruining the entire strategy.
By the way, have you tried to test some really weird looking c-bet strategies and see if the solver can still get close to equilibrium? Given that a lot of those hands should be mixed checks/bets on the flop, I wouldn't be surprised if you could do pretty much anything and "get away with it" as long as you play the rest of the tree perfectly.
Very interesting simplification. Thanks, Alvin!
Easy game!
Excellent! Turn frequencies?
Another great video!!Cant wait to have enough saved for the overnight monster course.
Can't wait for you to join us!
dont know if u did join yet, but man i can tell you it's some awesome content/community :-)
Can you say a word about sizing heuristics? 1/3 vs 2/3 etc.?
Awesome video once again! Keep up the good work :)
tytyty!
about the rules number 2, we just proceed betting turns that we improve? or should we also bet on blanks? how about turn sizes?
could you make a video with some clarification in capped ranges (atack/defense) spots?
omg, sry i have asked too much.... =p
u are awesome...
More or less, bet when the backdoors come in and check when they don't, yet.
"Some clarification in capped ranges" is extremely vague and I don't really know what you mean?
It seems the strategy you put in while nodelocking was a mix of your heuristics and the optimal strat - not purely the stategy you wanted. Its because you selected fixed in both bet and check. I think you need to leave the check range set to proportional. This changes frequencies and EVs a bit.
No, it's that the strategy includes card removal after super-imposed.
No it doesnt, if you look at 7:46 timestamp for example 44/88/KK should be bet at the same percentage (75%) according to your strategy and they are not KK is at 69%, 88 at 81% and 44 at 77% - there is no card removal that would explain this. When you compare it to the 5:22 timestamp which shows the original strat, the strategy is different.
@@yegonsk oooouu good catch! I ran these the night before with "fixed" during prep, I probably forgot to during the real run. Fortunately, I didn't even notice the difference in EV change.
@@yegonsk but thank you!!! please continue to keep me honest. I certainly mess up small details (and sometimes not-so-small ones!)
Thank you very much Alvin!
How about c-betting on 3 bet pots OOP? Some advice please?
I thought more rake was better?
I like to sit there all loosey goosey eating a rake sandwich.
This is all very well, but the solver still has to employ a ridiculously mixed frequency strategy on the turn and river to fully capture that Ev.
Only if you don't know the technologies and heuristics to play the turn. 😏
@@AlvinTeachesPoker Definately. But, I feel you missed the option of pointing that out in the video. People might leave thinking a flop simplification is all it takes.
Good luck Alvin. Greatly enjoy your content.
hi alvin, can you do a video about small (30%ish) donkbets?
Great video please keep these coming! :D
Great video! What sizing(s) do you suggest cbetting OOP on such dry flops?
God these videos show me that even if I'm currently a winning player results-wise, I'm really a massive fish because I'm not studying or labbing ANYTHING nearly this detailed or in depth. Gotta be intentional if I really wanna eventually be a high stakes crusher :/
Yeah, but hopefully the path is now clearer, I hope? Some people don't even know this work exists. My friends get told "solvers don't work" all the time.
I love the bit where you commented 18% cc range would be ‘total fish’, man this is the live reg frequency at my local casino haha
Oh yeah that's the mark. :) I mean, FRIEND.
Of course there are many more Qs that you can follow up with looking at this scenario but a good framework to work with 👍
Hahaha yeah this is the baseline. It's like asking how to play the first THREE moves of the Sicilian defense--you still need to study way more deeply if you want to be competitive.
I see pio likes to check QQ-99 a lot on this K-8-4 board,but some people say it is better to bet the lower pairs like 99-10 here rather than the QQ to deny equity to the over cards to those pairs.But i think these overcard type hands in the button would have 3 bet preflop anyway(AQ,AJ,QK etc) so we arent that afraid of them when button just flats.
I would presume that when in position(say button v BB) we can bet more of the K-weaker kickers KJ-K9 and the middle pairs?As we can check back rivers or maybe check back turns to induce bluffs on the river.
Does this heuristic apply to Heads-Up 3 bet pots on dry boards?
No only srp!
Not sure how I found your channel but I'm glad I did :)
The hardest and most subjective part of these simulations is selecting an appropriate range for villain. For example, you mention the first 13% range is a "GTO type range". Where do that come from since PIO does not solve for multi-way? Is this coming from a more abstracted software like Snowie or Monker? Are those other 13% bad-reg and 18% fish range your basic estimations of the field? I feel like if you don't get those inputs correct then all bets are off (no pun intended).
I also remember you mentioning either a forum or discord channel. Can you remind me of that?
Keep up the good vids!
wait did i get that right? you bet 100% of hands 1/3pot in position, no checking back range? whats the EV difference between a balanced checking strategy vs 100% bet?
My man, you're going to love this channel. Start from the early videos and this will allll make sense.
@@AlvinTeachesPoker haha great plug
This is a great video, thanks for that first of all!
I am an MTT player, can this strategy be used for different stack sizes? What would be the adjustments?
Alvin, could you do a video on river calls/folds? If you could look at some basic rules on the river when you are OOP and face a bet 1/3, 1/2, Pot...from an opponent on paired boards with a straight run out like 3d9c9dKhTc. Thanks.
Too advanced to put out publicly, sorry! That's a private dance in the vip lounge.
Alvin, when you paste the hands with your simplified strategy.. Where did you copy them from?
this would be great to have an answer on this yes :)
Wow, that's great strategy. Do you have similar strategy for wet boards? BTW, watched and liked every single video of yours. Waiting for more videos to watch and like.
Wet boards are much, much more complex to describe.
Would it make sense to include some amount of BDFD+BDSD hands in our check-calling range on rainbow flops to ensure that we have enough check-raises versus IP double barrels on various turn cards? For me, my most frequent turn check-raise semi-bluffs are turned combo draws (FD+SD), but if I automatically C-bet all of my BDFD+BDSD hands on rainbow flops then I won't have any combo draws in my range heading into the turn. Hence I won't be able to find enough high equity bluffs and my turn check-raises will be heavily imbalanced towards value (usually turned two pair+) in these spots. Curious as to your thoughts on this!
Hey Alvin, very nice video. Is it possible to apply this rules to many OOP cbet scenarios? For example EP/MP opens where we have much tighter ranges. Also i loved your course keep it up.
Yes many situations that are similar. ;)
Would you say 1/3 pot OOP does not accomplish enough for us, therefore we should use a 2/3 sizing?
What about bluff check-raising range in this spot?
That's built into your range of course.
Hi Alvin that’s great, I’ll be experimenting with this and randomising with a watch + suits. Also what bet sizing would you take on the example above?
66 percent!
This Cbet strat is for dry board. But for drawy board, do you play similarly as when you are IP ?
Sorry if it's a stupid question, i play micro LOL ^^'
The conclusion that I'm drawing from your video is to split your range into:
-bet value range(75% of the total 3 street hands)
-bet bluff range( bdfd+bdsd/gu)
-bet random hands(10%)
xr range(some of the hands that aren't in the 75%,)
xc range(hands that aren't 3 street worthy ex tpmk,some that aren t in the 75% )
Also I see we have no xr bluff range(although that is very V and board specific,so we take exploitative route there mostly).
Is my undestanding correct?
Why do we not have a xr bluff range? Did I say that on accident? No, we can definitely xr hands like bottom pair no kicker or qjhh on sdc.
@@AlvinTeachesPoker Does anyone know what sdc stands for?
@@vladvostok4785 spade diamond club
Calculating the loss in EV from implimenting the simple strategy should be made using the 32 EV (optimal EV) and not the 65 (size of pot) right? so its like 1,25% and not 0,6% EV loss....right?
Does this also work on boards where there is a flushdraw or an openender? What do I do with my flushdraws or openender then?
And: Does that also work on super wet boards?
No it's for one particular texture. This doesn't apply everywhere!
Hey Alvin,
Did you check the ev of 100% check? For example, on a K95 rainbow the ev of 100% check is greater than the strategy you've outlined. Or am I missing something?
Against various villains I'm sure depol check is very close or better! I just wanted to offer an alternative equilibria strategy to show there are multiple ways to approach the same spot that are both GTO and very reasonable to approximate in practice.
Thank you, thank you, its a great help!
Hopefully this is getting clearer and clearer now???
@@AlvinTeachesPoker It is, Im still no better than break even after 80k hands but my understanding is growing thanks to your help.
Hi Alvin, where/how did you construct those calling ranges preflop for the button?
One of them is from a GTO pack / solver solution, the rest are just scenarios and reasonable ranges I invented to test various bad-reg types.
Nice vid! Any way to extrapolate this to 3 or 4 way spots? I imagine cbet freq drops even more?
I might be playing with a multiway solver soon!
How bad is range check here? Especially vs 4-8% cc? I tend to not cbet at all in these situations
On some boards, probably really bad
@@AlvinTeachesPoker Baron have ~20% cbet SRP vs CC free positions. Could you tell exact non-intuitive board where range check is really bad(considering that we are playing vs good reg)?
is the bet size 2/3 pot? thanks
yes, it's shown in the models
can you do something like this but when in position
Great video!
Thank you!
thanks for your continued support!
Could you do this SB vs BB in SB's perspective?
Ranges are much wider so both player’s ranges would be comprised of a higher % of ‘nothing’,
that said SB has a pretty significant range adv. on A and K high card dry boards for which it can bet full range at 1/3 pot. From what ive studied SB favours the small cbet size vs BB on dry boards
For Q high dry SB mixes in 15% check and J high dry it’s mixing in 30% check
should we use multiple sizes on the flop out of position??
You can, but you really don't have to except for specific situations.
Great video and thank you for the content.
However i still do have 2 questions:
-What sizing did you use as your cbet? (i am guessing it is 2/3 but i don't am sure)
-Did you give the solver the option to use multiple sizes? For simplification purposes that may not be useful but we still need to look how much EV the solver can generate when he can choose his betsizes more freely. Shouldn't we try to get close to that number instead of the EV of 1 betsize that might not even be preferred by the solver?
Keep up the work!
Look at about 2:35 and you can see how he’s setting up the bet sizes. Regarding multiple bet sizes, fwiw (seeing the issue discussed elsewhere) I’d guess the ev difference is less than 1%.
@@ewallt huh? he's using 66% F T R and the sizes DO matter because all these sims are being solving using this sizing alone
I'm a bit confused given your cbet strategy in the overnight monster course is different? Do you mind PMing me which one you prefer?
These are different lines with similar evs when applied in the correct spot. And oop I recommend mixing in quite a few spots, so this isn't different than what I recommend in say "adjustments for morons" so maybe you need to study the course up more?
Henry from runitonce?
Sorry, I wasn't trying to come off aggro, I literally thought you were familiar with the course material and was suggesting that I don't say to big size / check in oop, I certainly do!
But I also want to be honest about my material: it's mostly a library of my existing work and is currently imperfect, and after looking at many preflop high rake solutions I'm going to have to recommend new, unorthodox ideas and admit where I was wrong or less accurate than before. It IS my hope, however, that because my work is a breathing document- obviously the side study group is "living" lololol--that I'll be able to update it with my best, top of line theory as my own knowledge improves. Even over the course of making this uh course, I leveled up dramatically.
But I do really like this simplification as a baseline is common mix spots, yes. I also think depol check, as someone points out, is a very close or slightly "better" simplification, which I certainly recommend in, as I said above, the section "adjustments for morons" in my course. Wasn't calling YOU a moron, sorry if that was confusing!!!
@@AlvinTeachesPoker Cheers for the reply. I agree with the vast majority of content you put out and think you approach the game very intelligently. Look forward to seeing more :)
Hi Alvin, just came across your channel after struggling immensely to interpret some solver strategies... can I ask, how did you come up with these simplifications? Was it just through observation and trial and error?
Thousands of hours in piosolver by myself, because there wasn't good information at the time, and then watching nosebleed players to understand their best practices and trying to justify them in piosolver. I watched a lot of sauce123 two years ago returning to poker after years away, but 99% of coaches hold back their really secret sauce so you have to go digging for gold your own. Even in my own pay walled material, I can't possibly cover even the basics of exploitative play, it's so deep and theoretical while simultaneously being heavily flow related. That's what she said.
Is this viable strategy for 10NL zoom?
Why would it not be?
Why is the 18% total fish range so bad if it makes the same EV as 13%?
Because it doesn't win as much as it contributes. More often.
The button should play to make money, not prevent you from making money. Agree?
Sure, Flatting becomes pretty bad in the presence of rake in general. It makes the raiser and caller both lose because it's not zero sum.
There is also the added chance of over-call from the blinds with multi-way playable hands and squeeze from them.
I just like to not flat a single raise preflop in live games at all, except in the blinds. The games I play has $1 preflop rake and flat 6$ postflop rake ($5 $10 blinds). Do you agree with my decision?
Is PioSolver your preferred solver?
Yeah, though I might review another slightly less common one soon
Is this what your course is like?
Yeah, it's about shortcuts to try and get close to ev as a baseline, and then understanding where and when to deviate.
@@AlvinTeachesPoker I like it - I'm saving up my pennies. Really appreciate your videos
What does gto mean? Just subbed, new viewer
Game theory optimal!
AlvinTeachesPoker thanks. I deal in ________ at a prominent casino. Just found your channel. I guess I am playing a bit of catch up. You have a wonderful channel. I plan on watching nearly all of your vids. And I wish u all the success.
I did not understand, you recommend 67% cbet here with that strategy?
67% bet size
I think a balance under betting post would be ideal
Good luck with that. Sounds too difficult for my puny brain.