# check my maths

• Bronze
Joined: 29.12.2010
can somebody check my maths on this please? haven't thought about poker for a long time so it's been a while since i've done any of this.

1. Facing a bet

pot odds = 'amount to call' / ('pot' + 'amount to call')
villain's odds = 'amount to call' / 'pot' or in other words, 'his investment' / ('pot facing him' + 'his investment')
amount we should defend = 1 - "villain's odds"
amount we should fold = "villain's odds"

example:
say the pot is 1. villain bets 75% pot, which means the pot facing us is 1.75. we need to call 0.75 and our pot odds are 30%. We should defend roughly 57% and fold roughly 43% of our range.

2. Placing a bet

our odds = 'investment' / ('pot' + 'investment')
required FE = 'our odds'
villain's odds = 'investment' / ('pot' + 'investment'*2)
our bluffing frequency = "villain's odds"
our value betting frequency = 1 - "villain's odds"

Example:
We want to overbet 150% of the pot, so we bet 1.5 into a pot of 1. Our odds are 60%, which means our required FE is 60%. We should have 37.5% bluffs and 62.5% value in our range.
• 13 replies
• Gold
Joined: 01.04.2012
example:
say the pot is 1. villain bets 75% pot, which means the pot facing us is 1.75. we need to call 0.75 and our pot odds are 30%. We should defend roughly 57% and fold roughly 43% of our range.
This is correct when having perfectly polarized ranges, which is almost never truth in real poker. So if you defend 57% vs cbet e.g. on flop, almost all villians bluffs will be +EV because his bluffs have equity. It is tough to estimate how much extra to defend to make his bluffs indifferent between check and bet, but i usually defend 5-10% more (defending more on wetter boards because his bluffs have more equity).
Also when you play OOP you should defend more than IP because villian will realize more of his equity with bluffs.

Anyway, I dont think that it is important to defend in a way exactly to make villian indifferent, but it is desireable to be as closer as possible to that, so it doesnt matter so much if you defend 5% or 10% extra. I think it is the worst if you defend less than you should, vs agressive opponent (it off course only matters vs agressive opponents to defend unexploitable). So imo it is better to defend a bit more than a bit less than perfect.
• Bronze
Joined: 29.12.2010
thank you for the response. you made some interesting points
• Coach
Coach
Joined: 07.02.2009
it's not as clear cut anymore as mlatasrb mentioned unless it's a river spot where you both get to with optimal ranges.

Because
1) both your ranges realize equity on future streets
2) most of the time there will be a range asymmetry so it's actually often okay to overfold in many spots in 1-A terms speaking I presume. This should happen e.g. in BBvBU scenarios quite a bit I'd think?
• Gold
Joined: 01.04.2012

2) most of the time there will be a range asymmetry so it's actually often okay to overfold in many spots in 1-A terms speaking I presume. This should happen e.g. in BBvBU scenarios quite a bit I'd think?
If you fold more than 1-a in some spots where you have much weaker range (asymmetric), it doenst mean that you overfolded and are exploited. We should defend 1-a bluff catchers, and hands that have 0% equity (or generally very low equity hands), you can discard. so in spots where you have asymetric ranges, a player with much weaker range usually has many low equity hands, so he shouldnt count them when defending 1-a. so it could be the case that you fold 90% of time, but still make villian unexploitable. It is similar example on river, when you have hands that are having 0% equity, you dont count them when defending 1-a.

In general those spots where you have asymmetric ranges shouldnt happen that often if both ranges are constructed solid. One simple example, villian 3bets only KK+ preflop, and you call with 22-KK for set value. Flop is e.g. AK3s. So in this spot, all your hands have close to 0% equity, and you should fold 100% of time, unless villian bets small enough, so that you can call for pot odds to hit quads.

In bb vs bu spot, usually you dont have asymmetric ranges, because even though BU has more nut combos, BB has many draw and pair combos (bluff catchers), and BU has still many bluffs in range, which means, BB has to defend enough %, otherwise BU can increase EV of his bluffs by betting.

Example where ranges would be asymmetric. You raise flop with all flush draws BB vs BU, and you call only bluff catchers flop. BU bets flop and turn, and river comes flush. So in that spot, BU will have only strong hands in range, and can value bet almost each combo, and has almost none bluffs in range. So if you fold 100% of time vs his bet, he cant exploit you.
• Coach
Coach
Joined: 07.02.2009
should still happen quite a lot in common spots tho on a lot of boards
e.g. standard HU 3b ranges

On e.g. 754 the bb has a signifficant range advantage, which will happen to some degree on vast majority of boards in pretty much all flop spots? (range distribution is hardly ever identical in 6max - can't really think of a flop where 2 players get to with the same range) so not taking R into account the correct fold frequency will almost never be 1-A in practice because one range always hits the board more than the other, or am I getting it wrong?

There always is an equity gap or difference in hand strenghts when I play with the equilab hand distribution tool

And again, practically speaking, position should again play a role and you should fold more oop than ip as the guy IP always realizes more equity on future streets?

That's like one of the things I tell myself for just folding quite a bit on flops on BB instead of fighting for it, the odds make it +ev to call preflop without the need to fight back too much on flops, this was one of the things D2 mentioned.
• Gold
Joined: 01.04.2012
hi,

On e.g. 754 the bb has a signifficant range advantage, which will happen to some degree on vast majority of boards in pretty much all flop spots?
You are right, here BU will have significant range advantage. But that doesnt mean that BB should overfold. Still, on flop, most of hands in BU range are bluffs, and if BB simply overfolds flop, thats big increase of EV for BU, since not only that his bluffs have a lot of equity, but will have now also a lot of FE. If e.g. BU bets pot size, theoretically BB should defend around 50% (or lets say 40% to make him indiffirent due to equity), but still BB doesnt have to defend very low equity hands, but only hands that can defend flop +EV. There should be enough of bdfd + overcards hands in BB range that could be floated +EV.
• Gold
Joined: 01.04.2012

(range distribution is hardly ever identical in 6max - can't really think of a flop where 2 players get to with the same range) so not taking R into account the correct fold frequency will almost never be 1-A in practice because one range always hits the board more than the other, or am I getting it wrong?
Yes, range distribution is almost never identical. Often ranges have similar average equity, mostly happens when we cold call vs UTG or MP position.
1-A frequency doesnt have anything to do with "one range always hits the board more than the other". It has only to do with making villians bluffs indifferent between checking and betting. So simply if villian has significant amount of bluffs in range, we want to defend 1-A to make him indifferent. If he doesnt have bluffs in range, or only small %, we dont care about 1-A.

In reality, 1-A is just a rough guide, how much we should defend. Most of guys at limits up to NL100 fold vs flop cbet around 50%, and vs turn 25-30%. So they should realize that they are doing very wrong, when they look at 1-A. We who know that they are doing wrong, should know that we can exploit them by betting flop any bluff, and giving up turn. So imo 1-A should be only used for that, nothing else.

We should actually defend a hand, only if we think that it is max EV to defend it. If we defend a hand which we think is -EV, just because we want to defend 1-A, thats burning money. And if we cant defend enough hands +EV in order to defend 1-A, that means that villians range is too strong, meaning that he is value heavy, and we dont have to defend unexploitable in that case.
• Bronze
Joined: 16.09.2009
Originally posted by mlatasrb

(range distribution is hardly ever identical in 6max - can't really think of a flop where 2 players get to with the same range) so not taking R into account the correct fold frequency will almost never be 1-A in practice because one range always hits the board more than the other, or am I getting it wrong?
Yes, range distribution is almost never identical. Often ranges have similar average equity, mostly happens when we cold call vs UTG or MP position.
1-A frequency doesnt have anything to do with "one range always hits the board more than the other". It has only to do with making villians bluffs indifferent between checking and betting. So simply if villian has significant amount of bluffs in range, we want to defend 1-A to make him indifferent. If he doesnt have bluffs in range, or only small %, we dont care about 1-A.
There are different types of range advantage. One is where a player has more nut-type or high EQ hands in his range than the other player. In such a case we should only defend if we can do it profitably against villains whole strategy all the way to the showdown. Defending 1-A would sometimes be incorrect in such a case, a good example is BB vs EP on Axx.
Another type of range advantage is where a player improves much more frequently and/or strongly on the turn/river than the other player. In such a case defending 1-A is different because certain bluffcatchers are very vulnerable by runouts. In such a case tactics are much more important than EQ. A good example is the one LemOn36 posted.
There are more types of range advantage/asymmetries, (like having too much SDV and not enough natural bluffs), and the more complex it gets the less clear it becomes what an optimal defending range is. 1-A is not only a rough estimate, very often it's plain wrong (in the multi-street game). That's why I think we see people overfolding the flop at the small stakes. I honestly doubt they're overfolding way too much on the flop, they just aren't as accurate when they do it compared to strong high stakes players.

Whenever I see a supposedly strong player in a coaching video defend a super-vulnerable eye-candy bluffcatcher on the flop when the texture does not warrant it, I feel I'm wasting my time watchin this. When he calls down and sees he ran into a hand that covers just about every single runout... it truly makes my eyes bleed.

In reality, 1-A is just a rough guide, how much we should defend. Most of guys at limits up to NL100 fold vs flop cbet around 50%, and vs turn 25-30%. So they should realize that they are doing very wrong, when they look at 1-A. We who know that they are doing wrong, should know that we can exploit them by betting flop any bluff, and giving up turn. So imo 1-A should be only used for that, nothing else.

We should actually defend a hand, only if we think that it is max EV to defend it. If we defend a hand which we think is -EV, just because we want to defend 1-A, thats burning money. And if we cant defend enough hands +EV in order to defend 1-A, that means that villians range is too strong, meaning that he is value heavy, and we dont have to defend unexploitable in that case.
Yeah, that's exactly what we should do. In practice it's a bit difficult though, so without further information we need a default gameplan that is as unexploitable as possible.
When you say that people are overfolding the flop and underfolding the turn, that's an observation that tells us to deviate from the optimum. It does not tell us that we should c-bet the flop with all of our hands. We want max EV, not just EV. If villain has a type of range disadvantage, we can check certain hands to create more value with them.
• Gold
Joined: 01.04.2012
hi ETBRood,

I honestly doubt they're overfolding way too much on the flop, they just aren't as accurate when they do it compared to strong high stakes players.
If somebody folds 50% vs flop cbet, you dont think he is overfolding too much so that opponent can +EV cbet any bluff? What about 40%? Just a little hint for you, I noticed that you have same pokerstars name and ps.com name, and once I played vs you NL100 zoom (a month ago), and I had almost no sample on you, but I knew that you are tight vs overbets vs unknown, also vs 3rd barrel, so I was applying more agression vs you (it was just few hands though). Just wondering, if someone who knows your strategy because you post in ps forum, can use it vs you in stars? I also have the same nickname by the way.
• Bronze
Joined: 16.09.2009
Originally posted by mlatasrb
hi ETBRood,

I honestly doubt they're overfolding way too much on the flop, they just aren't as accurate when they do it compared to strong high stakes players.
If somebody folds 50% vs flop cbet, you dont think he is overfolding too much so that opponent can +EV cbet any bluff? What about 40%? Just a little hint for you, I noticed that you have same pokerstars name and ps.com name, and once I played vs you NL100 zoom (a month ago), and I had almost no sample on you, but I knew that you are tight vs overbets vs unknown, also vs 3rd barrel, so I was applying more agression vs you (it was just few hands though). Just wondering, if someone who knows your strategy because you post in ps forum, can use it vs you in stars? I also have the same nickname by the way.
I don't post strategy as often anymore, and I try not to tell how I myself tend to play a standard spot. Anyway, sometimes I make really dumb plays because sometimes I am dumb, so people see me do stuff they wouldn't expect and then they try to exploit that somehow. Exploits can backfire really hard if you do it wrong, and many exploits I see against me are certainly over the top. So I don't mind, I doubt I make more incorrect plays than everyone else at 100.

If someone exploits me over just a couple hands, I really couldn't care less. As long as I play reasonably it won't cost me much, but the exploiter can cost himself a lot. Maybe I didn't have a hand to defend with. Maybe I adapt later. Small samples are tricky.

My belief is that folding frequencies are mainly defined by board textures. If you try to exploit me really hard by overbetting any turn card on most textures, you may end up spewing tons of chips away. At the same time, if you focus too much on exploiting a couple players but the pool consists of thousands of others, then you may exploit very well, but you could leave value out there in your standard game.
• Gold
Joined: 01.04.2012
I don't post strategy as often anymore, and I try not to tell how I myself tend to play a standard spot. Anyway, sometimes I make really dumb plays because sometimes I am dumb, so people see me do stuff they wouldn't expect and then they try to exploit that somehow. Exploits can backfire really hard if you do it wrong, and many exploits I see against me are certainly over the top. So I don't mind, I doubt I make more incorrect plays than everyone else at 100.
Yes agree. I could exploit you with agression for just max several hands, until you notice that, and if I would see bluff catch, then I would have also to adapt, so for that spot it is likely only short term exploit. But, if somebody knows your way of thinking, as I know (we discussed a lot over skype, with gingerkid), then I guess it is already edge. If you dont post much in forum, then you are not in a danger. I used to post a lot though.

Do you still play NL200? I switched recently from party poker to stars, want to try out NL200 zoom, currently playing NL100 zoom. I am surprised how regs at zoom nl100 are super agro preflop (3bets, sqeeze, 4bet, cold 4bet), but postflop they seem to play weak (overfold a lot, and play straight forward).
• Gold
Joined: 01.04.2012