Thanks good to be back .

Risk and Reward: how much does a dollar really cost?
I want to start of this post with talking about risk and reward in poker. Doing some of these research was actually inspired by Jeremiah William’s stream. He advocates, as a professional, a high BRM of around 200Bis. JW is a very good player and is respected in the poker streets, so today we will look deeper into his advice and see how much BRM does financial theory say we need.

The first post I will explore risk and reward. How much of our bankroll is at risk given our winrate, volatility of our strategy and what our risk of ruin % is. Risk of ruin is a calculation on the likelyhood a infinite series of bets ever hits zero. (We are doing this over a set number of hands, but the math is less clean and it won’t matter much anyway).
Risk and reward are coupled with each other because we must invest money to make money, and we risk losing the investment. In finance this is more apparent where more risky assets like bitcoin have a higher payoff then something safer like bonds. There are great efforts in finance engineering to optimize this risk reward ratio. This ratio is expressed as a sharpe ratio, which is the return / risk and helps compare different assets of different return and risks. For example the S&P 500 has a sharpe of around 0.7 – 1 depending on how/when you measure it. In general, the higher the sharpe ratio the better the asset.

In poker we often talk about maximizing EV, and this advice is great while playing at the table, but when we need to manage our money we must take risk into account. If a professional poker player goes broke it is like a fisherman without any bait. Poker players need money to make money, so losing it all is not a good idea. To a professional, the game of poker can be seen as a risky, uncorrelated, asset. In finance correlation between assets is a big topic, and they need to make great use of diversification. I will go into diversification, and how to use it, in a separate post.

The main goals of being a professional poker player is to harvest rewards from playing. If we can’t play we can’t harvest rewards. To put plainly, don’t go broke, and keep making lots of money. There are three factors that affect our risk of going broke: winrate, volatility of our strategy, and our bankroll. Most BRM strategies only look at bankroll, and when you can move up and down stakes they do a good job. For professionals there is a certain limit they cannot move down from as they need to make a living, so having a good plan for how much of a bankroll you need for a certain limit to continue to make money is paramount. You need money to make money, so the point of BRM is to protect your income.
For us to have a good, safe, profitable year then we can use our winrate, and volatility of our strategy to understand how much of a bankroll we need to stomach the swings from poker. Lets explore how this works. I used the formula here: https://en.wikipedia.org/wiki/Risk_of_ruin and build an excel to help understand the factors that affect our risk. I am simulating 300k hands, and looking at the required bankroll for a set of winrates.

Since we want our risk of ruin to be very low (we can’t go to zero) I will take our risk of ruin to be 0.01%, which means 1/10000 times this might happen. If we play 300k hands a year then we should only get into trouble every 10000 years. I chose a standard devation of 100bb/100 which is the default on prime dope.



Here are the results for various winrates. We can see that our bankroll requirements are heavily affected by our winrate. With a low winrate it’s a double edged sword since you need more bankroll to stomach the swings AND you are making less. I asked around from some of my higher stakes friends and the STD goes as high as 115, so lets look to see how this affects the calculation.



Again we can see how the higher winrate hands aren’t as affected by variance. It really punishes low winrates (1000 BIS?!). We can see the high winrates are WAAAAY more efficient than low winrates the return on investment on low winrates is worse than passive income sources (S&P averages 8-10% a year).

Now there is a common argument that you can take a lower winrate and play zoom because you get more volume. This is a logical argument because you can play twice the volume, but you only lose a few bb/100 on your winrate. However this argument is missing the BRM aspect. If we lose a few bb/100 on our winrate we need to have more BRM. Below I double the volume to 600k, and I will change the winrates to move away from break even and we can see how this affects our outcomes. (Assume winning player)

For our 300k sample:



For 600k (simulating zoom):



So our expected earnings we can infact make more EV if we lose a few bb/100, but our BRM requirements also go up. If we Move from a 6bb/100 winrate to a 4bb/100 winrate expect to make 30 more Bis over this sample, but we need to have 50% more Bis to stomach the swings. If you drop from to 3bb/100 to 1bb/100 it’s not even worth it. Going to a 10bb/100 winrate to 8bb/100 is where things start to make since since the high winrate lowers your BRM, and extra 15BI invested doesn’t seem so bad.
Now what conclusions can we draw from this?

Winrate is by far the most important part of your brm strategy. If you’re crushing the games you’re so much better off. You make way more and need to pay less. Your return on investment just isn’t worth it with a winrate of 1bb/100, you need to get better. You can think of your bankroll as money that is locked up to get a return. A 10bb/100 winrate is risking 45BI to make 300. BRM requirements for higher winrates are less affected by an increase in variance, I would take 10bb/100 at 120 STD over 3bb/100 at 80bb/100 any day. Keeping your winrate high means: study, play soft sites and play with recs. Don’t try and go pro with a low winrate. Keep a part time job and get better before going pro.

The other factor we can consider is a high winrate gives capital for other ventures such as staking, and other investments. For example, assume you have 150Bis. If you have a 10bb/100 winrate @ 115 STD you need 50 Bis for your poker. You now have another 100Bis you can use to invest in other poker players, and having extra capital allows you to invest in other poker players, generating a favorable return. It also means your coaching will be more valuable, and you can charge a higher hourly. Looking at it this way you can allocate your capital much better.

Investing in other players will give you some diversification properties, which I will go into in my next post. Players wanting to move to highstakes / nose bleeds will naturally have lower winrates due to there just being less edge, so making use of diversification is much more important to help stomach their swings. You also need a lot of capital to be able to handle the swings, so I would arguing keeping any extra Bis that aren’t required for your BRM into some for of return generating vehicle. You need money to make money, and the nosebleeds have lots of unavoidable risk.

If you do all of these things, you are running your poker like a business. In my 3rd post I will talk about how I think this should be set up. How to plan for taxes, covering costs, and how to pay yourself without putting your bankroll at risk.

In the next post I will talk about lowering your risk using diversification. I will explain how it works from a theoretical point of view, and how it can be used in poker to allow you to decrease lower your risk.

To conclude for players in a winrate of 2-4 bb/100 and that play a variatly of stakes JW advice looks pretty solid. Winrate of 2.5bb/100 you need 150 – 180 Bis.

Had to write this in a bit of a hurray, hope you made it through my awful grammar.

Diversification: the only free lunch in finance (and poker).
Today I want to talk about the benefits of diversification: how it is used in finance, how it is modelled mathematically, use that model to show how it gives us a ‘free lunch’, how we can apply it to poker, and why I think it is necessary for high stakes / nosebleeds. Diversification is defined by Investopedia (https://www.investopedia.com/terms/d...sification.asp) as: “Diversification is a risk management strategy that mixes a wide variety of investments within a portfolio. A diversified portfolio contains a mix of distinct asset types and investment vehicles in an attempt at limiting exposure to any single asset or risk.”

We can think of diversification as investing in a wide variety of companies, rather than a few. Going all in on gamestop, or bitcoin, has no diversification, but investing in the S&P 500, has lots of diversification. Why is diversification powerful? Well, when we invest in a lot of companies some prices go up, and some go down, and when you average them all out you will feel less swings overall. A 1% swing in the S&P 500 is pretty high, but for a single stock like Amazon, or gamestop it’s very normal.
What makes diversification a free lunch? Well, when we diversify assets, we will get the average return across assets. However, the risk is lower than the average risk of the assets. We get a better risk / reward ratio. For example if 5 stocks have an average return of 5% a year. Investing in each of them will give you lower overall risk than investing in any one of them, EVEN IF their volatility (standard deviation) is the same. Returns average out, and risk still drops. How much the risk drops depends on the amount of “covariance” between assets. In finance most assets do have some covariance, but in poker there is none at all. When assets are uncorrelated there is a significant drop off in risk. Infact I used this calculation in my last post for calculating the risk for a specific winrate over 300,000 hands.

Why is it that we have this free lunch effect? I can demonstrate it here. In poker we can assume our winrate, and variance follows a normal distribution (or bell curve). We use our winrates in terms of bb/100. So we model our winrate as drawing some winrate every 100 hands played from a bell curve that has a mean of our winrate and variance of standard devation^2.
When we want to calculate how much we are expected to win over 100,000 hands we can then think of our outcomes can 1000 draws from this distribution (once every 100 hands) and then adding them together. For a normal distribution without covariance (called independent) we can say these 1000, draws from a random sample follow their own normal distribution. We can use the formula below to calculate this:



Here the sigma is the standard devation, so we simply add the means and then add the squares of the variance. When we add the means for 1000 trials we get 1000*winrate, which is expected, but the standard deviation is the sum of the squares. So our standard deviation is then the SQRT(1000)* The rate at which our winnings grow, then is out pacing the risk from multiple trials. This is why we need to play hundreds of thousands of hands to have any sort of idea on our winrate.

If we want to estimate our winrate for 100,000 hands we have the following formula

Winrate = winnings / number of trials +- StandardDevation/Number of Trials.
= n * winrate / n += (sqrt(n)/N) * Standard Devation
= winrate +- (1 / sqrt(n))*standard deviation.

So we can see as we play more hands our uncertainty drops off at a rate of 1 / sqrt( number of trials). This is basis for how prime dope works under the hood.
Now this isn’t a blog post about statistical uncertainty is about diversification, and how it can be applied to poker. The formula above can still be used to show the benefit of diversification in poker.

The main form of diversification in poker can come from staking, and swaps. Lets assume we have two players with identical winrate and identical variance. If they swap 50% of eacother action we get the following winrate (w) and standard devation (s) for each player (1 and 2):

Winrate = 0.50*w + 0.50*player2 = w*0.5 + w* 0.5 = w.
Standard devation = SQRT( (0.5*s)^2 + (0.5*s)^2) = SQRT(2*0.25*s^2) ~ 0.7s
Which lowers their risk by about 30%.

If lets use the charts from the earlier post to see how this changed required BRM for a set of winrates.
Without the diversification:


After diversification:


This means two players could almost share a bankroll and have the same risk assuming they have the same winrate.
Now if you stake someone, you are getting half the reward, but assuming the risk, however if you stake multiple people you are getting this same diversification aspect if you stake multiple people.

Infact diversification is so powerful there is mathimetical proof saying that you will always get a better risk / reward ratio (not to be confused with higher reward), when you swap with someone..even if they have a lower winrate than you. (This doesn’t mean swap 50% with everyone, you want to swap proporonal to winrates. You need to do some math to figure our the formula.) I can derive it if people want to see it. When winrates are different, the higher winrate player loses some EV, but it’s offset by risk reduction.
The risk reduction from this swapping I think is particularly useful for shots. If you want to shoot a higher stake with your friend, you’re getting twice as many Bis and exposure to twice as many hands, so you can stick it a lot easier.

For staking companies if they stake 100 players they don’t need 100 BRs, due to this diversification effect. They need less money over all due to diverisication.
For highstakes / nosebleeds players imagine you have low winrates, but there is 5 of you… you can really lower the overall risk each of you take. Since winrates are low at highstakes /nosebleeds if you swap 20% with everyone your standard devation is now: sqrt(5*(0.2)^2) = 0.44 lets look at the chart for this.



Now you only need 33 Bis to survive with a 2bb/100 winrate. Lets assume a STD of 115, which is closer to higher stakes/winrate players.



44 Bis? Seems much easier.
So, the main take away from this blog post is to make friends you can trust. If you lower your risk, that means you need less Bis, and you can fire more money.
The one caveat here is that you want to make sure you have people you can trust. If you get someone who is lying, overconfident or is just running good the can take your EV. If their true winrate is too low you’re basically just donating your EV.

Most people are surprised by these results, but if you have any questions please let me know. I skipped a few details to make the blog post simpler but the main idea is still there. More complicated calculations are doable but they just take time.

Great post. Thanks!

You should probably run your poker roll like a hedge fund.

In my last article on this finance series I am going to make two arguments:
You should separate your poker roll from your life roll.
You should run your poker business like a hedge fund.

The first case I will make is to separate your poker bankroll from your life roll and pay yourself out of your business. This is for the simple reason that you don’t want going busto to put you out on the street. I will argue, and this is all just opinion, if you separate your life roll from your life roll you won’t go busto nearly as easy.

We want to structure our finances into two main categories:
Personal finances.
Business finances.

This was covered in a blog post from Mobius Poker: https://www.mobiuspoker.com/blog, and it’s similar to how I do it too.

In general your personal finances should have two funds:
Emergency fund (NOT FOR POKER).
Retirement fund.

In general you want to keep 6 months worth of expenses in your emergency fund. If your home needs emergency repairs, or if you run bad, or go busto you dip into this fund and pay it back out of the savings. Your retirement fund is where you put money when your emergency fund has 6 months of your life expenses and you have no debt. The savings you make from poker need to have two allocations: expenses, and savings. You want to start putting money into your personal savings as you as you can. In general when calculating your cost of living you always want to factor in savings if at all possible.

From for your personal finance standpoint you want to allocate your “savings” money in the following priority:
Emergency savings
Debt
Retirement fund.

Treat your retirement savings as locked in. Don’t pull it out unless you are absolutely ****ed.

So how much money do you need to make from poker? Well you want to calculate your expenses in an excel spreadsheet. Things like: rent, cell phone, clothes, haircuts, power, etc. Once you have this number you need to add anywhere from 10%-50% onto it for savings. I think it is very important that you always try to save for retirement. Poker is very uncertain and the burnout rate is very high. I would be as aggressive as you can.

For retirement fund, there is a lot of options. You can invest in real estate, or equities. In general I think people have their own ideas, but don’t let it sit in cash. For more personal finance I recommend checking out: “The money guy”, and “Ben Felix” on youtube. I am not an investment advisor, but in general low cost ETFs are never a mistake.

So, now I think it’s more interesting to talk about the business side. I would set the business up the following way:
Low risk cash fund.
Poker improvement money.
Risky cash fund.
Tax fund.
Bonus fund.

The low risk cash is to be used in the following way: you want this to be enough buy ins to cover your cost of living at all times. Like an emergency fund for your business to make income for you. This is completely dependent on your living expenses, and your win rate at the stake. You will need to run some math on on your winrate / stake to calculate your cost of living. You can calculate a number you can reach without too much issue.

You want to use the funds in the following way:
Low risk cash fund - Using the RoR calculator you can calculate how big this needs to be to cover your life expenses from playing poker. This way you always have a source of income.
This is money you allocate for the year for coaching, courses etc. You want to invest in yourself to improve. From post 1 you want a high winrate…really..really..badly. Invest as much as you can into this. How you allocate this, is up to you.
Risky cash fund - This is the fund you want to use for high stakes, nosebleed shots, staking, etc. It’s important to plan it out, but this is where you want to use money for higher stakes than what the low risk cash fund is for.
Tax fund - This is to hold the taxes you will need to pay. Pull it out of the money made each month, and leave it here so you don’t run into issues with the government.
Bonus fund - This is where you put all your extra money into. You can pay yourself a bonus out of this fund. Don’t take any money out of this until the end of the year.

You can use the risky cash funds for whatever you want to do in poker. I do advise you do some projections so you don’t punt all the money into the sun. You higher stakes play should be controlled and calculated. For example: playing NL10k should have a pre-defined number of shots, where the ROR is still low…but it doesn’t need to be 0.01%, you can have 5-10%.

If you are shooting nosebleeds you want to have a defined plan. Take small shots..sell some action or swaps..don’t plan on losing this money, but this can be significantly riskier, and you can afford to have a bad year. Don’t have 100k in risky assets and send it all off in a 10BI shots at Nl10k.

Pay yourself out the bonus fund at the end of the year. You will have a cushion for things to go wrong. At the end of the year fill up the coaching fund, add some more $$ to risky investments, plan out shots, and extra stuff you can pay as a bonus to yourself.

Really what you are doing is investing this money in yourself, others, and in training. Which is why you want to run this like a business.

Use the diversification talking about in blog two to help manage this money. If you ran bad you can sell some action and use the risky investment fund as well. Investing in yourself and getting a high winrate will make you valuable and getting a stake will be easy.

Run this like a hedge fund. Minimize your risk of going broke, but take some risks. You will make a lot more money this way. I think the secret to making 7 figures is in diversification and money management. Much more so than finding those epic river bluffs.

I feel that's way too life nit. If I have 25.5k to my name 100% im playing a 25k mtt for the win. I will play a super aggressive style and play to win. If i lose I got $500 which I can run up to 2k through blackjack. if i lose that then I can go to the nearest homeless shelter to get a free feed and look for employment. that is how i live.

Do you still think you can build an exploitative solver ?

Short answer is yes, but the long answer is it depends. You can do it two ways..try and model population's game tree, and then max exploit that, but the problem is you could be exploiting noise. If the model is wrong you could be doing some wild stuff that doesn't work in practice. So if you wanted to go with this approach you would want to 'regulate' the strategy to not try and exploit every last 0.0000000000000001 chips. With the current CFRM algorithm this is kind of tough to do. Also you would need an absurd amount of data to model the whole game tree.

Option 2 is to just model the population frequencies for actions, and for the solver to match those frequencies. Which I think is the simpler approach and would give strategies that are more actionable, but then you need to add frequency constraints into the algorithm, which also might be hard. There are some tricks with deep learning out now where you might be able to do this, but it's one of those things where you need to see how it works. I am in the Ruse.Ai discord, and asked for this feature, but there was no ETA on it.

Blog post

So far I think poker has been going well. Studying a lot of the time. I am making flash cards in Anki, and using them to drill certain spots. It's very helpful reviewing spots where you have trouble all the time.

Results have been pretty good. Shot taking NL50 and it was a bit of a ride but we are still in there.



Going pretty good. Trying to make the right plays, but the volume is really lacking. I am the on-call for work this week so I won't be playing as much. But in general I haven't really dropped more than 4-5 BIs yet, so it's been nice. The winrates are here.



So far things seem good. It's hard to really feel confident in your game though. I have been mostly working on IP BTN vs BB, but will be moving to the BB part of the game next week.

Been using the GTO trainer in PIO to aid my study for thresholds, and making cards in Anki about it and I think that has really helped..especally with finding thin spots. Knowing roughly what your handstrength is worth on a given board is helpful.

That is it for now I have a few posts on solvers coming up, but things are busy right now so just thought I would post an update.

Mindset has been very poor lately.

I have never felt better about my poker game, lately. I feel I have a solid understanding of how to improve. However my mindset is garbage. My job has been stressful. There has been a lot of overtime, and a lot of pressure and it’s really starting to affect me. Right now I am averaging 10-12 hours of work a day. It’s been like this for a while and will probably continue until may. I didn’t grind very much this weekend, only about 700 hands. Friday I just needed to get out and see people, and drink some beers. Saturday I slept most of the day. I played maybe 200 hands of poker and just slept. On Sunday I played 500 hands, slept, watched twitch and went to the gym and just tried not to think about going back to work.

I really don’t want to do it anymore. The effort to job satisfaction ratio is very low. I work work work work, something goes wrong, get blocked, then I have to do it all over again. My tech lead works more than me, but he is a Principle level in Seattle and probably makes $500,000 USD a year.But that’s it. No one else needs to work 50-60 hours a week, and they all make twice as much as me. I work in Vancouver, and I am at an intermediate level. The pay difference from Seattle to Vancouver is about 50%..two hours away they make twice as much as, and still have to work twice as hard. I am very mad about it. My province you need to pay overtime, but it’s a rule no one enforces.

Last week while I was working (work from home) I was just talking to myself out loud about how I want to quit. The coding practice is so poor that everything breaks, and I end up having to constantly work overtime in order to keep on schedule. No higher ups want to spend time to make things reliable because they want to ship out new things which get them new big raises so they can pay their big bills for their stupid luxury cars they don’t need.

If I quit I need to pay back a signing bonus which will be about $5,500, and I told myself I would hang on for two years. I am hoping that I can get some relief from this. This should be done in May, and I am going to hopefully feel better. When I am stressed like this..it’s impossible for me to have a normal life. I can’t work like this for the rest of my life. I want to move forward with a fulfilling relationship, and I just can’t do it when I am in this state of mind.

Big companies are just a giant travesty. They talk about having these great core values, but when it comes time to put their money where their mouth is they hide behind bureaucracy and policy. Nothing great comes out of them anymore..they just spend billions of $$ on acquiring other companies that actually do cool stuff and scale it. Even at these big companies with big pay cheques exception people are still hard to find. Most of them just want the 6 figure paycheck and then use politics to be lazy

I know I am good enough to go out on my own now for AI. I can do both deep machine learning work and deep software engineering work and that is hard to find. I really want to quit now, and just start my own life where I work for myself. I can do it…but it’s not the right time..only 6 more months.

Even with poker I know that I can get to a point where I can live off it now. It’s not a question, it's just time. Right now I think about packing everything up, studying the things I enjoy like poker, Jiu jitsu, and AI that has real applications..not just maximizing a click through rate. No one cares about how to sort pictures by probability of a click..it’s a stupid problem the only reason it exists is to farm more data for ads. Imagine if that money went to cancer research, or understanding psychological disorders. I want to start a company that will actually solve a problem to help people..not just give them a superficial dopamine hit.

The title of this blog is: “I am done with being a life nit” but here I sound like I am scared to quit my job, but it’s not that..it’s that I made a commitment to myself about doing this and I don’t want to give up. I don’t want to give into mental weakness. This update has been one big vent, and I am sorry if it sounds like I am playing the world's smallest violin…but I just feel like I am trapped. I need to vent.

This is all only temporary, once I am done this stint I am going to travel the world, play a lot of poker, and do a lot of jiu jitsu. I may never do anything else.

If you made it this far, thank you for understanding.

What would happen if you just worked a little bit less

Very interesting posts about winrate, brm and reg vs zoom. Everybody knows and everybody is telling that you should always pick reg tables tableselect, even my coach. but somehow I still prefer zoom. One crucial point you left out from the calculations is that, most or almost all regulars play zoom because of the rakeback not the winrate, I got something like ~1bb EV winrate over 70k hands in zoom this month, but my rakeback is 20% gold chests, 40% rakeback challenge and some amount from the leaderboards, some month you get close to nothing, this month I bagged 200$ from 25z, few month ago 100$ from nl10z leaderboard, and plenty of 2-40$, that will give atleast 5-10% extra rakeback, this month I totalled atleast 15% extra from pokerstars leaderboards already (got 220$ from already, let's assume I won't get any more dollars from leaderboard and I have to pay 1500$ rake this month for 600$ bonus, something like ~15% extra rb.) So in total I make 75% of rakeback from my 1500$ raked this month. I could easily be -2bb/100 player and still make a profit.

It's way easier just to start 4 zoom and eend after 15 minutes, and start new session in 30 minutes. with reg tables getting the games up and looking for tables is so ***** annoying that I rather play 0EV winrate with rakeback than farm these whales, fishes and bumhunt for high winrate with 20% rb.
each to their own I guess.


In total I will make this month 1.1k$ just off rakeback, even when im not winning a single bigblind from my tables. In the end it probably evens out if I play 100 hours of zoom or I would just nitpick my tables and play 400 hands an hour without possibility to complete my 40% rakeback challenges.

now if you could even make a slight profit in your zoom games like 2-3bb/100 EV you already make like 1.3-1.7k USD in 25z. imo its just as hard to get the same figure bumhunting and crushing. pretty much evens out in the end .

obv I also work fulltime so I don't have to win, it's not crucial for my survival, I just like to play massive volume, I work 184 hours this time and I have already played around 65k hands this month.

I think the 600k volume for year or 300k volume for reg tables is a bit laughable imo, if player is playing fulltime as a professional and only regtables, the volume should be atleast 120-150 hours per month x 450 so like ~600-700k hands with reg tables and with zoom I think if you play fulltime 150k hands per month should be realistic, atleast 120k+ so around 1.2-2m hands per year, now add up all the rakeback with it and maybe add some 1bb to 2bb WR to it. pretty ****ing good imo.

So true that WR is everything in BR management and so few people talk about it.

I would suggest that diversification is better achieved outside of poker(not buying pieces/staking). So many ways to do this. In general, I think it is important to pull money out of poker and move it to some type of investment(stocks,bonds,real estate,business...)

The corporate grind sure can suck. I hope your figure it out

GL on the felt and at work.

A very fair point. If we don't make our deadlines then performance reviews suffer greatly. When performance reviews suffer you can go into PIP which is a far worse hell than I was in above.


For the numbers I posted just use your winrate after rakeback. The output is the same. As for your point about rakeback grinding for volume. I think if you want to make $1k a month and want to play 100 hours a month, then you're strategy is perfectly fine, but this has a ceiling. It's $10/hr, and if you're doing something you enjoy then that's great, but from a pure money standpoint there are likely better paying part time jobs.

The post above was more aimed to mid-high stakes players who are making a living, and are trying to make 6 figures. Pool liquidity really changes. If you're 4 tabling zoom for 100 hours a month that's 100,000 hands a month, and you're making 1000/0.25 ~ 4000 big blinds thats 4bb/100. It's a nice winrate, but if you don't study and improve you've capped yourself. So, either way you still need to focus on improving to keep moving up....where you might run into liquidity issues. Also 70% rakeback is very high..it might not last forever.

You point about volume is a little bit off, as most of the mid/high stakes regs I know still need to study, so they don't play 8 hours a day. They split play and study. The games are tougher and they need to keep improving or their winrates will go down, and I don't think this happens at NL25z.

Also NL25z is very liquid, the games run 24/7 and you can just gogogogogo. High stakes it doesn't happen as much. NL500z has stopped running. So when you're trying to play NL1k/NL2k on a softer site you only have so many hours in a day to play. Sometimes the games aren't good etc, so you have less freedom.

Yep I completely agree. I really think separating your retirement savings / investments, real estate is very important. This is something I didn't mention, but if you hurt your hands, or have some impairment to stop you form playing you want some other income coming in.

Thanks, I really appreciate it.

Oh, I thought you said you should diversify into those things as well. Yeah I think if you have idle bankroll pieces and staking offer more liquitdiy etc. Like I said in my post, poker has no covariance, so you get all the diversification benefits you can, but the options you mentioned offer passive income, so I think you want all of them between poker assets and personal assets.

Data Analyst from Vancouver here. Hoping to become a DS one day, and also similarly use my skills in the poker world. Good luck in your journey, followed


Sent from my iPhone using Tapatalk

How about some good looking people on there I’m sorry but some of the ppl there is such an eyesore I’m sure it hurts viewership

Thanks! Good luck to you as well!


A closer look at solvers
I very often frequent the twitch streets, where the GTO vs exploit debate still goes on. I frequent myself getting pulled into these arguments as well. I am not here to talk about GTO, or exploitative strategies as it is done to death, and the “GTO or Exploit” question isn’t even a good question in my opinion.

What I want to do is get a closer look into what solvers are doing, and I think this will help clear up uncertainty. I will try an avoid the heavy technical details and illustrate what is happening with examples. I am going to need to gloss over some details to keep things simpler, as this is already going to get technical.

Solvers use something called “regret”, which is how much we missed out from the best choice. They seek to “minimize their maximum regret (minimax)”: https://en.wikipedia.org/wiki/Regret_(decision_theory).
Suppose we want to invest in three markets, depending on what interest rates do to our returns will fall into the following table.



Here our regret for each of these asset classes is how much we would “lose out on” from picking the worst performing asset class. Our regret is the difference in actual returns from the best returns.



If we can only pick a purse strategy we would pick bonds, to minimize out maximum regret. Notice how we don’t win the most with this either? If each of the cases are equally as likely bonds have an expected return of 1/3(-2 + 3 + 8) = 3%, but stocks have an expected return of: 1/3*(-4 + 4 + 12) = 4%. So we aren’t making the most with this framework. We will just experience less regret. The most money overall is made by picking stocks. Does this sound familiar to something from poker? 😊

If you can pick a mixed strategy the optimal outcome is to mix between stocks and money market to minimize regret. I will leave this to the reader to look up the answer on the Wikipedia link.
The above example is different from poker, since it is not a game, but I think it does a good job at addressing what the solver is really doing. An example for a simple two player game is below. In this game each player choses a number between 1 – 3, and they have the following payoff matrix:



Here if the number is positive, player A gets paid that amount from player B, if the number is negative, then player B gets paid that amount from player A. The regret in this case is the number you need to pay to the other player.

Using this payoff matrix and our above framework, the solution is for player A to choose A2, since their regret is at most 1, and for B is B2 since at worst they lose nothing. If both players are thinking players they will both pick 2 and make nothing. Again there is an alternate solution for mixing but I will let the reader figure this out.

I hope this builds intuition into how a solver works, and where there is so much mixing and protecting their ranges. They are trying to protect from getting put in one of these big loss spots.
Poker solvers use an algorithm to find their equilibrium that works differently than how we did it here. (We just looked at the table), but the solver takes a random strategy for P1, lets P2 maximally exploit P1, then P1 maximally exploits p2, and they repeat this process until there is no change in EV from exploitation.

The result is you have a strategy with the highest EV when being maximally exploited and when being maximally exploited your EV is at a minimum possible EV. This is the solution to the minimax equation by definition: we face maximum regret when being maximally exploited, and the solution is finding the strategy that has the minimum regret when being maximally exploited: and thus minimizing maximum regret (or maximizing minimum ev same thing). There are youtube channels /streamers / information out there that are getting this wrong.

I hope the two examples above build some intuition into what a solver is doing. It’s looking at the worse case possible. We also now know that EV in the solver isn’t actually EV.. it’s the EV in the worst case, or minimum EV.

Does this mean that solvers should be thrown out? Absolutely not. Solvers should be a part of everyone’s study process. What solvers do very well is they uncover the structure of the game. You can see how ranges interact and understand how they should be played. Solvers are responsible for the rise of common strategies today: range betting small, over betting etc. You need them to help learn the game. I love solvers. I find a lot of lines that I wouldn’t have thought about.

What I think is the common misconception is that you need to play like one. No one good is trying to copy the solver exactly, but they will only choose bet sizes the solver chooses. Knowing what we know from the examples above this isn’t nessicary. If a 2/3 sizing shows 0.1% more EV than other sizings, that means in the worst case of you being maximally exploited you’re going to lose a small amount, where a 33%, 150% are likely just as viable. I want to stress: you aren’t losing 0.1% by choosing another sizing, you just have a maximum regret that is 0.1% higher just as stocks have higher regret, in the above example, but remember they still had higher ev overall. However, a huge EV drop will show there are some sizings that are bad, Overbetting when you are super capped is an example of being bad…you give the solver a overbetting sizing in that position and it won’t choose it, and if you node lock it you will have a very low minimum ev. You can see what are huge punts, and the exploit is probably very easy.

I will argue a solver isn’t a strategy in a box, but it is a calculation for worst case, a tool you can use to answer questions. However the questions should be simple: “How should I play perfect equilibrium” is a complicated question, with a complicated answer. “Can I use this betsize here?” is much simpler. You can look at the min EV compared to a more complicated model, and see if it’s a punt.

In general, and in my opinion, I see solvers as a tool to tell you what to CAN’T do, rather than what to do. If you pick a bad sizing you will nodes with very high regret, and it will show up in the solver. Even then I expect the nosebleed slayers like Stefan are picking strategies with higher max regret, in an effort to make more EV. The counter might be very hard to find.. much like the stock example above they are risking a high regret, to get a higher EV by exploitation. This is where the fun strategy comes in: “How can you hide your high regret nodes to make more money?” This is exploitation explained using a regret framework.

I believe in using solvers to build your own strategy. Another possible scenario is to simplify to certain sizes, and you can use things like data/exploits to help choose sizes will low regret, but high upside. Here is a hypothetical example, it’s a common population read that river raises are underbluffed. A big part of why solvers put good hands into small sizings is to lower their regret when raised. They will get raised often so mixing strong hands will give them value in the raise line when being bluffed, but if they are under bluffed..do we want that sizing with good hands..we might have a low max regret but what about our overall EV? A 150% river sizing and 30% river sizing might have the same minimum EV but since population doesn’t raise light the 150% will give you more EV in practice. I would pick the larger sizing as part of my strategy, cause I just won’t get value from bluff raises.

I really want to stress is solvers are working with the minimum EV, not the real EV. This makes a big difference in how you think about the game.

For this reason I don’t think the argument of “GTO vs Exploit” makes any sense. The above example shows us exploiting population, but we aren’t becoming exploitable. It’s not one or the other.

A note on EV loss

I see a lot of tools out now where you can upload your hands to something like GTO wizard and it will grade you on mistakes. The common idea is they use EV against GTO as a way to measure how close you are to GTO. This is wrong. Very wrong. Don’t think this or it will cost you a lot of money.

The hands are grading your EV loss against their “GTO” strategy. It’s not, and I repeat IT’S NOT telling you how close you are to their strategy. If your EV loss against GTO is zero that doesn’t mean you are playing GTO, and it doesn’t mean you have an unexploitable strategy. Phil Galfond has a good video about this somewhere, but I cannot find it, anyway he said lets take the equilibrium strategy for two players. The EV loss is zero for both players since they are playing GTO. Now for the first player, take all the mixed bluffs, and make them a pure bet strategy, and the then all the mixed calls and make them a pure strategy. The EV loss is still zero, but player one’s strategy is super exploitable, and they are not the same strategy. There is no uniqueness property here. An analogy is the sets: [0,0,0] and [-1,0,1] have the same average, but they aren’t the same numbers.

There is some use to this tool for finding big punts, but be very aware that having a high GTO wizard score doesn’t mean you are playing perfect GTO, or even close. In my opinion I think it’s very easy to use that score to get put into a false sense of security about your exploitability, which is the worst because you can be exploited and think you’re protected. I think this feature does way more harm than good, and I feel very strongly about it.

With GTO trainers I wouldn't put much attention to EV vs, just make sure you aren't making giant punts, and you understand the principles behind your decisions. Thinks like range advantage, nut advantage etc. GTO trainers are still very useful for looking at things like value thresholds etc.

That is it for me on my thoughts about solvers. I hope this is helpful for understanding what they are doing.

Do you mean this cool video?

Yes! Thanks! Phil G is great.

The past few weeks have been busy again. I have been studying and playing poker quite a bit. My game feels better and better and I feel like mapping out the nodes, writing out heuristics by texture and then distilling that into a smaller set of heuristics has been very helpful.

Generating the "right" heuristics is hard though. The more compact and simple the easier it is to remember, but it can take some time to ask the right question. In general this is the most time consuming part.

I try and use relative terms, but you can get too general. "Overbet the 3+ nuts or 4+ nuts with a blocker to the nuts" looses is meaning. So I usually end up going back to absolute terms by texture, and trust I will be able to brain solve any weird spots later.

With the above workload I had before I have kind of hit a wall mental energy wise. I am studying and getting better, and enjoying playing but I only have enough mental power for an hour or so a day. If I can't find recs I usually just pack it in. I was sprinting for so long now that things have calmed down I think I am just tired.

I got my click ranker working at my job. I did it in 2.5 months we have gains. From start to finish. MY tech lead said I should be proud of that. I don't think I have herd him compliment anyone like that before.....so was it worth it? Not really. I really don't feel proud of the work done. It was forced to a time line and everything is rushed and it's going to be a pain fix and modify later. Basically was the exact thing I said I didn't want the project to be..but I am a foot solider not a sergeant...and the sergeants want their boxes ticked. I take my holidays end of June, work a month in August, then quit middle of September. Almost there.

I think I am going to take it light on the playing time for a few days. Yesterday and today I just didn't get a lot of hands it.

I also just am crawling myself out of a 12BI downswing. Was bound to happen, but I really took it as a game. I took it as a challenge to make sure this 12 BI downswing wasn't a 12BI downswing with 8 punts on top of it. And I think it went well. We are climbing back out of it.

Technical punts are fine. I do them all the time. You need to make mistakes, but mental punts are leaks. Plain and simple. If Linus with all his knowledge punted off every time he ran bad...he wouldn't be rich.

Mindset is part of the game. My main leak right now is volume again. I like playing poker. I like building the heuristics and strategy and then executing it and fixing issues, and plugging holes, but I am just toast. Volume is my main leak right now. Seems to be the running theme.

I catch myself saying..if I could just focus on this..I would be gucci. Almost there.

That's it for me.

Thanks.
Chowzor.