Thinking about fine-tuning of explicit probability

I understand what you said. I just tried to talk not too much technically.

Yes, of course 1/n is 100%/n, I preferred use % for avoid misunderstanding... maybe a bad decision of me.

And you are right about "deterministic", it is just a way of talk non serious. Im talking about the predictability, the chances of predict a event with success.

You can predict a event with a 90% of probability more easily than one of 50%.

When I said that the 75% of a event represent just a 50% of unpredictability/predictability its because a event with a 50% of probability is just pure randomness... you cant predict absolutely nothing about it.

When you move out of 50% of probability your chances of success in prediction increases to the absolute predictable points of 0% or 100%.

I know that the things changes when you repeat a random success or you do multiple random events at once (like throw 2-3 or more dice). I know binomial distribution, permutations and the combinatorial basics.

Bur what I was thinking is about the meaning of the numbers. If I have some meaning on them I can fine-tune a game more easily.

No problem man, you are kind. Your point have value, Im not the best on probability mathematics and I like A LOT maths.

I think the core of maths are in probability... from the theory of groups, theory of numbers... I really dislike when maths of probability are taken as a "not as important part of maths", you know that these maths are more related to economics and less (at least in a classic point of view) to physics or engineering.

Anyway: my knowledge is poor. The approach to maths searching for "meaning" is "wrong" (because maths objects are pure abstract "geometry" and the "meaning" is some perspective ever, philosophy of language can explain this very well... I dont have the words on english to continue a text about that and anyway this is off-topic) but useful and valid (in the history of maths it have some important). It can create some perspective.

Yes, I wrote a very similar commentary here.

I understand what you says X3M... We need to avoid, as much as possible, a deterministic nature of a game to evade boredom or annoyance but, at the same time, we need to let that a player get stronger by success in his decisions.

This type of "contradiction" is what make a game interesting. You can see, by example, that a bad move in a chess championship early can cause the player to abandon because he knows the advantage of the other player is unbeatable.

And if you put too much random on the game or just deny value to success plays of players then the game lose his competitive dimension. For a social game its ok but for a competitive game of course not.

So a important point of analysis in a game is how important a decision is in the stage of the game: in the early, mid or late stage of any game, in others words: how the weight of a decision evolves (weight of a "move" or "play" related to the probability of win the match or the round).

Generally in classic games early decisions have way more weight than mid or late decisions. And because this the game on mid and late stages it is generally determined more by mistakes than success of the player.

Anyway this is very arguable, I just says here some of my perceptions of some classic-board games as chess and baduk.

On poker or other games maybe different because the weight of a decision is not strongly determined by the time is played because the strength of a bid is chosen by the players circumstantially. Anyway some degree of weight-determination exist on poker due to accumulative nature of the pass of time than generally mean accumulation of some kind of points or something similar.

And, of course, in board or cards games probabilities narrows when the time pass (less positions, less cards, less valid strategies cause difference on score... less degree of freedom in general).

In goofspiel this is an explicit core of the game itself: the narrowing of probabilities when the turns/time pass.

A balance for the narrowing nature of many games i.e. the evolution to deterministic state of many games is the concept of round. When you play a game divided in several rounds you are forcing the players to play from zero (reset the state of game) over and over. So the best player is who accumulate more successful rounds.

This concept is used in all sports: chess, football, tennis, poker, etc.

EDIT: I must add a last rumination about the contradictory nature of a game: any game have a end but, at the same time, the funny of a game is being played.

So the contradiction is that a game consist of a determinate final state (the end) and a undetermined state of properly game. If the final of a game is determined in some point but it continues then there is a no-game, just pseudo-game, at least in a competitive vision about what a game is.

So the point is that a competitive game must not be a pseudo-game or, at least, must not be a pseudo-game the greater amount of time of play.

Anyway in some point the game that is being played must be quasi-determined, i.e., must be a potential (very high probable) pseudo-game.

If the game is a real game all the time/turns (undetermined final state beyond a reasonable probability) but the final turn/move/play then the game loses the competitive nature or maybe very random. In others words: if the qualitative final state of a game (qualitative: major winners/losers) is determined just in the last move/turn then the game may be excessively random.

What I am trying to says is that a game, to be competitive, must have a portion of pseudo-game on itself because a game represent a evolution of some kind... evolution to the final state, from a pure undetermined state from a pure determined state.

This transition from undetermined to determined is present in all competitive games. If there isnt an evolution then the game is extremely random (or extremely complex) so it isnt competitive. So, in some point, the game that is being played is completely determined or, at least, in a high degree of probability it is determined (=pseudo-game).

EDIT 2: Another strategy to avoid excessive complexity/randomness of a game is the concept of points. The points itself, if there isnt a big difference in score, arent the direct representation of a state of win/loss.

This is why the combination of scoring by points and set up a game in rounds is very useful to control the depth and evolution of a game.

It depends on the effect of the roll. You can setup the roll to any probability for something, 10%, 50% or 70%. But the effect of the roll (snowball) it is the thing that make you put some probability or another.

By example: you can setup to a 1/6 of probability something that make change your strategy for this turn or the next, not something that change the strength of something if not that change your options.

If you setup something at 50% it will be more to add some atmospheric effect or maybe something not directly related to a player, maybe just some variable to create a mao or something (something imitating brownian movement or random walk by example).

These are just some examples... games are a thing to wide. All depends about the effect of the roll and what you want to feel/make with a game. I was just discussing the possible meaning of a probability but anyway all depends on the context of the roll and meaning of the roll to see if is what you want to do with the game or not.