Played significantly intoxicated for the 2nd time ever (first time was all the way back on page 1 of this thread, good memories), now I *finally* understand after thousands of hours of live poker how people need to be reminded it's their action, why people ask how much the bet is when they can clearly just look at it, how some people can't remember the action from a hand that happened an orbit ago, etc.

Can't believe I never understood this before after thousands of hours of watching it... but now I FINALLY GET IT

I play 100% sober and can't remember the action from the last hand... It even the CURRENT hand

page 1 post is epic

Ah I meant that like me being intoxicated is on the same level of awareness of like an average bad player being sober. But I never knew what this level was like until now.

I know I don't need to qualify that statement, but just to be safe if anyone thinks that sounds condescending- I am not trying to be, TBH it would be a disgrace on my part if a random rec player had my awareness level given that I've basically dedicated the recent years of my life to poker. Furthermore I'm actually trying to maximize EV instead of splashing around while watching football on TV etc.

Yes. All of page 1 is epic TBH, I'm sorry to the readers that the thread has not lived up to it's former quality. I've been posting hands and writing stories, they just don't show up here anymore. I suspect I'll bring them both back to the thread eventually when I'm in the mood.

I often ask how much the bet is but I mostly blame bad eyesight (although it has been corrected) and online poker (because they always just tell you what the bet is).

Was it below your usual stakes?

5/10 PLO

I still remember like all my big hands from that session too. Clearly wasn't fk'd up enough

If one wanted to pursue poker as a money making business venture in 2015 should he/she focus on learning all of the games or just one or a certain few games?

Focus on NLHE IMO

The other main options would be PLO, or limit games, but they are obviously more limited in quantity. Furthermore, there are often no "low stakes" versions of those games, for example the smallest PLO game in a room can often be 5/10+ and the smallest limit game in a room can often be 20/40+. The #1 main reason though I think is you will just hate poker if you become a limit player, this is what I observe every time I walk by LHE tables and no one looks like they are having any fun.

LHE might be alive in states but I have not seen one in europe (played in 8 or 9 countries).

I think NLHE (and PLO as well), at least in a live format, have enough variety/game space where even players like myself who have been playing for a few years now routinely encounter unusual/interesting situations. A big inspiration to me was snamuh who has been playing I think 6 years and says he still gets a adrenaline rush every time he's involved in a 100bb+ pot.

Obviously I'm not experienced in limit, but I personally find it hard to wrap my mind around that also being true for a game where no individual decision would ever cost you more than 2bb at a time.

it can cost more than 2bb if you incorrect fold in a 40 bb pot

ahh i didn't know you could fold in limit

Every big bet saved is a big bet earned

Haven't posted in here in awhile, here's some quick theory work that I did for CLP that I thought was pretty interesting and I did promise to post it here. It's not particularly important at all, but if you've ever been curious why people tend to set up turn bet->river shoves at roughly equal percentages of the pot, it gives some insight into that.

OK so at the end of the first hand in my latest CLP podcast I talked about the game theory optimal breakdowns of turn->river betsizings in that particular hand. However, for this analysis, it is better to use a more simplistic model so I will go with a completely lockdown board (perhaps AAAA in PLO) on the turn with the SPR being 1.5. So let's just say 100 in the pot, 150 behind. If we bet half pot on the turn, we can jam for half pot again on the river (50 into 100, then 100 into 200). Alternatively, if we take a more atypical line of betting full pot on the turn, we only have a 1/6th pot sized jam for the river (50 into 300). We're also further simplifying the situation by assuming we have a range of nuts or air, and villain only has bluffcatchers (if villain can have nuts, which is often more realistic, then it becomes more complicated).

~~~~

OK let's first look at the more typical half pot turn, half pot river play.

So for him to call a 1/2 pot bet on the turn, basic pot odds says he needs to win the hand 25% of the time. To make the math simple, let's just say we bet an amount on the river that makes him indifferent to calling or folding, and he always folds- so we need to bet 75% of the time. On the river, his calls vs. our same 1/2 pot bet need to be correct the same 25% of the time, meaning we need 3 times as much value as bluffs when we bet. Therefore, where V is our value percentage, G is our bluff percentage arriving to the river that gives up, and C is the bluffs that continue on the river, the following must be true:

V + G + C = 1 (obviously all 3 ranges add together to equal 100%)
V + C = 3/4 (we bet our entire value range, then C, and all this together adds up to 3/4)
3C = V (because of our 1/2 pot bet sizing, we need V to be 3 times greater than C)

4C = 3/4, C = 3/16, V = 9/16, G = 4/16 = 1/4

OK so we've calculated that we can arrive on the river with 9 parts value and 7 parts bluffs. In other words, going with the half pot turn, half pot river strategy allows us to bluff the turn 7/9 as often as we have value.

~~~~

Now let's look at the full pot turn, 1/6th pot river strategy.

So following the logic from the previous example, he needs to win the hand 33% of the time to call the full pot turn bet. On the river, his calls only needs to be correct 1/8 of time vs our 1/6 pot bet, meaning we need 7 times as much value as bluffs on the river. Therefore,

V + G + C = 1
V + C = 2/3
7C = V
C = 1/12, V = 7/12, G = 4/12 = 1/3

So we need to arrive on the river with 7 parts value and 5 parts bluff. In other words, this strategy allows us to bluff the turn 5/7 as often as we have value.

~~~~

Hmm that's interesting. Can we do better? What about if we reverse our betsizes from the previous example and do 1/6 pot turn, full pot river? (16.67 into 100, 133.33 into 133.33)

So here to call the turn he needs to win the hand 1/8 of the time, meaning we bet river unexploitably 7/8 of the time. On the river his calls need to be correct 1/3 of the time, so we need 2 times more value bets than bluffs.

V + G + C = 1
V + C = 7/8
2C = V

C = 7/24, V = 14/24, G = 3/24

This line lets us bluff the turn 10/14 = 5/7 as often as we have value, which turns out to be the exact same as the previous strategy. Perhaps there is a simpler way to show that it'd be the same; while the result was not surprising, it definitely wasn't obvious to me that the result would be equal.

~~~~

In conclusion, the intuitive answer is oftentimes the correct one: from a game theory standpoint, the half pot -> half pot strategy is better than either of the extremes. Without doing the math, I would assume that balancing your betsizings in terms of percentage of the pot between as many streets as possible is optimal in any simple model where the board is static, our range is polarized, and villain's range consists of bluffcatchers. Of course in real poker, none of those 3 assumptions are completely true, but the model is still a good approximation and this is a good exercise to get some insight on why our standard betsizings have evolved to be what they are today.

One thing that is definitely an important takeaway though, is that while the half pot -> half pot strategy is theoretically better in our simple model, it is only very very slightly better (allowing for a 44% vs. a 42% bluff frequency). It is negligible enough that in a live poker setting where you rarely have a good reason to attempt to play unexploitably, you should probably just completely disregard GTO betsizings.

That was a lot to digest, but you said when our range is polarized that the half bet sizing is optimal...what about when it is not, what is most optimal then? Do things, due to balance, have to touch extremes to counteract what we are doing, theoretically, when we are polarized or is it just a portion that does not sway things entirely?

No, if possible full pot -> full pot is theoretically better in a model where board is static and our range is polarized (in a pot limit game- for no limit, a massive overbet is even better). The stack depths did not allow for it in the situation above.

Is this an argument that whenever polarized and deep, and wanting to play GTO, we should massively overbet?

Oh, and welcome back.

If those 2 assumptions in the model are true, then yes in theory a balanced jam is the most +EV betsizing vs. a perfect opponent. However it's often discouraged in practice due to a chance of running into the nuts, also in favor of playing exploitably (e.g., overbetting exclusively bluffs or exclusively value depending on villain/situations).

As far as live goes, theory of perfect play is nice but overshadowed by exploitation. Something along the lines of 2 rec players limp, you raise 12x with 32o in the bb because you are very close to 100% certain they have no absolutely no hands that will limp/call vs. that sizing here, etc.

Yes. This is pretty trivial theory - one of the first toy games anyone learns is the perfect polarisation OTR game, where jamming, regardless of stack size, is an equilibrium strategy.

Oh okay got you now, basically the more FE when we are polarized is going to just increase our winrate in the situation with deep enough stacks, theoretically, correct?

Ya this is fairly basic as far as theory goes- again, using the model our range is polarized (i.e., we don't have any thin value that loses to some bluffcatchers, and villain can never have the nuts). The simplest way to think about it is that the bigger your betsize is, the more bluffs you can use when betting a balanced range that makes your opponent indifferent to calling. Why is more bluffs better? Since our betsize is unexploitable, we can assume villain always folds to calculate the EV of our bet (no matter what calling frequency you give villain, the EV is the same). Without needing to do the exact calculations, looking at it this way makes it clear having as many bluffs as possible is best.

For an easy "common sense" visualization on how larger betsizing allows us to have more bluffs, just imagine if you bet $1 into $1000 on the river in position. You basically can never bluff since your opponent will pretty much always call. As your betsizing goes up, the more bluffs you can add to your betting range. Again the easiest way to visualize this is to imagine the other extreme, where we bet $1000 into a $1 pot on the river in position- in this scenario, we can bet with almost as many bluff combos as value combos since our opponent basically needs to be right 50/50. Note that we can never unexploitably have more bluff combos on than value combos*** unless the pot is somehow worth negative dollars (one way in which that could happen is if you were playing "winner of first hand of the hour pays the time rake of $70 for the whole table" and you bet $50 into a $50 time pot).

***on the final street. In multistreet situations in our model of hero holds nuts/air and villain holds bluffcatchers, you can certainly have more bluffs than value on previous streets.

Thanks for the detailed break down of bet sizing. Interesting stuff!

I usually don't post theory, since so few people appreciate it and those that do are probably the ones I need to worry about most, but you can show that betting X on the turn and Y on the river let's you have the same turn ratio of bluff to value as betting Y on the turn and X on the river.

Let a = the fraction of the pot you bet on the turn
Let b = the fraction of the pot you bet on the river

On the turn we bet a*Pot, so our opponent needs to win a/(1+2a) percent of the time in order to call. Hence we need to bet the river 1 minus that percent of the time, so (1+a)/(1+2a). So we have V+C = (1+a)/(1+2a).

On the river we bet b*Pot. We are offering our opponent 1+b:b in terms of odds. To make him indifferent to calling, we need to have b/(1+2b) percent bluffs out of our entire river betting range.
In other words, C = [b/(1+2b)] * (V+C)
Simplifying, we get V = [(1+b)/b] * C

Using V+C = (1+a)/(1+2a), now we can solve for C. The actual math is left as an exercise for the reader. Hehehe
We get C = [(1+a)(b)] / [(1+2a)(1+2b)]
Now we know that V = [(1+a)(1+b)] / [(1+2a)(1+2b)]

Remember, we also have V + G + C = 1. Our turn bluffs are C+G, which is equal to 1-V. Our turn value bets are V. The ratio is (1-V)/V.

As we can see, if we swap the a's and b's in the equation for V, V is still the same. Thus the ratio (1-V)/V is still the same. Hence, swapping our turn and river bets (in terms of percentages of the pot) does not change our turn bluff to value ratio.