Page 276 suggests betting 25% pot on a brick turn when our opponent checks to us after check-raising the flop. Aren't we pricing him in to check-call his draws here?

Going to answer the simpler questions now, been kind of busy but will get to the tougher ones at a later time.

Probably, but it's pretty common to be unable to make our opponent's draws +EV and if he CR the flop he probably has a pretty polarized check-raising range and not all that many draws. The general idea that is on board textures where the opponent will have a difficult time check-calling (such as on semi-drawy boards where our opponent's range is pretty polarized) we can make our bets smaller and that will make our opponent's check-raises less effective.

If you think the opponent's range has a fair amount of draws then I'd just bet a bit bigger, but still try to bet reasonably small if his range is polarized and we're betting a lot of marginally strong hands that will hate facing a check-raise.

This is pretty much just the same thing as a spot where you turn a made hand into a bluff. If your range is very strong every line will be +EV (both betting and checking with the intention to check-fold), but since your range is stronger than your opponent's he'll fold a lot to a bet. So this means we should value bet our best hands and bluff with hands near the bottom of our range (or hands that aren't very strong and have very good removal effects).

It'd be really hard to get to the river with a "merged" range, fwiw, but you can definitely get to the river with a range much better than your opponent's if you just get very good turn and/or river cards.

Damn, my question didnt fall into the easier category lol, thanks for still being active in this thread Matt, i think thats awesome of u

It is really hard to answer these questions without writing down a ton of text. I'll do my best here and hopefully it will clear things up a bit, but these aren't questions that can really be answered without writing a couple pages.

1) We can't calculate the EV of opening any hand, so I believe you are referring to our overall EV once we've been called. In other words, using the numbers in the book if we open the bottom hand in our range and are called, we should expect to lose overall less than -0.29BB for the hand for opening to be profitable. If we are losing less money than this when our worst open is called (i.e. our post-flop EV is higher), than we should open wider. If we are losing more money than this than we should open a tighter range.

2) There's no way to calculate the EV of our hand post-flop. It depends not only on the strength of our hand, but also the strength of the opponent's range and the strength of our range. For example, a very weak hand in our range might actually be able to make ++EV bet provided our range is very very strong. Yet a reasonably strong hand in our range might actually be only marginally +EV if our range is overall very weak and our opponent can bet very aggressively and likely outdraw us with his bluffs.

3) You can never make the opponent's EV less than 0 as the EV of folding is 0. Make sure not to confuse someone's EV for the entire hand with the EV of a specific decision treating all invested money as dead money.

Example:

EV for entire hand for folding in the BB to a button open= -1BB (you'll have 1 less BB than you started the hand with)

EV for folding in any given situation when you treat previously invested money as dead money = 0BB (this includes folding pre-flop)

Other Pre-Flop Stuff:

Most people (myself included) would probably agree the blind 3-betting ranges vs a cutoff and button open are significantly too polarized. The big blind should likely defend more aggressively against CO and BTN opens than the hand chart should indicate and the blinds should likely 3-bet more aggressively than the hand chart would indicate. Please see post 62 for an example of a more updated 3-betting range vs a button open.

You CANNOT even come close to solving for what is correct pre-flop. I remember making some theory videos for CardRunners 4 years ago and saying "It looks like we need to defend in the button against a 3-bet with hands like KJo, QJo, and ATo and being told 'that seems awful.' Now just about everyone I talk to would agree folding these hands to a 3-bet after opening the button is very bad. The math always indicated folding these hands pre-flop is wrong, but if people don't 3-bet aggressively enough it may be best to fold marginal hands to a 3-bet (though not necessarily hands these strong) especially if the 3-betting range is strong and polarized and you're not very confident with your post-flop skills.

Your best bet for examining pre-flop play is asking yourself 'does this seem to make sense?' when you analyze some numbers. My biggest mistake when writing the pre-flop chapters was trying to use certain models/ratios/etc that don't actually work that well for pre-flop play, but I think they would pretty well for post-flop play. Ask yourself "how could I be exploited with these pre-flop ranges?" and go from there, and if you're like most people you'll realize you're folding in the button too much when facing a 3-bet, not 3-betting aggressively enough, and not calling from the big blind aggressively enough. Again, see post 62 for how to make a more aggressive 3-betting range, and be aware you'll have to learn how to play those ranges post-flop and you'll often be "guessing" after check-calling since you're no longer playing a very polarized range.

I would ignore the pre-flop ranges in the book and instead analyze your own pre-flop ranges using the methodology discussed in the book. In other words, figure out how much money but the button must win or lose when his worst open is called for his open to break even. Figure out how much EV a small blind or big blind 3-bet "bluff" must have when called to make the 3-bet break even.

Again, you'll probably find out with the ranges you're using right now that from a GTO perspective you are defending way too little when facing 3-bets as a button opener and not 3-betting aggressively enough from the blinds when the button opens. You can analyze other positions in a similar manner, but I'd mostly focus on the button and CO as they are the most important and easiest to analyze.

I think the flop is the most important street in general as if you play the flop well it makes the turn and river way easier to play. If you're one of those guys that "just bets" on the flop without much thought since betting is profitable then you're likely going to end up on the turn with a pretty inefficient range and are going to find the turn very difficult to play.

Thanks, i look forward to getting started on working these into my strategy

Great! thanks for clearing things up!

Got a simple question.

If I arrive to the river that wins on an average 50% vs opponent's calling range, how many times can I bluff? I feel like it would be 0 combos, since the bet is basically a 0ev bet (other than it wins the pot on average). But that is looking at it from our perspective and not villains.

Villain's calling range will be determined by how big you bet, so this question doesn't make a lot of sense. It also depends on if you are IP or OOP.

It's actually pretty common to "value bet" when OOP even when you are expecting to lose when called. This is explained in detail n the book but not something that can be explained well with a couple of sentences here.

Let me know if that clarifies anything or if you're still confused.

Trying to simplify it, I came up with this:

We bet 5 into 10, with 10 combos of KK on 22233.

Opponent calls with AA and QQ.. How many bluffs should we have for these 10 combos of KK?

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The reason I ask, is I've done defense ranges to the river vs 3 barrels. On the river, I will check equity of different hands vs defending range, to see what opponent can valuebet, and how often their valuebet will win when called.

10 combos?

Typo. I meant 1000 combos.

You are assigning villain a fixed calling range, correct? Like you know what % of the time he calls?

In that case you'll just bluff if it's +EV and check if it isn't. So if you are betting half the pot, if opponent folds 1/3 of the time or more always bluff. If he does not you should never bluff.

A friend of mine had a question

Yo yo yo janda mein nizzles I gots a question about your maff. When making a pot sized bet you say to have a value to bluff ratio of 2-1 or 66-33. I am confused because I think I found a contradiction. On page 99 you state the bluff rate y = x/(x+1). When using DUH formula 1/2 = 50%. Should I be bluffing at a 33% rate or 50%?

Scratch that example.

Say on a board of A9428:

I raise UTG, my opponent defends HJ. I figured out his postflop calling range defending at least min on flop and turn (never raising for simplicity). Then on the river, exactly 2/3 which comes to AKo, AQs, AQo, AJs, and 99.

I then ran the EV of possible valuebetting hands vs this river range.

AA has 100% so with a halfpot bet, I would bluff 1 combo for every 3 combos of AA. AQ has roughly 52% equity. How much should I bluff for my AQ combos to make him indifferent? I'm not even sure what I'm making him indifferent to what.

My thinking is that since we are bluffing 1/4 times with AA, for AQ we'd have to bluff something super rare, like 1/16 times.

I'm not sure if I'm doing this correct.

You're confusing how often your bluff needs to succeed with how often you should be bluffing.

If you bet 1 PSB, you are risking 1 to win 1. Your bluff needs to succeed 50% of the time.

If you bet 1 PSB, your opponent will be risking 1 to win 2 when he calls. He thus needs to win only 1/3 of the time, so you should only be bluffing 33% of the time.

On the river if you are betting with a polarized range (you should be) then you need to make your opponent indifferent to calling with hands that lose to the value bets but beat the bluffs. If your opponent has a hand that beats some of your value bets, then you can't make that hand indifferent to calling a bet (since his call will beat all of your bluffs and some of your value bets)

The problem is your examples are likely to cause much more confusion than they clear things up. If you bet AQ in your example, you're losing to 9 hands in his calling range and beating 2. So it's probably too weak of hand to value bet to begin with.

Looking at the concept of larger bluffing ranges on earlier streets on pages 105-116. Trying to put the numbers together.

Page 106: "Suppose our range on the flop consists of two types of hands, the nuts, which occur 20 percent of the time and will never lose, and bluffs, which occur 80 percent of the time and which can never win."

Then, on page 107: "...remember all our river bluffs are in a sense winners, and since (in this example) we win 30 percent of the time on the river (when we bet), to offer 2:1 odds it now mean that on the turn we must bluff another 15 percent of the time to balance the 30 percent we bet on the river."

I'm having trouble piecing this together.

If I offer 2:1 and have 20 value combos on the river, then I need 10 bluff combos. I understand this is 70% of a 20/80 value:bluff mix, but you say that mix exists on the flop. So, I don't see how I win on the river 30% of the time.

Are you saying we win on the river with 30% of our flop range?

Does this scenario look like this?

Total flop range:

20 value combos
80 bluffs combos


Flop:

Bet

20 value combos
47.5 bluffs combos

Check

32.5 combos


Turn:

Bet

20 value combos
25 bluffs combos

Check

22.5 combos


River:

Bet

20 value combos
10 bluff combos

Check

15 combos


Also, perhaps the example wasn't meant to be optimal, but isn't the goal as it were, to get to the river with a distribution strength corresponding with the bet size left in relation to the pot? So, isn't it "bad" to have these 15 combos to check on the river. Wouldn't we want to arrive on the river with just the 30 combos and be able to shove the entire range with a psb?

Thanks for the help.

I'm trying to figure out the overall EV of 5bet jamming in a certain spot. Here is my example: I open QQ to 2.5bbs, BTN 3bets to 8bbs, and SB cold 4bets to 23bbs. We'll assume BTN always folds and SB has QQ+ AK when he calls. Do I use the formulas that are on page 47, which is EV of 4betting or folding? For example: If SB is playing optimal and is folding ~50% to our jam. So .50 x 34.5 = +17.25bbs when SB folds. When SB calls we have 40% equity. So .40 x 209 - 100 = -16.4. Then (.50)(17.25) + (.50)(-16.4) = 0.425. So our overall EV for jamming is 0.425? Is this correct?

Think I worked it out correctly. Guess I took "we win 30 percent of the time on the river" to mean...the more literal meaning, for lack of a better description.

I've not worked out other scenarios, but I'm wondering if there's a connection between our bet size and the portion we c/f on each street. Just noticed we basically fold 33.3% on each street (bit less on the flop), which is how often the opponent must be good to call.

If you did arrive on river with just the combos that can bet, that would mean you had too few bluffs on turn (i.e. your range was so strong it could have supported more bluffs).

The flop numbers just come from the setup of the original range. If you had 20 value hands and 200 bluffs on flop, the flop check-folding percentage would be bigger. On later streets, they'd stay the same after the initial "flop pruning".

"It is not too much of an exaggeration to say that the goal of a poker hand is to arrive at the river with a distribution that contains a mixture of strong, medium strength hands that did not reach their full potential due to the cards that fell, and weak hands and a pot size correlated to the strength of that distribution." -MOP

Seems to me from everything I've looked at and worked on so far, the concept (as I understand it) from MOP holds. Given the example we have in Janda's book (we bet and they decide to call to at least the river), if our bluff:value ratio is out of whack with our effective stack to pot ratio on the river, we've done something less than optimal. So, if we get to the river with a psb remaining and have 20 value combos, if we have anything other than 10 bluff combos, we could have done something better.

That's my understanding at this point, anyway.

Hey guys I will try to get to your questions relatively soon but I just moved and have enough stuff that I need to get sorted out that I'm going to try to avoid all things poker related for at least a few days. That said I will get to this when I get a chance.

Unacceptable! GL with the move.