Good luck - very impressive start to the thread! I'm jealous about the rake back.

I'm super impressed by the way you talk about the hands you've played - I think we have a similar approach.

I'm also playing 50z, and just graduated from uni (UK) this year . Maybe we could all talk some hands on discord?

Thanks for the engagement and gl on the 50z streets! I've private messaged about discord.

If anyone else wants to talk poker with me then please reach out regardless of stakes or anything else - only condition is that you enjoy the game.

Nice, count me in for Discord!

Applications of Prospect Theory to Poker

Introduction
In this article, we explore a theory from behavioural economics about decision making under risk called ‘prospect theory’. The first conclusion of this theory is that people tend to be risk averse when offered positive options and risk seeking when offered negative ones. We also explore the idea that these prospects may be affected by recent changes in the person’s situation to which they have not yet adapted; recent losses can make all options seem negative and hence provoke risk seeking and vice versa. Finally, we attempt to apply some of these principles to poker, drawing on examples of common mistakes made at the tables.

Prospect Theory
In 1979, Daniel Kahneman and Amos Tversky published “Prospect Theory: An Analysis of Decision under Risk” [1]. This paper presented a critique of ‘expected utility theory’ - the prevailing theory of decision making under risk at the time - before proposing an alternative model, ‘prospect theory’. Based on the responses of a student body to hypothetical choices, Kahneman and Tversky demonstrated that several core principles of expected utility theory were systematically violated in human behaviour. Prospect theory was an attempt to integrate some of these deviations into the decision making model and its success was cited in Kahneman’s 2002 Nobel Memorial Prize in Economics.

The first deviation observed in the paper was that “people overweight outcomes that are considered certain, relative to outcomes which are merely probable - a phenomenon which we label the certainty effect”. In other words, given two options with similar expected values, where one is guaranteed and the other involves chance, the former option will be artificially emphasised by it’s certainty. To demonstrate this, we examine the following problem which was presented to 95 participants.

Problem 1
A: 80% of the time receive 4,000
B: Always receive 3,000

In this study, 80% of the participants chose option B over option A despite the lower expected value. These same participants were then given the following problem.

Problem 2
A: 20% of the time receive 4,000
B: 25% of the time receive 3,000

Now, 65% of the participants chose option A with the higher expected value. Note that problem 2 is simply problem 1 with both probabilities divided by 4. Since the value of the prizes did not change, these results suggest that “reducing the probability of winning from 1.0 to 0.25 has a greater effect than the reduction from 0.8 to 0.2”. So far, this phenomenon could be described by the principle of risk aversion, but this solution promptly fails when considering the next deviation raised in the paper.

What would you expect to happen when the gains in problem 1 were replaced by losses? Option A would remain the riskier option and would also now have a lower expected value, so surely an actor whose decision was governed by either of these factors would always choose option B.

Problem 3
A: 80% of the time lose 4,000
B: Always lose 3,000

Despite this logic, 92% of participants now chose option A - the riskier option with lower expected value - directly refuting the solution of universal risk aversion. This pattern was named the reflection effect and can be summarised as “the reflection of prospects around 0 reverses the preference order”. This pattern is obvious in a simpler context: Would you rather receive 200 or 100 units? Would you rather lose 200 or 100 units? It is clear here that your choice would swap when the problem changes from gains to one of losses, i.e. when the prospects are reflected around 0. The interesting point raised in the paper is that this pattern continues when considering more nuanced decision making.

While we witnessed risk aversion in problem 1, we now see risk seeking behaviour in problem 3, despite the lower expected value. The implication of this is that “risk aversion in the positive domain is accompanied by risk seeking in the negative domain”. In problems 1 and 3, this is a direct consequence of the certainty effect. In each case the guaranteed option is overweighted, reducing the appeal of the risky option for positive outcomes (risk aversion) and increasing the appeal of the risky option for the negative outcomes (risk seeking).

We now have a model that predicts an inflection of preference around 0, but this reveals an important ambiguity. Until now, we have assumed that the gains and losses offered in the problems were being compared to some reference point that was treated as 0. In many situations, this is not an accurate reflection of the decision making process. In fact, “a discrepancy between the reference point and the current asset position may arise because of recent changes in wealth to which one has not yet adapted”. In particular, recent losses may lead to the perception of all immediate outcomes as negative when compared to the reference point of just before the loss. This negative translation of these prospects would lead to risk seeking behaviour.

Applications to Poker
In order to apply these conclusions to poker, we must first establish the relative risk of various actions. I propose that, in general, the more aggressive actions in poker tend to be more risky - primarily since they involve putting a larger sum of money into the pot. Therefore, betting and raising are more risky than calling or checking, which are in turn more risky than folding.

With this in mind, consider the first implication of prospect theory - positive prospects produce risk aversion while negative prospects induce risk seeking. One scenario with almost entirely positive prospects in poker is being in position on the river with a value hand facing a check. In this scenario, the expectation value of both betting or checking would surely be positive and hence we may expect to see risk averse behaviour. Indeed, I think that a common mistake made by poker players in this spot is to be reluctant to go for thin value - justifying their actions with phrases such as “I’m happy with the pot”. In other words, when faced with a more profitable option which has higher associated risk, people will tend to choose the option in which they are certain to see a showdown.

In theory, it is impossible to construct a similar situation in poker with purely negative prospects since folding always has an expected value of 0 relative to the money already contributed. Despite this, the second implication of prospect theory is that decision making does not always occur with an appropriate reference point and recent changes in wealth can shift new prospects both negatively and positively. As mentioned at the end of the previous section, if one has just incurred significant losses, following decisions may be compared to the reference point of just prior to the loss. This would artificially make all options seem negative and hence lead to risk seeking behaviour.

I think that this is a valuable lens through which to view ‘tilt’ in poker. Trying to “win back” losses is a common phenomenon across gambling, with poker being no exception. The behaviour that this encourages comes in the form of playing more hands preflop, folding less draws or bluff-catchers postflop, and generally seeking greater risks despite lower expected value - just as prospect theory predicts.

This effect can also be seen after a recent positive change when many players are tempted to “book a win”. This mentality leads to playing tighter preflop, avoiding difficult decisions, and overall playing more passively - in summary, playing more risk averse! We can see that regardless of whether you have recently won or lost significant amounts of money, both of these can have a serious detrimental effect on the quality of your decision making.

Conclusions
This article has covered some of the key concepts of prospect theory - namely the certainty effect, the reflection effect, and shifts of reference. We have looked at how these were first recognised from empirical data and considered their implications in the wider context of decision making under risk. Finally, we applied these lessons to poker and suggested some real life tendencies which may be manifestations of these ideas.

I hope that this has been an enjoyable exploration of a concept from behavioural economics and that it has offered insights into a few common errors made in poker. Thank you for reading and good luck at the tables!



[1] Kahneman, Daniel, and Amos Tversky. “Prospect Theory: An Analysis of Decision under Risk.” Econometrica, vol. 47, no. 2, 1979, pp. 263–291. JSTOR, www.jstor.org/stable/1914185.

Week 4

I've had another really good week for my habits with a clean sheet (and on track to finish my book for the month in the next couple of days). I think it's important to take the time to be proud of yourself when you stick to your goals and that this is an invaluable part of the process of improving. Saulo Ribeiro talked about this in a RIO video titled "A Systematic Process for Strategy Development": he said that the final step of an effective process is to "feel good about yourself" - this is vital for the long-term sustainability of your efforts.

I'm also introducing a new goal aligned with completing the rakeback challenge once this period at 50nl.

New aspirational target

• Poker Volume : Play 4.5k hands per week (up to completion of rakeback challenge)

Goals
[x] Sleep
[x] Meditation
[x] Exercise
[~] Reading
[x] Poker Study
[x] Poker Volume

[-] = incomplete
[~] = partially completed
[x] = completed



Results

It's been a while since I've felt like I really crushed a session. I think this is in part due to the Dunning–Kruger effect (i.e. I am more aware of the extent of that which I do not know) and also because my study goals are somewhat ambiguous. To attend to this, I will devote some period of time in the coming week to consolidating my study goals and coming up with an overarching strategy.







Hand Histories

Naughty


Nash

Nice work.

I think it's right that study needs to be an active engagement with your subject rather than passively watvhinig RIO viideos or whatever.

Thanks!

Yeh, I very much agree with you.

January 2021 - Results

Just a quick post to collate my monthly results.

Really interesting post looking at prospect theory applied to poker.

I absolutely loved reading "thinking, fast and slow". The "undoing project" - by Michael Lewis is also a very interesting if you've not heard of it. It is more a biography of the partnership between Daniel Kahneman and Amos Tversky.

I think poker players should always be trying to work within the framework of maximising EV even if it is very difficult to avoid the biases you highlighted. As you say, often we are risk averse and take a lower variance but lower EV line (not thinly value betting is a excellent example).

This is why mental game and bankroll management are so important - you need to be able to take high variance lines and ride the resulting swings. Perhaps it is unsurprising the best poker players seem to be emotionally detached from the real monetary value of the chips in front of them.

Keep the updates going!

Thanks for the book recommendation - I'll add it to my list.

I agree that overcoming natural human bias is a challenging task - working on mental game is certainly key!

Week 5

Another decent week for habits in the books. Drinking over the weekend was the only reason I missed the sleep and volume goals this week - unsure what I think about this at the moment. I've decided to record the reading habit as a success if I read on at least five occasions in a given week. I've also decided to modify the poker study goal to 3 hours of intentional studying - i.e. not necessarily hand reviews. I'll expand on the reasoning behind this later.

Goals
[~] Sleep
[x] Meditation
[x] Exercise
[x] Reading
[x] Poker Study
[~] Poker Volume

[-] = incomplete
[~] = partially completed
[x] = completed



Results

Further, I've decided to stop posting weekly results. I'll probably still post monthly graphs going forwards but I'm just not that interested in my weekly results. If I'm not interested then I don't imagine they'll be entertaining for others and I also think getting enjoyment out of my own posts will help with the longevity of this thread. A really common problem in poker is drawing unreasonable conclusions from small sample sizes and providing copious small samples of results seems entirely conducive to this.



Study Plans
In a recent study session, I noticed an unproductive thought process that hero was applying regularly. Often, hero would: identify one or two key properties of the situation; quote a learnt heuristic; take the prescribed action. This approach had two major downsides. Firstly, it overlooked any nuance in the scenario which would be necessary for more refined decision making. Secondly, and in my opinion more importantly, it served as a "black-box" into which hero no longer had access.

An example
1) Identify one or two key properties of the situation: Hero is PFR and the board includes high cards.
2) Quote a learnt heuristic: "Hero has the range advantage here so should bet small and often".
3) Take the prescribed action: Range bet for a small sizing.

The consequences of the first downside can be seen as hero only considered two, relatively superficial, factors in their decision and then applied their conclusion to every hand in their range! This is particularly detrimental if the learnt heuristic is flawed, or built upon inaccurate principles, as it will repeatedly provoke suboptimal decisions. The possibility for the heuristic relying on inaccurate principles is why I claimed the second pitfall was more harmful. At the time of learning the heuristic, hero likely understood the foundational ideas and how they culminated in the final product. Despite this, when recalling it at a later date, these concepts were no longer available and hero was forced to blindly accept the conclusion drawn long ago. This means that, if the flawed heuristic was never challenged, it may become a permanent blind spot in hero's strategy which they would find no motivation investigate.

In response to this realisation, I have made a few modifications to my general studying plans and imminent studying goals. Overall, I intend to do less frivolous hand reviewing and more intentful, structured studying. I think that there is value to be gained from arbitrary hand reviews, mostly in refining intuitions regarding certain thresholds, but I think that it should be complementary to a more defined, underlying improvement plan. Moreover, I don't think that theoretical knowledge is the bottleneck in my current results. Undoubtedly, there are still many areas where I could improve my grasp of strategy in both depth and breadth, but I think that there are other, more demanding, facets of my game which I have been neglecting. Specifically, EVERY OTHER ASPECT! Currently, I put over 98% of my efforts into improving my technical skills and I'd like to redistribute some of these in the future. I'm not sure exactly where or how but I'm working on this.

Thanks for reading, all the best, and gl!

Nice post - it's so important to remember in poker that there is rarely a plan that you can just blindly implement in every situation. Everything is a 'it depends' kind of thing. Training our minds to solve problems on the fly is far more important that memorising a load of 'rules'.

That isn't to say learning solver lines isn't important as you move up but understanding why the solver does things allows you to make educated guesses about plays during the game when you might not know the solver play.

Thanks for the engagement and I strongly agree with what you've said. Trying to figure out "why" is far more valuable than remembering "what".

Week 6

A happy, productive week! I missed the longer meditation session but did a short session every day. I've also recalibrated the volume goal to match the remainder of my challenge.

Goals
[x] Sleep
[~] Meditation
[x] Exercise
[x] Reading
[x] Poker Study
[x] Poker Volume

[-] = incomplete
[~] = partially completed
[x] = completed



Studying

I'm still in the investigatory stage at the moment but I'm putting in plenty of effort and will continue to refine my plans going forwards.



Short update, gl all

Meditation is ****ing hard

Impressive work ethic, GL Leth!

Meditation is surprisingly challenging given the main goal is to do less! Thank you for the kind words

Really enjoyed the OP. subbed and good luck!

Thanks Ben, it means a lot to have you jump in the thread

Week 7

A clean sweep this week! Admittedly I squeezed in the longer meditation and second intense exercise session on Thursday evening but it's a victory nonetheless. I finished my rakeback challenge on the evening of the 16th and have happily received another for the coming month.

Goals
[x] Sleep
[x] Meditation
[x] Exercise
[x] Reading
[x] Poker Study
[x] Poker Volume

[-] = incomplete
[~] = partially completed
[x] = completed





Shot-taking 100nl
Some recent heat at 50nl and the rakeback challenge have given my bankroll a welcomed boost allowing me to take shots at 100nl. I've been playing this stake for the past few days and hopefully I'll be able to remain there going forwards. In this case the rakeback challenge would require much less volume and I'm unsure whether to: complete it twice in this period; play some volume on other sites (such as RunItOncePoker); undertake some additional studying; or something else altogether.



Studying
In the past couple of weeks, I've been enjoying lots of 1-on-1 sessions with members of my study group. The overarching goal of these sessions has been to discuss our general approach to poker and the key factors we think are relevant for decision making at the tables. I'm planning on synthesising the conclusions of these conversations in the coming week which will hopefully provide some clarity as to where I would like to devote my studying efforts next.

Gl all and thanks for reading

Week 8

Poker took a backseat this week - as it usually does immediately after each rakeback challenge. Despite this I still had a 1-on-1 study session and played a few thousand hands. I'm slightly adjusting all of the goals as I go and one addition I've made to the "Poker Study" goal is to have at least one 1-on-1 call per week. I find these incredibly beneficial and you can build a much deeper understanding in these direct conversations that in a group session. Despite this, I also find a lot of value in being part of a larger community and I don't want to neglect this either.

All the other goals went swimmingly, not much to report there. One aspect I would like to work on is consuming more theory content around meditation - while my practice has become quite regular I'd like to learn more about some of the underlying ideas and different techniques.

Goals
[x] Sleep
[x] Meditation
[x] Exercise
[x] Reading
[~] Poker Study
[~] Poker Volume

[-] = incomplete
[~] = partially completed
[x] = completed



Thought process exercise
As I've mentioned in the past couple of updates, my studying in recent weeks has taken the form of a big picture analysis of my decision making process in poker. I've tried to break down my game into some meaningful categories and then identify the key factors that I believe to be relevant in each scenario. I think that this type of holistic, course-grained exercise is great to undertake occasionally as it helps to align your weekly studying with your broader objectives. I also asked members of my study group to engage in this activity individually and we have had numerous discussions about our conclusions.

If you're reading this then I'd strongly recommend you try it for yourself! As a launchpad, here are some questions to start with:

• Play out an imaginary hand in your head (or use a hand history). What are the key factors you consider at each decision point?
• What attributes of a strategy do you find desirable? Can you rank these in order of importance?
• What is your fundamental goal when playing poker - what is your main objective with each decision and what consequences does this have?

If anyone does engage in this activity then please reach out to me as I'd love to discuss it with you. This goes to people playing any stakes and of any level of experience - the only condition is that you're keen to improve.

I will be using the lessons I've learned from this activity to guide my approach going forwards, both on and off the tables. Most importantly, I feel that it has offered clarity into what I should be using a solver for and which other tools I should be using for other tasks. Notably, I intend to spend a lot more time preparing my thoughts before running a hand and checking the factors I considered rather than whether the line is "solver approved".

All the best and thanks for reading. End of February update coming soon!

February 2021 - Results

February has been a pretty decent month with 50nl going particularly well and some small success in the start of my shot at 100nl. I'm on track to continue playing 100nl as my main stake at the moment but I'll probably move down at around -$500 from now. Either way I'm very happy with the mix of volume between reg tables and zoom and I feel like I'm playing quite well (which is easy to say when you're winning). If this shot at 100nl doesn't work out then life will go on and I'll continue putting my main focus on improving and playing my A-game at every opportunity.





I think it's healthy to take a step back and recognise how far you've come every now and again. I remember grinding up from 2nl in the latter half of 2019 and being amazed by sun-running past 25nl and taking a shot at 50nl. Almost immediately after this, I remember being distraught after a $500 downswing and wondering if I would ever be able to compete at the lofty heights of 50nl. I'm a much better player now in many aspects and, more importantly, the process I've developed for improving is significantly more effective. No longer do I create new preflop ranges every time I go on a 10BI downswing, or become enamoured by every 10k hand sample I see on social media (though sometimes still this second one tbh).

I'm proud of the path I've walked so far and I'm looking forward to seeing where it takes me next.



2021 Year to Date - Results

What would you say the main differences between 50 and 100 are?

-

Congratulations on a nice month, seems well deserved.

I don't think there are any huge differences but it's also a bit soon to be drawing any firm conclusions. The main difference I've noticed is that the smaller player pool makes the reg speed tables a bit more competitive. I find myself sat with 4 regs more often than compared to the 50nl reg tables. I also imagine that I'll get check-raised, overbet against etc. a smidge more - but again, too soon to say.

Thanks for hopping in and for the kind words.

Great results! I find it so hard to see the bigger picture too, especially when building up a sample takes so long when playing full time. That's having a thread is so nice, in a year's time when you're downswing at 1knl be able to look back at how far you've come

Thanks for the kind words mate, I look forward to sitting on your direct left on the 1k tables!