Are you serious????????????????????????? And say this after accusing me of arrogance and think others have the same idea about me (you represent them all now?). If that is not the definition of arrogance, what you just did, then i dont know what is.

The very fact you ask if C will change the value of the system shows that my toy model was very needed actually because it offered an answer to this question. It also shows you didnt notice it.

I already gave you an example to see how C can make the company viable and take its risk of ruin from eg 55% to 15% or less even. Isnt that something C is offering to the value of the enterprise?

If B can always find later someone to support them even after a failed example, its another story, but to A it must matter how easily he can lose his investment and realize the long term profits from it and adding another makes that less likely with a winning player. However adding another at any price isnt always a good idea for A. In sometimes if A has put a lot of money C is not really needed and isnt adding any more value, only reducing the EV for A. But in the example given 50 is very little compared to the apparent entry fee if the first profit is say order 20 hinting its only a few buy ins (3-4?)

In fact if B is planning to occasionally take out some profits and not retiring from the enterprise any time soon to go on his own, A and C stand to make a ton of money from him because he will always need their backing. They can simply also take some profits out every now and then and only add as needed to keep things running. That way they can exploit B indefinitely. If that is true then A actually likes to see C come and make the enterprise hard to go bust. Isnt that true with eg an insurance company as well? The more investors back it the less likely it is to go bust (by having to pay a big claim) and realize profits for them. Same for a casino etc.

This is why all these details are needed.

The risk of ruin if people take out profits from the system will be greater actually unless they do it much later. Of course what keeps the system running other than not busting is the fact B keeps using profits for life expenses say and not building a bankroll of his own.

That way the projected say 500 i offered as example to stop the company can become 5000 if B only saves 10% of his profits. That skyrockets the EV of A and C. For A then the most important thing is to not bust and C secures that by adding more cushion. C in fact extends the EV of A then a lot. I believe i gave an example that this happens that C actually increases the EV of A in some numbers i used (the 50 vs 110 deal). That example can be made even more extreme if B is not a very strong winning player but only a small winning player. An average winning player is definitely requiring more capital than 3-4 buy ins. Maybe 40 even.

For example if the player was 52-48 then the risk of ruin is 79% with what A just started it. So adding C then with eg 2 times the capital takes the ruin down to 30%. That definitely helps the EV of the company ( A and B). It makes more likely that both A and C will see B reach his bankroll goal of say 500 at which point the company ends. The more time this takes (if B takes out money from his profits to live) the better (eg A and C can even make 5000 if B takes only 10% to build bankroll from his own profits) provided it has escaped risk of ruin by using some of their own profits to create an even larger cushion.

Nope. I think trying to boil this down to EV is stupid. I'm just exploring your stupid idea in the simplest way possible. One step at a time, and looking at the assumptions that go into each step, rather than pretending like cranking out complicated calculations is really getting to the bottom of things.

What do you think the overall change in EV is with another investor? Will it be significant or negligible?

Aaron why dont you do your own numbers?

I have 3 buy ins to give to a good player that has 55%-45% sessions at a level they cant play with their own money because its expensive. That 55-45 means they have 55% chance to double their stack before busting.

The risk of ruin of such system is (0.45/0.55)^3=54.7%

If the player survives ruin and reaches say 25 buy ins of their own they will retire from my help. So i stand to make 25 buy ins having risked 3.

My EV is 25*(1-0.547)-0.547*3=9.68 buy ins.


Now C comes and adds another 9 buy ins. The risk of ruin goes to (0.45/0.55)^12=9%.

The EV of A now (that splits 50% with C) has become if B retires again after 25buy ins profit;


(1-0.09)*25/2-0.09*3=11.1

Isnt it true that A went from 9.68 to 11.1? (EV for C is ~10.5)


Isnt that an improvement? The same happens for B also. It is now 91% certain he will reach his 25 buy ins profit.

What if B always takes 90% of his own profits to live and saves only 10% requiring to win 250 buy ins to save 25.

The EV of A now has become

(1-0.09)*250/2-0.09*3=113.5 with C vs 250*(1-0.547)-0.547*3=234.7 when alone

That is now a significant reduction for A's expected profits.


As you see different details produce different outcomes in EV.

Because I don't think an EV calculation makes sense for investment. If I wanted to buy stock in Amazon, doing an EV calculation really wouldn't accurately represent the thought process of making the investment.

Notice that you didn't even answer the question. Do you think the overall EV significantly changes as the result of another investor? All you've shown me is that you know how to do arithmetic. I don't doubt that you can. I'm trying to see if you can do more than just grind out calculations.

Come on now this is trolling level worthy of the guys in politics. What did i just do above?

Didnt i just create a company for you A+B 3 buy ins 55-45 player lets go for it 50-50 and calculated the EV of both A and B and then did the same with C and posted the differences?

Dont you believe in averages for sessions? If we have a more complex distribution it will be a more complex calculation but the same logic.


And for investment you better believe it that a similar calculation can be done but its very hard to be accurate because the world is now very complicated and you have to go over a thousand problems with it like overall economy, competition, inept management etc cash flow to the market (like available cash for investment i mean), income of people, how exposed they are already, model tulip manias, crashes etc.

But if you can do it properly you can find companies that are definitely undervalued by a lot. I think for example one such case is intel corporation that has been undervalued for over 15 years, runs all the high technology of the planet easily and is badly managed because actually its a more ethical company that doesnt produce gadgets that waste people's money and lives like apple does creating an entire industry that milks each one of us every month for over 80$ in order to provide a service that is not even 30% of this cost in reality. Sure enough a lot of it is useful but their business model is not about giving us useful things but most importantly about giving us things that are entangling us to more and more paying services and dependencies like addicts. Of course some of it has to be useful too. Google is another killer company that is shameless (how they treat everyone) but has the perfect image in the surface.

If intel wanted to put itself like apple did on every device we have like our car (yes cars will soon need top level AI to drive) and make smart appliances even the entire home computerized they could create a ton of income running on their own cpus everywhere. Instead they let others do it and use all kinds of different chips from competitors and they are left chasing and trying to adapt to them instead of leading the market on their own there.

That is a crystal clear case of bad management that if it can be transformed can lead to an explosion of 5x easily like apple did last decade.

In fact for investment you probably can start doing path integrals to value stocks properly and go over all possible things that can happen (from going out of business to becoming market leader) in diffusion of all metrics and modeling the entire future and seeing which company has potential to explode even if it doesnt look promising yet because it is involved in something that is very volatile and not easily appreciated in advance.

You can even select a number of companies from different areas that are correlated or are competitors and create a combo portfolio that will
be self correcting ie when you miss on something the others pick up. If you do the selection properly anticipating who wins big if one bet fails you may create a good position that has potential to move. You can only do that if you can simulate forward how they will evolve as companies based on complex interactions that are emerging. You can anticipate battles between companies and who third parties benefits from them if they happen etc. You can do all kinds of imaginative games like that if you have enough data to be able to simulate things reliably well. But of course you need a special insider access to all kinds of information to do it right. It wont happen from your home.


You can also model what companies to short puts to death after every market decline like say the recent one because they can never go below book value say etc or you can hold them for 3-4 years if the trade goes bad and be destined to recover eventually etc. By that i mean you can simulate the progress of the company under a variety of bad markets and good market outcomes and see what the strategy does. You just simulate their future earnings using all the information you have about their sources of income etc. Many multiple interacting diffusions.

You can simulate for example oil price and what happens if it goes down or very high in terms of how it impacts various industry choices and opens new fields or new types of oil markets and how these crash if the price drops sharply etc, how fast they can recover if a rally happens etc. You can follow what happens to the economies of markets that depend on oil being expensive and how a decline affects other markets there on seemingly unrelated things and create very complex synthetic positions that exploit each other's developments. The ideas are limitless if you have access to good information and connections and know how they all work together. Look at a movie like "the big short" recently out and you will see in there some pretty true things about how you can uncover moves before they happen by precisely relying on fundamental analysis.


But all those efforts are very hard i agree to obtain legitimacy unless tested in time.

The situation here though is very clear. A player can have indeed an established history and we can model their return with a distribution that doesnt take 55-45 as if written in stone but uses some averages and we perform an integration to find the true EV.


Are you able to discuss with me seriously with respect or trying to find insults in every chance you get? What is it about the 55-45 example that you dispute as not reasonable modeling?

You inserted all sorts of random assertions to make it possible for you to do an EV calculation. But you didn't answer the question.

What do you think the impact of a third investor is on the overall EV?

* If you think the overall EV will increase somewhat significantly, then you must be making some type of assumption that the player is grossly underrolled and is taking shots of some sort. This would suggest that the long term data you need to do the calculation isn't actually available.
* If you think that the overall EV will not increase by very much, then the only person that stands to gain is the new investor, and we can immediately discard the option of putting in an additional investor based on your EV concept.

The reality is that EV is a pretty stupid way to look at this. It's pretty obviously so because this is an investment with no specific horizon with the potential of people entering and exiting in the future (like investing in the stock market).

You are placing some sort of valuation on the player, and investing money with the hope that it will grow. You can cash out at any time, which means you don't need to hold until ruin. And for all the words you've put out there, none of them reflect even that faintest idea that you actually have any functional knowledge in the things you're talking about. Instead, you've got an imaginary model in your head about how you would imagine such things could be done.

Yes. I'm doing just that. You're just rambling and pretending like it's knowledge, and then getting pissy when confronted with simple questions that show how terrible your model is.

Everything, if you're trying to address OP's question. Nothing, if you're playing with your own models inside of your head for your own benefit. If you want to do stuff for your own benefit, have at it and ignore what I have to say.

Are you saying that we cant put a value to a company that is so easy to describe as this practical situation of 3 people and only 1 playing with known avg results or updated results based on some initial distribution? If we have no distribution its a lot harder of course. What makes it hard to actually trade the value of the shares of the guy in the future? What happens is that someone comes and replaces C for example at exactly the correct price that keeps the system intact. Or C just leaves and we adjust what the exit price is with simple calcualtions at the spot that again relate to the EV of the system depending on what has happened so far. Certainly the profits C has received are intact.


But why would A or C sell before its over before B stops playing? If you have a winner you keep using them until you meet a target. If you exit before that target you realize the profits up to that point, we will use exactly what you have gained so far to exit (ie take your money and your profits minus some minor adjustments to not undermine what others have there still going if needed). Sometimes the exit of C is irrelevant and a good news for A actually. Glorious news! The risk of ruin is long gone often and now A is sitting on pure profits going forward. If it happens on the way down we can estimate that too.


The stock market is hard to do this because the system is very complicated and as you said it doesnt have well defined horizons plus it involves millions of players. Selling shares doesnt impact the operation of the company as it does here. Its a different and far more complex system.

But this company is actually very simple to put a value to it. We will need a distribution for the performance of the player and then update it while we run it and end up with a bit more complex system than i described but only in an integration sense. Its still the same logic of assigning an EV to all players as they are positioned.


Feel free to offer me a particular scenario before the end i placed at ruin or 500 (or whatever money you think B will use to retire). The simplest solution is the player C say takes their money and profits so far and possibly with some tiny adjustment based on the details at the time cashes out and leaves.

Why is that hard to do? If it is doable to value how to price his entry, the same logic will be used to price his exit.

All i want to give you numbers is for someone to actually come and tell me how this is going to be done in detail (like if we take out profits or leave it in always, how often player plays games and the distribution of the games (ROI), interest rates etc). Once i have that i think its very easy to evaluate at any point how much the enterprise is worth with or without a particular member. It is always possible to evaluate how much something is worth by letting it hit the barrier or ending it prematurely. We might even price it as an option using stochastic processes.

A small penalty may be in place to discourage such run but more or less it will be along the lines of take your money and profits/losses and leave.


Holding a position to the end for a positive player offers maximization of EV. If you leave earlier you cut down on this. Why is that hard to evaluate?

It will also depend on the initial agreement. Something has to be there to secure things for all players that we are in it seriously and we wont run out tomorrow. But there must be room to do that too at some minor penalty.


To put real numbers to things i need a very precise system to be given to me to know how it works out for all. The risk of ruin is very different if constantly people take out their profits for example.

I'm saying that if you want to work out a system for buying and selling shares of an individual's gambling, your system is needlessly complicated and doesn't actually help someone develop a system for buying and selling shares of an individual's gambling. It answers a completely isolated scenario with lots of arbitrary assumptions.

Why did you declare in your model that you'll pull out at 25 buy-ins? Your model cannot work unless you've got well-defined stop points. But most people enter into investments without such things. So your model can't possibly be that helpful.

No, you're just under the illusion that you've placed a meaningful value on this situation. Just like people who are crappy day traders look at charts without having the slightest idea what they mean, and use that information to make decisions. Or like people at the horse races that look at the DRF and pick based on how much they like the names of the horse.

First we need to know how this whole thing works. A value can be provided under the conditions i set. Why is suddenly the example i offered to illustrate a valuation effort a problem for you? Give me how the players play this game and how often they cash out or take our profits and i will develop something else.

Until this is offered i gave you a way to value a system that sensible people come together to do. If you want to cash out and its you and the player you simply take your money and run unless you have a contract in there that locks the money for a fixed number of trials.

So i dont know what is your problem if i play a game that in my initial agreement i have these numbers in place to offer some stability.

If someone nevertheless in the absence of contract wants out they can take their profits so far and their initial cash position and leave minus some adjustments or plus some adjustments depending on the position this happens.

For example if C leaves after much profit is created A will be happy to see that development. I can then see that C leaving may result in C taking more than their initial cash and profits because their decision to leave opens the door for A to make even more now with 0 risk of ruin practically. Some correction bonus to B may also take place there because he acquires a slight risk of ruin increase with C leaving.


I am trying to answer some cases even restricted ones and you are trying to oppose anything i do. Intelligent people in this thread know very well what my objective is here and what is yours when you play like that. I never said here this is how you value it period. I only explained a situation that was in agreement with all involved how to do it (eg when they stick around to some target or ruin and cash out only then). Other details will lead to different models.

If i enter into an agreement with others to do this i want some bloody stability. I am not starting today and you leave tomorrow, because i put my time and effort into this. So i will contract the sh#t out of you upfront to avoid little bs things like that or allow them with penalties. I dont have to do this but different systems of rules have different valuation. Rules offer stability and help the plan here that is for all to make money in a fair manner without doing volatile reckless things.

The question that OP was asking was whether we could find a way to make the whole thing work. You're the one who started off with the declaration about expected values as being the way to approach it. I disagree that this is useful, and you're showing me in every post how right I am about it.

You keep saying that the game is checkers when we're looking at a game of chess. Yes, they're both played on an 8x8 grid, but you're not playing the game that corresponds to the pieces that are in front of you. You're doing something else entirely.

No sensible person will use your system. That you still think that's the case just shows how poorly you understand what's going on.

As another analogy, I've been recently watching some videos on machine learning. The lecturer took about 20-30 minutes of a lecture to talk about all the practical pitfalls there are when people are trying to do machine learning.

Machine learning is a complex system that has several distinct processes. And if the overall system isn't working, it's easy to waste a lot of time tinkering on one part of the system to get actual improvements, but the end is negligible improvement. The reason is not that there's anything "wrong" with the improvements being made (maybe enhanced convergence or gathering more training data), but that all of those efforts are going towards the thing that's not the problem.

You're doing precisely that. You're so invested in tinkering around with EV calculations that you haven't seen the big picture and recognized that the EV calculation isn't the flaw in the system. You keep demanding that I make this or that assumption and insisting on how reasonable your assumptions are. I'm looking at the whole system and telling you that EV calculations aren't even the thing you should be looking at. But because you're so wedded to the investment of time and energy that you've spent building up this excessively complex EV calculation, you're never going to be able to walk away from it and make the whole thing better.

The issue that OP has is not the valuation process, but the share division process. You think that if you could just get everyone to agree on the value of the player, that they could then go from there to agree on a fair price for selling off shares. I'm just telling you with a very high level of confidence that your process is wrong.

Maybe one day soon you will realize that all i am doing here is that in the absence of rules and details by OP i created rules of my own that appear rational (clearly a rational exit point is one that B feels he has enough of a bankroll to no longer need backing so set it at 1% risk of ruin or ask him!!!). We need to know what player we are dealing with here also. If we have no clue we need to still use some distribution and update it with each result. Investing in a bad player is negative value!

So all i did is i created a well defined situation to show how to value that share there under these assumptions of operation of their agrrement.

Your objection here is what exactly? That what i said is not the right way to do it under my assumptions? Then show us what it is under these assumptions. But you are not doing that. Instead you take a different situation and argue things there away from my assumptions. Well thanks a lot for failing to see that i selected my assumptions as a reasonable example that an answer can be delivered, not as a general answer under broader conditions. This was never a claim that its an answer under different conditions that people may find more desirable like for example to not need to know how good player B is or be able to leave as soon as they like.

I know that you created your own rules. I disagree that they're particularly rational rules. I've stated this very clearly already, and I'll say it again: Your model sucks.

Anyway, to get back to the original question, I think the thing that makes the most sense is a shares system.

Let's just say that there are a total of 100 shares and that no more shares will be introduced until some point in the future at which you break up the agreement and create a new one.

Presumably, since the investors get 50% of the winnings and you only have one investor, B holds 50 shares and A holds 50 shares.

At this point, if C wants to get into the game, he needs to convince either A or B to sell off their shares to him. This can happen at whatever price is agreed upon.

And that's all you need.

Edit: Although it's not needed, B should write himself an out clause that he can buy back his shares at some point in the future for some fixed price. Otherwise, B is screwed in the long run if he's actually good at poker.

Aaron W. Once and for all know that i only want to interact with you as if you are someone i respect and find value in discussing things and exchanging information, including of course corrections and suggestions to each other in a kind responsible manner. When we disagree in my side at least it is on ideas not who you are as a person, your style or anything like that. My only complaint regarding personal issues (is in reaction to what is directed at me, it is not a personal initiative) is that i have a very different way to disagree with others that doesnt ever require me to denigrate their ideas or who they are, to be generally nasty towards them. I dislike when not treated similarly.

I have never said to anyone their ideas suck for example or to start from scratch erasing their work or that they are fixated with different problems than the original, unable to rethink something if necessary, only willing to see their own way work out or accused them that the length of their posts is of no substance and isnt used to support logically and mathematically an argument. And you do those things that i find undesirable and unproductive. I do not have a boss attitude towards other people when i talk with them. I respect their efforts and anticipate there is a reason for them that i want to understand and appreciate better. Its not too much to expect something similar.


I find your criticism of my suggested example model puzzling. See why.

2 people come together and B has charts showing he is a 55-45 player in cash games from past activities there (plus A knows that independently - or he has a distribution, same thing) and says to A, look i want to start something profitable for both of us. I am currently unable to put together a bankroll but i can play well at this level and we have an opportunity if we work together. My objective is to create that bankroll by playing and to thank you for making that possible produce profits for you. I will play for you 50-50 on profits until i have created a bankroll of 25 buy ins (ie 50 buy ins net profit for the team). After that i do not need support and will go on my own.

In fact a lot earlier before that i likely do not need support (eg at 10 buy ins with some small 13% risk of ruin) but i will show my appreciation for the opportunity by taking our progress to these higher levels (<1% risk of ruin at 25). I wont take any profits out of the common bankroll and i want you to do the same (so that we can reach target faster or even compound on our growth), we will either bust losing your 3 buy ins that you start me with or get there and then we can separate. We can set a number of games for this to happen or a time-frame if we do not want to play until it naturally happens. I will play as often as ....(details). Do we have a deal?

A will say fine lets do that, i will support you up to 3 buy ins loss (or hopefully more in a real agreement because 3 is too little but anyway if 3 so be it) and will also keep the profits in there until we reach the target or lose everything. I only want from you to protect my anticipated profits here under this agreement if another person comes who also wants in and price them or split profits with them accordingly. Furthermore if in the future we have a serious reason to break before reaching target we can do it after 1 year from now (or say 50 sessions whichever comes first) for a small penalty of 1 buy in to whoever does it plus all get their profit money from the fund splitting profits down the middle (after that 1 small fine is taken out) and the initial investment is returned to me. If the player becomes unable to play for whatever reason the company stops and all cash is distributed properly returning profits and initial position to both parties without any penalty.

(of course this is just an example - i think highly responsible - others may put somewhat different rules etc)

Basically you are saying that this entirely rational way of doing business (or something similarly structured etc) sucks! I disagree. In my opinion it is an honorable way to go about it in a rather well defined manner that is essential to the progress of the operation offering to both sanity and security.



When people get together to do something they need to be fair to each other and be effective towards the success of their goals. The above will do exactly that.

If additionally both need to take out occasionally some small part of the profits we can evaluate the system again for this condition.


Any other things we try to do if they do not address properly the EV of other partners are unethical and inferior ideas. The player that works and the first investor that provided the initial opportunity must be protected. The others can pound sand for all i care if they are unable to see these first 2 protected and then only then, after that, see a profit of their own.

Under these conditions seeing how much C must bring to the table and under what additional rules/stipulations in order to also have 50% of the 50% of the profits is a well defined problem.

In fact for certain initial configurations (when the skill of B is well documented) it is not possible to do that (the 50-50 split of the 50% of profits) unless C also pays directly something to A outside what they bring to the "company".

When you come into a party/company of others you need to be offering something to the party in order to receive yourself a plus EV opportunity. Otherwise feel free to play in a world that people back-stab each other and play irrationally.


As for what you suggested i have no problem with it because the price that C will have to pay to the fund or A or B or both in that example will be derived by the ideas i presented that relate to how good player B is (or all 3 agree he is) and the risk of ruin plus anticipated overall profitability of the system until it stops. In general its wrong if B is a good player to allow C to pay the same or only slightly more than A. It undermines the EV of A right away who was there first. Of course if all come together at the beginning its very different.

Also if the skill of B is very uncertain (not sure to be a winning player) it may again prove that the price C pays is close to A. We can work these details with exact models of performance unless we are completely unable to know anything about B other than a few results already. Then we must use a general player distribution if we can find one among those that are backed typically or even a total player distribution updated with the results seen so far and further improved with additional future results. That may affect the prices other investors pay later. Things can evolve towards a different valuation as player B shows performance. In general if B is strong every additional investor that comes substantially undermines A if they only pay as much as A did and get equal share in the profits. I showed why.

To interact with me or not is a decision you make. You will notice that I've chosen to pick particular points to disagree with rather than trying to engage in the full quantity of words you put on the screen. The reason for this is because I perceive a great deal of irrelevance in the words I'm not responding to. So we all make choices about what to respond to or not respond to.

I will point out that you used the following phrase with me:

And you followed it up by accusing me of looking down my nose at you. So I would suggest to you that you've got far more arrogance and nastiness in how you treat others than you are pretending to have. You have plenty of "boss attitude" and you don't seem to recognize it for what it is.

My criticism of your suggested example has been the fact that you make way too many irrelevant assumptions that don't tie to anything in particular that OP is asking questions about. I only need to go one sentence into your explanation to see that you still have not abandoned it in any way.

I can also see that you still don't even understand the criticism being leveled since the very first thing you did when trying to understand my criticism is to do exactly the thing I'm criticizing.

Sometimes, you need to throw the whole thing away and start over if you want to move towards something better. You are choosing not to do that, which you are in your freedom to do.

In other words you do not see the difference between ;

"Are you sure you understand what is going on here as well as i think i do?"

and the real attack that would be ;

"Are you sure you understand what is going on here as well as i do?"

That statement came only after repeated criticism on the example i gave that was just an example intending to show some of the possibilities involved in deciding this.


I stand by that statement actually (it is not an attack on your intellect) because i insisted in giving details to the OP by example that is well defined (so why you think its irrelevant when i tried to show to OP how putting details to it impacts the answer - i repeatedly said that if you change the details the answer and modeling will change too)

You appear as if you do not understand the purpose of my example and think its an answer to all possible OP situations.

You continue to imagine as if what i specified as example is the general answer to many such problems with different details. You should not have any problem at all with the details i put to it because they are postulated (and explained why they are that way as an example of an honest agreement) to show why a specific situation can have a well defined answer unlike the general question that lacks details. OP can have another case in mind where his skill is not at all known and there is no 25buy ins target etc. I expect that of course.

So i continue to ask if you understand it as i think i do because you treat it differently and you insist that the investment of C doesnt impact the value of the enterprise that is most definitely wrong in the general case because it substantially alters the risk of ruin if A put in there so little and B is not a massive world class skill player to have huge edge.



Arent you seeing that if i start with 3buy ins and B and then someone comes and deposits 9 buy ins there the change is remarkable in the survivability and longevity of the operation? Furthermore arent you realizing how introducing another investor that splits by 2 the profits of the investors, changes the EV of A in some cases that the skill of B is either well known or its distribution definitely positive and not very wide in uncertainty?

If you wanted to not attack, you wouldn't have said that sentence at all. That you think you're going to parse that like that to prove yourself right just shows how desperate you are to convince yourself that you're the victim.

Look at the posting history. I responded to one post, making a point-by-point observation of the list of assumptions you were making.

Keep playing the victim. I've acknowledged several times now that you're free to do whatever you want. If you want to do some random offshoot, go for it. But up to this point, you have made no argument that your model is relevant. You've only tried to get into an argument about whether your calculations were correct.

I've already commented on this. If you think that B is playing so grossly underrolled that this extra cash infusion is going to significantly alter the risk of ruin, then it's highly doubtful that the long term data that you need for your calculation is available. Hence, your proposed solution is basically impossible to implement in any real manner.

I understand both these things. I don't need to grind out calculations to understand that. But you're still not seeing the point. The point is that you've made all sorts of arbitrary assumptions that don't seem to be addressing OP's question. And by the time you get to the end of your calculations, you've offered OP no practical resolution to the problem.

I'm simply saying that this model that you're using is over-engineered and not particularly useful or applicable. You have shown great aptitude in grinding out arithmetic. You have not yet shown any particular intuition about reality. Trying to reduce this to an expected value calculation, as if that's the problem that needs to be solved, is the evidence I need to think that you don't understand the problem that needs to be solved.

This is absolutely correct. You want to know the expected (average) return AND all the dispersion measures (volatility, skew) AND the number of bets that will be made AND what the period of time will be over which such bets will be made AND what the risk free rate of return is over the heretofore unknown investment time period to even begin to consider whether it is worthwhile to even consider the merest possibility of doing a calculation of the value of the investment.

I might have left some bits out in what you need in the above.

Utility theory decides it in investments. You wont put all your money in a 1% game that you have 200%avg return but 99% of the time you lose. But in general in situations that do not exhibit big life impacting volatility EV will be the deciding thing. It is true in my examples. If A has 55% risk of ruin of his investment of 3 and 45% chance to win 25 and C comes and make it 13% to lose 3 and 87% to win 25/2 then A experiences a small boost in his EV (9.6 to 10.5) and a reduction in volatility too. Its an improvement (ie C overpaid by paying 7 say).


However if C only adds 4 units (player B is a 55-45 player based on past data) the risk of ruin goes to 24.5% and now A has seen EV drop to 8.7 vs 9.6 and the volatility is not massively affected because 3 units loss to him is no big deal.


So you better believe it in this case he looks at EV only within a reasonable time horizon.

Of course if he had 3 homes and risked all 3 with 55% risk of ruin to win 9.6 homes on avg obviously going to 24.5% or better 13% and even 0.01% if possible with some drop in EV of even 25-50% would be seen as desirable in terms of utility as long as the bet remained big positive in absolute terms.


But in simple cases that the investment is not life changing, EV is what matters in reasonable realized time frames.

Your return/month or year (ie EV properly adjusted for time passage etc) is the metric not the volatility if the volatility is not ridiculous to begin with and the investment is small/medium.

If a player is 55-45 they will reach a target of +50 within 1.5 years if they play every day. It is reasonable to wait 1.5 years for a potential risk of 3 to win on avg 9.6. and not be happy to see that go to 8.7 just to cut in 2 your bust probability.

We can deduce from this that C must pay more than A in general if B is good. I expect that to hold in general. The stronger the skill of B is the higher the price C must pay compared to what A did to be at even split of profits. If C pays a price a bit larger than A that drops the Ev of A they may also have to pay A directly some small refund to compensate in cases a skill distribution for player B is available which determines those numbers exactly. This model assumes both stay until B reaches +50buy ins (it was an example, make your own and see how things change, the price C pays will always depend on the details of the deal and the skill of B).

No. EV assumes a shared valuation between all parties involved. Two people can look at the same present tense facts and come to two separate conclusions about the value of an investment. This is why your principle of using EV is simply wrong.

If we could do a proper valuation in an investment then yes EV (based on utility theory of course adjusted) would decide it. It is that its very complex that this statement is not applicable because random investors cannot ever properly describe future earnings etc in way that they can agree or even be very accurate.

But when i give you a reliable way to calculate EV because the conditions justify it (a much better cleaner situation) then not doing it is wrong choice.

If B has a 55-45 edge +-1% in some normal distribution sense we can price the share of C if A invested 3 units first and B has declared to both he will play until he makes a bankroll of 25 and A accepted and they decided to cash out only in the end. If those are the terms then the concept of EV is very realistic measure. I dont know why you do not understand that. What else is there? Even if B is not very well understood a common distribution can be agreed up eventually because then why the hell are they investing in him if he isnt at least a winning player. Any winning player no matter how small winrate will always force C to be a higher price than A.

You are not offering a way to value things in my example that is better than what i suggested. How do you price the situation i described 55-45 3buy ins 25 target for B. What is C to be 50-50? Show how you get an answer to this example. The 55-45 is what our player B has averaged in past tests say. I am Op for a moment and ask you to price this example deal. Why isnt this a reasonable question?

If this were true, then risk would be irrelevant. Risk is relevant, hence you're wrong.

I said utility theory to take care of the risk in general. I made it clear. The Op here is talking for some facking $50 now lets get real. But for small fluctuations who cares if i lose 300$ 50% of the time and win 2000 50% of the time vs 20% for 300 and 80% for 1000. The first is better even if more volatile. If it was 50% to lose 3 homes (say all i have) in order to win with 50% 20 homes then yes EV is not a proper approach moreover how nice the EV is still and the second is more desirable because we are not destroyed as often and still have solid EV.

You are still not answering to me how you price a A=3, B=55-45% (feel free to make B a coin for all i care) play until profit is 25 units or bust. What is C for 50-50? What does risk have to do with this here. C is investing in something that has a clear outcome either way. If you want to exploit C and his risk fears we can arbitrage the crap out of him in this example if he doesn't pay the only correct price possible here.

Risk was just one of any number of examples I could pick. Unless you're just using "utility theory" as code for "whatever I can make up to cover whatever contingencies you could possibly imagine" in which case you're not really saying anything at all.

There are rational reasons to forego a +EV investment. There are many ways for two people to come to objectively different valuations of the same investment opportunity.

Ultimately, the claim that this is an EV calculation is simply wrong.

My answer is that I don't care about your completely arbitrary example that has no bearing on anything of interest to me, and which appears to be irrelevant to the question that OP raised. If you want to go on your own little tangent, go on without me.

I will let Op tell us instead what the details of the situation are, given that i have already provided many ideas about how a deal could go and he can easily see any differences and declare them. I expect it anyway as my 25bi and 55-45 is arbitrary personal choices that are obviously not ever such a lucky guess.

And by the way i have you down for refusing to answer my question ok. Dont answer it. But you didnt explain why you are not answering it by giving me a different valuation model to the precise system i described. I hope Op comes and after describing his own situation then asks you to answer also my own situation example because he plans to run it that way too (and provide of course his own percentages and final profit targets where the company ends since he cant play for others indefinitely and be a slave to them if he wins enough!!!). Yes OP go for it you can break the hypocrisy here that what i propose is not possible example for this case.