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A probability problem


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  • Root Admin

As i was building tournaments section of this game, at some point i needed to find a better way to present a tournament, than to show the total number of maps to be played in it. 
For one individual player, the total number of maps played is not that relevant, as it is to know how many maps he has to win to win the tournament.

Lets imagine this for a bit. There are 8 players, and they play in pairs of 2, a total of 4 games. This would be the first round. Then, the 4 winners of the first round, play in the second round of 2 games, and obviously just 2 players win.
There are no draws, you either win or lose. The remaining 2 winners, join a match for the final fight, and as usual, only one wins, lets call him John. John wins the tournament.

So far nothing abnormal, every match has 2 players, and one winner. Overall the tournament has one winner.

Maybe its obvious for you, but for me it was not obvious without specifically thinking about it, that all John's fights are consecutively won fights. John had to win every single time to reach the end of the tournament.

Imagine this was not about strategy at all and it was a game of coin flipping and pure chance.

Imagining this as a game of coin flipping excludes any possible explenation that one of the participants is terribly skilled in any way, so lets think of it in this way.

All 8 players flipp a coin and only heads move forward to the next round, and so on. Over 3 rounds, the winner would have always
flipped heads, against all odds.

Flipping a coin and heads 3 consecutive times, its not big deal, but if you follow same rules, and increase the initial pool of participants, the winner would need to get more and more consecutive heads to reach the end of the tournament.
The winner of a tournament with 100 rounds for example, would have hit heads 100 consecutive times, each time having 1/2 chances to hit either heads or tails.

Seen from the start to end perspective, nothing looks abnormal, as each time one wins one loses, but seen backwards, from the winner perspective, the chances to flip just heads so many times, is insane.


I've been thinking about this, and i realised that regardless how you put it, given enough number of initial participants, you can "force" one participant to hit just one side of the coin, every single time...every...time.

Its irrelevant how lucky that person is, you could bring together the most unlucky people on the planet, and one of them will always be the one that at the end hit heads every single time. ...crazy no?

It is as if you could force the luck into one person just because you put him the right competition.

Any thoughts on this?

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It's not random coin flipping, it's sorting. 

After a battle there is 100% chance of a winner.  With coin tossing, there is a 25% chance that both lose.

With no random fluctuations, you get a totally flat distribution, which is only one of the many possible random outcomes.

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27 minutes ago, Muratus del Mur said:

It is as if you could force the luck into one person

It is a funny thought...and it's what makes games fun to play: there's something totally logical in a game that would be completely irrational in real life. 

and some people would carry on in a game forever and ever because in there the chance of having such luck is actually possible

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  • Root Admin

Its obvious what is going on, the less obvious thing is the final outcome, regardless how it is explained, its still a fact that the winner is somehow forced into a streak of lucky tries, and as a big picture, such a system will always yield such a player.

 

Think of it, given enough participants, you could break any world record of consecutive flips. The numbers become outrageous, but the "luck" comes out with mathematical precision every single time.

 

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With N rounds you must win N matches each with 1/2 probability, so (1/2)^N chance of winning the series. There will be 2^N contestants, only 1 of whom will win.  Either way you approach it, your odds of winning (all else being equal) are 1 in 2^N.

Yes as N goes to infinity, that's a big number worthy of astonishment, but 2^N is even bigger, and accordingly harder to fathom.

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  • Root Admin

@Fyrd Argentus yes, thats the math, i dont argue with that, i am just more interested in the philosophical conclusions. From this its clear to me that system is always picking its participants, not the other way around. There is no "room" for multiple winners, and more interesting, one is forced to be  as part of that system.

 

@Lazarus nobody is pushing anything to anyone. MD is my only community of friends and gamers, and this is an other project i do, same as i work on md. I see nothing wrong in talking to you md people about it. Consider it advertising if you dont understand what i just wrote. 

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4 hours ago, Muratus del Mur said:

From this its clear to me that system is always picking its participants, not the other way around.

This sentence...means we have no free will, right? I think it was the 17th and 18th centuries that were so focused on this, trying to say we are different from animals because we have free will (also, Christian theology is putting emphasis on this).

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  • Root Admin

I am not sayibg this, because in this example, nobody has free will, all fights, or coin flips, obay strict rules. Having free will in this example would mean to be able to land a coin on its edge (thats happening in reality), or both participants simply not show up for a fight (also happening).

Maybe this is more of an example of how things would look without free will, its hard to tell what its relation to free will is.

Its clear to explain it mathematically, and there is no mystery about why it happens or how...but still its hard to accept that its happening at all.

 

I will do this experiment with coins, actual physical coins, and see what happens. If i am right, then one coin in a very large number will have to always land on one side. I am curious what would happen if a cheating coin is introduced, or other factors. Maybe childish games that a matematician would laugh at..but i suck at math, i like practical :D

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  • Root Admin

Let me explain this again differently. If you have a pile of coins and you flipp each 4 times, you would normally think that it is not mandatory that one coin will flip 4 times on the same side, why would it, right? However, if you do the same thing, but just flip them in a different order, like the game described above, it IS mandatory that one will flip 4 times in a row on the same side....how crazy is that.

This is the endless fight between probability and chance, and i must admit i am having a hard time to understand it properly. You have equal chances to flip one or the other side, so in theory you could flip 1million times on the same side, or alternate sides 1mil times,right? No, not right.. :)

if you distribute all possible outcomes, some scenarios happen more than others, but one happens just once.

 

 

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So what you're saying is...it's like some people always seem to win their matches (always get a contract, always get first place etc) i.e. they're on a roll . Normally, you'd think it was about time for them to step down, or for someone to beat them in a match, but that rarely seems to happen

Even if the chances of them winning are 50%, they manage to win every time

I find it hard to accept a system chooses its winners, but maybe it's true...

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  • Root Admin

super hard to accept indeed.

I say the system chooses its winners, because if you change the rules even just a little, an other winner might emerge. 

Its equally hard to accept that elements of randomness such as coin flips, or of free will, such as players, somehow have some degree of "awareness" about what the other, unrelated participants, do. Grab the first coin you find and flip it... you have 50/50 chances to get either side.... yet do this on a pile of coins, and you will see an abnormally even distribution of results, as if the coin flip "game" you just did had a knowledge of what side to pick next to achieve such an even distribution. In the organized form i proposed, having one of the participants that _always_ flips on one side, its equally strange. Again, all this is mathematically logical and not abnormal, but from a huma perspective, its not so logical.

 

The explanation, in my belief at least, is that the outcome is so "fixed" that it causes its roots in such way. In reality, a coin can land on its side sometimes, or two players deciding on a draw, but in this example i eliminate such possibilities from the start, so the "genes" of such an event, are simply not there, so the final outcome can not be one of draw or undecisive flip. What happens in the coin flip experiment, is that we eliminate all possibilities that don't match the rules.

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Ahaha, now I get it why you went on with MD like that- you thought about what you wanted to get from it and let that shape the 'roots' of the system. So the confidence was all in this one idea...

Actually, isn't it how life orders things? Birds of a feather flock together, all you need do is show your feathers. And in one superior universal order, you get what you want, somehow. But, hmm, this is a positive interpretation - the talk about winners and losers (same idea behind) isn't so positive when you think you may have never had a chance.

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  • Root Admin

retrocausality

either you agree that events in the future are "stronger" (maybe more real) than events in their past, then it means that whatever you experience in the present is following a purpose in its future, and everything are just "roots".

or

you consider events in the past "stronger" than whatever might follow them, meaning that everything in the future is totally meaningless and just a causal result of whatever happened before.

The second version is what people find easier to accept and the first is for some plain outrageous. 

There are niche experiments that proved events in the future change events in the past (scientifically, look for "quantum eraser"), there is religion that talks about similar concepts (regardless of religion).

However, direct, simple, observation can only tell the story of causality, you do one thing then the next event is the effect of what you did, cause and effect. 

My personal belief is that viewing things as causal, is dark ages level. I strongly believe that we observe reality (or our side of what we call reality), in a single, causal way, but it actually holds both sides. I think events happen at some point in "time" then spread their roots into the future AND the past, joining "threads" that will eventually confirm their existence and lead to it.

Spoiler

At some point i wrote something called "the genetics of events" but i don't remember if it was here on the forum, or in the book notes i have somehwere on some desk, or if i put it in md research clues...can't remember, but its "there".  Since i wrote that, i got better at understanding retrocausality and how it can be "used and abused" to "make things happen" in ways that make no sense for someone just observing things from a causal perspective. I'll share the secret of those docs, and with this i'll end the talk. 

Feelings, in ourselves, have a timeless nature. Feelings are things in our control that can reach both in the past, but also in the future, and events in the future, the further they are , the easier it is to influence.  In less fancy words, one could find its own way of believing into something that has not happend yet, then aware of that event, he could help find its roots, like slowly pushing a ball down a slope till it starts rolling on its own.  

 

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  • 2 weeks later...

i believe the present to be the most real as it's the most actionable and holds the most potential. the past is more real the closer to the present it is, but it degrades over time as we drift further from it. memory degradation distorts events and "reality" and makes them less real, more an ideal. the future is potential, we can visualise potential in the present and use that to create causality. 

future is strange, for some, near futures is more "real" , others the opposite, it depends on how easy it is for a person to visualise events, some people have it easier to imagine what they will have for breakfast tomorrow, others find it easier to imagine their lives 10 years from now. but generally the people who are good at visualising events further away from them, will have a stronger path because they have the ability to oversee their present a lot better. people who can only see strongly tomorrow, tend to live more day to day and don't have that many goals. perspective is key

Edited by Syrian
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I wonder if there are better terms for future, present and past, because these ones remind you of a linear perspective of time and of course it's outrageous to say the future influences the past when looking at it with these words in mind.

and then, there's this problem of the observer...what self is casually visualizing itself as a 'better self' in the 'future'? and when you look at all the desires a self has, and how programmed they are (in the sense that all children develop certain wants at certain ages), it really looks like from the moment the cell has split in two, everything has already happened, because everything that was going to happen was already decided...it's a scary self, that knows it all

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  • 1 month later...
  • Root Admin

it has already happened, but at the same time its "identity-less". Imagine all this as a "plane" of possibilities, crossed by routes that connect "checkpoints". One idividual can go one way or an other, changing his own path, having free will, and create his own series of checkpoints on this plain. I believe time is not linear, we just see it as linear because we can only interpret it based on our experience, and see just its causal nature. For one individual, there is past present and future indeed, but if you could look from above, this is just a road on a field of events that already exists, like a map. Things could be more boring than it looks like, because this field of possible events, its not some fantasy map, its just the "area" between "existance" and "nothing".  At this level things can gen really complicated to visualize, but give it a try. I discovered long ago that a strong feeling can create "checkpoints" on this event field, and while you might think a strong will or desire can get you where you want, this is just partially true. You could create an attractor on this time field, but its not given that you will be the one that reaches it, this still depends on your actions. Someone else might be attracted and its path could be changed, based on something you wished into reality.

 

When the cell splits in two, might just be a checkpoint of that path. Think that people evolve based on their DNA, and most of the times a child continues the curses and blessings of his parents, they are part of the parent path, as well as distinct individuals on their own path. I don't know what to consider the start or end of such a path to be, but i know the overall form of how these things work.

 

Long..complicated..talk. Many things to understand, and so weird to discuss this in writing without knowing if the one reading this follows the chain of thoughts or not :)

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8 hours ago, Muratus del Mur said:

if you could look from above, this is just a road on a field of events that already exists, like a map.

this might explain why some get at that checkpoint in a matter of days and others need years, setting themselves up (circling around) for reaching it. A feeling that is not right or not ripe will not let you get there

however, your existence is linked to those checkpoints, reached or not, they're always in your mind and your behavior, it's just a difference between ''fulfilled'' and ''incomplete'' - you're destined to roam on that map forever

8 hours ago, Muratus del Mur said:

so weird to discuss this in writing without knowing if the one reading this follows the chain of thoughts or not

y'know, i think some things are better left misunderstood/not understood :)) staying in the dark of a thought like ''there's no meaning to life, it's all a battle'' is no good, but then again, how's this thought of ''i'm just dragging my ass around a map of possibilities, having some form of free will, but knowing that the winners are decided by the system anyway''?

i like this discussion because, as you say, emotions are that illogical, unaccountable thing that may alter paths. it's a thought to hold since logic is too cold and, ultimately, irrational

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