'balance'

Pre-flop, the most common and sensical arrangements are to swap or 'shift' connectors with high ranks, and change as your opponent catches on.  This is true IP and OOP.  There are other ways to tweak these ranges, but your options are more limited because pre-flop your choices are to call or raise (i.e. not to check, check-raise, donk-bet, etc).

Post-flop it gets interesting.  The cool thing is, though, that no matter where you make decisions post-flop, your options are all the same (with slight differences IP vs. OOP).  For example, if you check-call the flop, this provides you with options for a calling arrangement.  If you're VBetting the flop (you must then consider your opponent's current 'arrangement' which I sometimes refer to as a snapshot or strategy) and they raise and you call, your range that was your VBetting range now becomes your calling range, and has it's own arrangement with all the same components/options as any other time you call!

Before we get into all the arrangements, there's one more concept that's important to understand.  While value and bluffs can be swapped (by the way this is what people refer to as 'balance' except that many people think this means do both in proportion all the time, when really you should go back and forth using the same size range for cover; these balances are meant to be tipped!) to exploit how much your opponent calls/folds, the CR is a tool, specifically OOP, to implement when you need to control how much your opponent CBets each street with their marginal value (you can control their bluff % just by your calls, but then they can exploit your bluff catchers with their value, so this is when you need the CR).

The balance with the CR is how much you do it; i.e. how much you add/remove it from your checking range.

Within the CR is another balance: how much you CR with value vs. how much you CR with bluffs (or semi-bluffs).

And a third balance being check-call/check-fold.

A visual would be a large balance containing two smaller balances on each side:   

_CR-V__________CR-B_            C-C                 C-F    

                  ^                                          ^                   

                                         ^

There are actually many ways to arrange the balances (what it actually is is a decision tree), but the above isn't how I'm going to view it actually.  I'm going to put the hands that continue on one side, and the folds on the other.  I'm also going to try to keep the typically larger groups as main branches on the tree.  Lastly, I'm going to incorporate into my diagram the betting (VBets & Bluffs) hands.

Here's the tree when you have the option to bet or check OOP (note: when you check, you are also deciding what to do afterwards if your opponent bets since that will decide the EV of your check, and that your opponent may also check behind, which also contributes to your EV).  Also note: 64 possible combinations of arrangements if it's all or none when tipping each balance:

_CR-V_____CR-B_     C-C lower   C-C higher           

              ^                                 ^           

                                ^                                       C-F 

                                                         ^                               Opp Check       Bluff        V-Bet          
                                                                                 ^                                        ^    
                                                                                                            ^

By the way, this previous one would be built on another one for pre-flop ranges of either 3-bet connectors or top ranks!

Here's the tree when you have the option to bet or check IP (4 combinations of possible arrangements):

                   Bluff-Bet        V-Bet          
Check                         ^      
               ^


Here's the tree when you're facing a bet IP (note: if you're OOP, you're using the first tree where you check with a decision of what you'll do afterwards).  Also note there are 16 combinations of arrangements:

                    Call-Lower             Call-Higher               Bluff-Raise          V-Raise  
                                         ^                                                         ^  
 Fold                                                              ^   

               ^

I'll address the Call-Lower/Higher in depth later on.  There's a bit of an exception to the 'balance' model on that one; basically when you call, you can call more by either calling with more bluff-catchers (lower side of your calling range, instead of folding it) or call with more of your higher value hands (higher side of your calling range, instead of betting it).  And in fact, it's an even more special exception because you can do both at once; in the model, this would be like keeping the Call-Lower and Call-Higher balance level, while the whole side of the balance underneath it was heavier.

Here are some perhaps familiar and/or frustrating arrangements you and/or your opponent might have.  Later I'll provide some visuals and math behind them, and talk about which ones exploit which ones / how to adapt to each.  I'll also go through every possible/relevant arrangement so as to not leave anything without being addressed:

A)  (opp is OOP) Your opponent bluffs > pot odds by a lot, and starts calling with at least some of their stronger value.

B)  (opp is IP) Your opponent VBets a much wider range than 50% of value on the board (ex: BP+) and practically stops bluffing.

C)  Your opponent both VBets and bluffs a ton (i.e. they CBet 100%).

D)  (opp is OOP) Your opponent checks a very wide range, calling a lot, almost not folding at all, and they CR all their value hands.

E)  (opp is IP) They CBet low value and best value, but check behind medium value and bluff-catching range.

If you noticed in the example scenarios above, I also compared the ranges to the pot odds, as well as to a 50% amount; these are common thresholds that must be considered when you decide 'how far' to tip each balance.

Ok, that's it for this post.  In a coming post I'll go through each arrangement and how to exploit it.

exploiting GTO

In my previous post I talked about the 2 poker rules to 'triage' your game, now we need to follow up and adapt.

GTO (Game Theory Optimal) is something talked about as a style of play, contrasted by Exploitation of non-GTO play as another style.  But I don't believe there actually is GTO unless you allow there to be.  In order for there to be GTO, your opponent must know what ranges you're playing with (note: I'm not saying what hands you have at any given moment, but what range of hands you have).

Going back to the calling but folding > pot odds so that your opponent should bluff, this is assuming they are bluffing at all.  If they're not, you should never call with bluff catchers because they're losing value to your opponent's made hands.  Similarly, if they would bluff just as much if you never folded, you should call with 100% of your bluff catchers.

Again with your own bluffing, if your opponent never folds, you should never bluff (note: until they change by perhaps folding to all your value bets!).  Similarly, if they will always fold too much, you should only bluff (maybe start calling with your value hands instead since otherwise your opponent will fold to your VBets and you'll make nothing from your made hands; more on this in a moment).

What I'm describing is basically how to exploit a GTO player.  All I said with the 2 rules is that your opponent can't exploit you by their bluffs or bluff catchers.  I never said they couldn't exploit you with their value hands.

Pre-flop is the perfect time to knock a 'GTO' player out of any GTO advantage.  OOP is a commonly recognized scenario when you 3-bet.  If you 3-bet with your top 20% (my recommended range) they may start folding (until they do fold, you profit though).  Once they start folding, start 3-betting your connectors and suited connectors 20% of the time, but not your top 20% anymore.  They'll then be folding to your 'bluffs' (which will sometimes still improve and win you a big pot because your opponent didn't put you on that range).  This argument holds true for the SB open-raise too, but with different % amounts.

Why 20% OOP pre-flop?  Because your opponent cannot effectively call you don't when even 1 paint card comes on the flop (note: top 30% is close, so I'd be ok with that too as desired).  This brings up range shifting.  When you move one hand type from one of your ranges (ex: pre-call, flop bet with draws made from connectors) to another range (ex: 3-bet pre-flop OOP), then what happens to your other range?  Well, in this example, you put your higher value in place of the connectors, and vice versa.  Here's an important concept: they can't be in both places at once.

There are common 'arrangements' of hands, such as connectors in the 3-betting and top 20% in the pre-call range.  There are similarly arrangements post-flop.  My next post will discuss these and more.

2 poker rules to be inexploitable, and more

This post may be a little out of order from other things I have posted and will post, but those other things are on paper, and I've got to get some thoughts down.

There are 2 things you can do to instantly plug any major holes in your game; this may be more true for HE LHE than other forms, but in theory can be considered to guide actions in other forms as well.  Note that these 2 'triage' rules require understanding/application of the >= 50% value 'rule' I posted before with my scanned post-it notes.

i) When in a calling scenario (i.e. your opp. is betting), you should fold enough to make their bluffs correct (while folding < 50% effectively by the river, i.e. 'absolute' % from the beginning of the hand).

Why?  a)  If they do bluff, you still collect those bets with your value hands, which is > 50% of the time.  This means it's impossible for you to actually lose money because of your opponent's bluffs (you may not be calling optimally if your opponent is always/never bluffing for example, but you won't effectively ever lose money in the hand from calling the wrong amount vs. bluffs by your opponent). b)  If they do NOT bluff (i.e. they check), then your bluff catchers will win at showdown.

ii)  When in a betting scenario (i.e. you are betting), you should bluff enough to make it correct for your opponent to call (while not bluffing >= 50% effectively by the river, i.e. 'absolute' % from the beginning of the hand).

Why?  If they do call (i.e. with bluff catchers), they're also calling vs. your value hands > 50% of the time.  If they do NOT call, then your bluffs are profiting from their folds.

This brings up an important theoretical understanding of where profit comes from.  When you bluff, you are effectively NOT profiting.  You are putting in more than 50% of the bets any time they fold (i.e. you are risking > 50% to win < 50%).  So when they call down > 50% (i.e. as they should, just like I recommend you do), you end up putting in more bets that lose (from the start of the hand) vs. their calling range than you ever make vs. their folds.  In this way (here's the important theoretical statement...) bluffs do not profit, they only reduce your loss.

This being said, reducing loss is important.  If you don't bluff, you'll effectively forfeit (lose) all the bets you put in with the hand so far, as opposed to a % of the bets you put in so far.  Also, if you stop bluffing, your opponent can then make correct folds when you do bet.  Remember, when you put money in pre-flop your hand had the equity to do so, so you didn't actually start out losing money.  You can't ever know you had a 'bluffing' hand until post-flop (ex: Q7 is a fine hand, but if the board comes AJ2 it's now a bluffing hand).  But when you do realize it, you are then trying to salvage money already spent.

Lastly, bluffing is important because you should be doing so with the hands that can't stand a showdown, but out of that group the ones that have the most equity; this way the longer you stay in (i.e. by bluffing), you will also make more hands that can end up seeing a showdown, in addition to the times your opponent folds and you wouldn't have improved (which of course you can't know before you bet).  To summarize this, when you bluff, you win in 2 ways, when: a) they fold, b) they call but you improve.

Ok, I'll stop there for this post.

What to do if the SB splits their pre-flop range, and more.

If the SB splits their pre-flop range (which the BB can do by sometimes 3-betting, or sometimes raising vs. a limp) you must play differently than if they either open-raise or fold pre-flop.  (There is also, by the way, great benefit vs. 'good' players who don't fold their BB too often pre-flop to sometimes open-limping, and other times open-raising; I'll discuss this second).

Scenario A)  If the SB raising range is stronger, you play vs. that range as you would if they played an open-raise/open-fold strategy.

Scenario B)  But if the SB raises with weaker hands (after making you think they're doing it only with strong hands) to gain fold equity, you must become aware of this and adjust.  Vs. this range, you'll be able to...

1)  call down a lot more with stronger made hands on higher boards (since your opponent will think they have bluff/fold equity).

2)  You can also VBet on lower flops since they'll have lower pairs using the same board cards.

3)  Play your range that matches their now-stronger limping range vs. their range as you would if they open-raised (except of course adjust for a smaller pot size/lower odds) using your matching range.

4)  You'll then need to just ditch a lot of your worse hands since they don't play well vs. your opponent's strong limping range, but that's ok because you saved money vs. if they had open-raised forcing you to call!  Plus you'll make more than that back since their lower hands are going in for twice as much money, plus worse odds throughout the hand as mentioned above.

Simply swap these above scenarios (A and B) if they shift their ranges back to open-raising with strong hands, and open-limping with weak.

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

This range-splitting can be good if your opponent doesn't realize it's happening right away.  Vs. observant opponents it's not a good idea (because of how terrible it performs if your opponent does what I just described above), but if they don't adjust and fall for your range swapping, you'll make a good profit.  Pre-flop it's tough to pull this off, though, because it's pretty visible once they see one of your hands at showdown.  But if hands aren't going to showdown, that means it's probably working (i.e. they're folding to your raises with junk), so keep it up.

This bring up an aside: why should I not open-raise or call pre-flop 100%?  For the same reason as above: it's pretty obvious if you never fold that you're playing 100% of your hands, thus allowing your opponent to play vs. your range as a whole perfectly.  If you open-raise 90%, then 75%, then 90% again, it's tougher for them to know exactly how tight you're raising, and so they won't be able to play perfectly.

Lastly, BB 3-betting pre-flop is the same idea as the SB range swapping.  You want to sometimes 3-bet with strong hands, then sometimes with weaker hands.  But don't do both together as you do on the flop (where you maintain > 50% value to showdown) because you can't guarantee to have any specific amount of  top combos on the flop (i.e. sometimes you'll hit with your pre-flop 3-bet 'bluff' hands like 87s perhaps, and the flop is KJ8).*  You need to change it back and forth as in the SB example above.

*note:  if the SB will let you 3-bet (without them capping), a somewhat effective strategy could be for you to check the flop sometimes, and others CBet as you would split your ranges if you had just called pre-flop, and sometimes VBet/bluff, and other times check-call.  The reason this can be good is that it does allow you to get 1 extra small bet in pre-flop with your better hands and still get your flop bet in too.  Conversely it does make it harder for your bluffs to succeed...

...because splitting up your ranges, then deciding how to proceed on the flop is much more complex than simply calling 100% pre-flop from the BB, this is why it's very opponent-dependent.  If they play poorly enough vs. your 3-bets, it can be worth sacrificing some 'correct' plays (because it's more complex you'll make plays that are sub-optimal) to gain value from their mistakes.  An example would be if they fold way too much and allow you to 3-bet with garbage and bluff them off many pots.

Couldn't sleep, more poker.

As I'm sure everyone interested in Poker has heard, we may be getting our Full Tilt money back.  Hopefully the U.S. will soon host online poker too.  And when the hoards of fish come, I'll be ready.  :)

My cat was sick last night, and I ended up not sleeping much.  Instead I worked on poker in my head.  Came up with a few things...

1)  The first person to tighten their range (ex: pre-flop would be a good spot) has the advantage if the other person doesn't adjust, since they'll be behind throughout the rest of the hand.  There are 4 good scenarios to show what happens.  Take for example the SB open-raising tighter (say 60% instead of 90% suddenly).

a)  BB is behind on higher made hands vs. SB made hands.

b)  BB is ahead on lower made hands vs. SB air.

c)  BB is unable to bluff on lower flops vs. SB air.

d)  BB must fold more often vs. SB bets.

Recourse #I:

i)  BB should VBet made hands more on the lower flops.
ii)  BB should bluff less (both on high flops because SB has a hand more often, and on low flops because SB will be calling with HC more)
iii)  BB should fold more/not call down as readily with bluff-catchers (high & low flops, because SB more often has even better HC hands than your bluff-catchers).

Recourse #II:   My preference

The BB (in the above example) can avoid having to worry about any of these adaptations if they simply contract their pre-flop calling range to match the SB open-raising range (if the SB folds when they don't raise).  You can always 'match' the folding frequency of the SB, and lose very little in the process.  Example: opponent folds bottom 10%, you gain their 0.25 big bets = +0.025 bb.  You fold 10% of the remaining 90% and lose your 0.5 bb blind = - 0.045 bb.  That's a net of 0.025 - 0.045 = - 0.02 bb.

The pattern, at 50%, wil be EV = 0.  You gain 0.25 the 50% they fold = + 0.125 bb.  You lose 0.5 bb 50% of the time you fold to their 50% open-raise = - 0.125 bb, so EV = 0.

After that you'd be ahead, except that by that point your opponent shows an immediate profit by open-raising and could decide at that point to not ever continue, and they'd always be ahead in EV.  It would be very odd to see an opponent open-raise less than 50% from the SB, and if you did, you could certainly find ways to exploit that.

So your EV is somewhere between 0.02 bb and 0 if you match their pre-flop folding % when you're in the BB.  In my opinion, this is worth it so as to not have to severely adjust my post-flop approach.

Your post-flop hands, then, will be able to be played 'normally' as you would if your opponent simply raised 100% pre-flop and you called 100%.  To explain: your VBet range will, on average, match your opponents on the flop.  This will give your bluffs credibility (i.e. it's balanced), and will allow you to call down with HC hands on lower flops still because your opponents won't on average have better HC hands than you.

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


Quick update to my 'notes' post (scanned notes).  VBet range should be 75% made, 25% draws (roughly) so that vs. a raise, by the river I can drop the 25% draws, and then also 25% points of the made, and still have 50% of the made hands range.

My poker notes (literally)

I've had poker thoughts brewing in my head for a while; things I could almost see, like images.  Was actually giving me a headache as they swirled around, but couldn't quite gel.

Pieces finally started snapping into place today, and with each piece the others came faster, until they all were totally lucid, and I quickly scratched them down.  Too tired to put them into electronic form today other than scanning them.  Plus I thought it would be cool to have these available to look back on...

...they're my most comprehensive, important thoughts to date.  I'm sure of this because I've both used them in part at high-stakes HU LHE play with great success, and the rest of them directly relate to those that I've used.

So, without any more talk, if you can decipher them, then congrats - feel free to use them in your HU LHE game!  Otherwise you may have to purchase my future book :)

Lastly, a few extra things:

These are specifically for HU LHE; some things I'm fairly sure don't apply to other forms.

Bluffs don't make profit; they recoup loss they've already incurred.  They always lose value effectively.

VBets and VCalls are the only places to make value.

Things still needing to be addressed:

What happens with pre-flop contractions/expansions of ranges IP and OOP?

Also, I'd like to develop a way to play both sides of a match against myself, so I can always practice with somebody who wants to 'train,' i.e. myself.

flop donk > CR ? I think it's likely.

I've got 5 reasons why I think a flop donk is better than a CR when OOP in HU LHE. Here they are, in order from my rough estimate of importance, from lesser to greatest: 5) by acting first, you force your opponent to choose the correct response 100% of the time, and since no player is perfect, you force them to make the first mistake. 4) I actually WANT the times that I check/check-call the flop/turn to be exploitable, where I'll often call the flop but then fold the turn. This will encourage my opponent to CBet-bluff the turn, which allows me to then shift otherwise VBet hands into my check-calling range to gain value (while bluffing more in my betting range), and then to shift those hands back if they catch on, allowing my weak hands to get free cards on the turn (and then VBetting more strongly when they're then calling more often vs. my donks). If I CR the flop, I don't have any options to incentivize my opponent to make these mistakes. 3) your opponent never has an option to simply check back the flop or turn to realize more equity with hands you want to VBet/protection bet against (like AH/KH hands, or QH with a GS, etc). (note: even if they raise the flop for a free turn card, then they'll run into my #1 point below). This becomes an even greater issue if they tighten up pre-flop and have a higher % of HC hands on average when there's a lower flop/turn. 2) you're getting 20% price on the flop for pure-bluffs instead of 33%, which I feel is more important than getting extra value from value CR on the flop since in the end, VBets/raises are EV neutral. 1) you force your opponent to put in extra bets for a bluff raise, giving yourself either 2:1 profit on your own Value:Bluffs if they raise the flop, or 2.5:1.5 if they raise the turn. This means you can get paid off on your value hands from their bluffs at a higher price to them, which allows you to bluff twice as often as you VBet (in the 2:1 structure). Ex: if you VBet (donk) 20% of the time on the flop, you can donk-bluff as much as 40% of the time, while if they try to bluff-raise the flop, in small bets your EV = 2(0.2) - 1(0.4) = 0. For a flop CR, you're getting 3:2 on both either the flop or turn, which if you V-CR 20% leaves you with EV = 3(.2) - 2(.3) = 0 for EV neutral, showing you can only bluff max 30% of the time. This feeds back into point #2 above, where not only can you bluff more often, but those bluffs are then more profitable.