Your mathematics are wrong. The value of a win is 1 and of a loss is -1. Let’s say you had plus-infinite value to win; you didn’t find the holy grail there because you’d have MINUS-INFINITE value to lose with a high probability too; so you’re not helping the product gain value on the positive side but you only had a bias looking mainly into the wins instead of the losses too.
TL;DR
Defining a game win/loss to +1, -1 or +infity,-infity is nonsense without justification.
Okay this seems to directly contradict what you wrote
Emphasis mine.
If I understand your latest post your saying you use the Bayesian utility function to arbitrarily score the value to the player of a move/play. So instead of considering just one outcome you score all outcomes to evaluate the expectation of a position:
E(P) = \sum_i u(i) p(i), where the sum is over each outcome enumerated by i, and where u(i) is the utility you assign to that outcome. E is an expectation or evaluation, and P is the current position you are computing it for. Lastly p(i) is the probability of outcome i occurring.
Here you seem to play fast and loose allowing the utility to be -1 or +1 for a loss/win, or -infty +infty without much justification for choosing one or the other.
That’s more correct, but that’s either vastly oversimplifying, or at least not understanding where the difficulty lies in correctly reasoning using the above formulation.
First, you should convince yourself that, lacking justification, the correct value for u(i) is not some arbitrary choice (such as you allude to by giving a win +1+infty, loss -1/-infty), but the percent chance to win if outcome i occurs. The reason is simple: you want E to mean something useful, and if you use the definition of u I just gave you, then E means the expected chance to win in position P. If you use your own arbitrary definitions of utility functions you will get SOMETHING, but that SOMETHING will not be useful**, as it won’t represent any known quantity. If you don’t understand this part, what follows is not going to make much sense.
Next, realize that this is a recursive formula. For example in position P you may play a card which has several side effects and can land you in any number of positions/outcomes Q_1,..,Q_k. You must then repeat this evaluation for each Q_1,..,Q_k which can land you in positions U_1,...,U_h, and so on and so forth. If you compute enough “layers” or (as it is usually termed) “plys” of this recursion, you will eventually exhaust all possibilities/outcomes of play. You can then backtrack to compute the original value E(P), tallying up each terminated recursion, computing the ratio of wins to losses for each possible outcome i in P, to give you the value of u(i) (the percent chance to win if outcome i occurs.)
I hope you can now appreciate that its nonsensical to talk about arbitrary values for your utility (without specific justification), and if you do, then the expected utility you are computing is nonsensical itself. Likewise, I hope you can appreciate the difficulty in even approximating the value of u with some degree of confidence in accuracy.
** I’m leaving a footnote here, because there are use cases where you would want to use an arbitrary scoring function underpinning the utility u(i). One such use case, is if you are building a engine to play the game, in this case, you can hand-craft or otherwise tune (based on data) this evaluation function (as is typically done with say a chess engine.) I’m going to assume that for the sake of discussion you did not mean this, and you just arbitrarily chose -1/+1 for your win/loss because it seemed “reasonable” to you.
In any case, if you do use an arbitrary evaluation function, say scoring between -intfy, +infty, you want u(i) to be the expected value of said evaluation function if outcome i occurs, and the recursive definition I gave above is how you compute it. The reason for this is because the expected value of an expected value is the expected value, mathematically, meaning E(P) then represents the expected evaluation of the given position P.
The main reason to code things with an evaluation function instead of probability of win is to give a means to terminate search at a given ply and (hopefully) have a reasonable score for the current position (and each possible move/outcome.)
You strawmaned me and you overthink it. 1 and -1 was the MAXIMUM and MINIMUM hypothesized outcome of a play; e.g. you may assume 0.8 outcome to win with a “high roll” play of 20%; you will then do your products of Expected Value according to typical economic theory.
Obviously the hypothesized outcomes especially but secondarily also the chances of success of the plays rely on both education on the game and experience and they’re never clear to a typical gamer so that’s where knowledge and experience of a good player shines.
I think the more pertinent factor is that if you can somehow mathematically compute all of this, either tool-assisted or otherwise, AND still have time to make the optimal play, ALL before running out of the ~1:15 or so you have for your turn? That would mean you are the reason life sucks, because you’re wasting your time and your effort on Hearthstone, instead of solving world hunger, ending cancer, establishing world peace, etc.
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Nobody is literally calculating the odds to a singular number. This is theory of how a good player guesses the odds given knowledge and experience. It doesn’t have to be “20% to high roll” and “40% to win” to be useful; “a bit likely to high roll” and “most probably a win if I high roll” are often enough for comparisons to alternative odds because you only need the inequality of their comparison and not their absolute values; mathematics aren’t as stupid and impractical as you think.
Are you guys building hearthstone bots because this is way too serious for a 5 minute popcorn game.
You are so full of cope, it’s sad
Come on buddy I think the VS report isn’t out for another week… I think you should keep quiet until then so you can get your next talking points.
Quite hypocritical to attack people for caring about a game, and then caring to stick around its forums posting about the game.
You are not that special; e.g. personally I don’t even play for more than a couple of matches these days; you assume too much.
You are quite right there. What I was doing in that post was being sarcastic in an attempt to inject a small sense of brevity to the otherwise very technical and math-heavy conversation; it’s kind of like when you’re at a lecture and the speaker pauses to tell a small joke. It relieves some of the tension and signals to the audience that they can “pause” their attention for a moment.
I appreciate you taking the time to explain the topic to me. (not being sarcastic here)
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Obviously, no amount of math knowledge or experience can help you calculate something like that fast enough to be more precise than an intuition of a pro player with thousands of hous played
That being said, without doing the work offline, the traditional way, you’ll never hone your intuition on that level, which explains me being stuck between the pros and hardcore amateurs
I just don’t put in the work to hone my intuition
If I feel something is right, I’ll do it, because relying on intuition brought me this far, but I know that our intuition about probability is skewed and that we should calculate as many cases as possible to make it better
There’s literally thousands of things I’ve learned in my life which at first seemed counter-intuitive until I learned why that’s not the case and then the counter-intuitive became intuitive.
It should be the same for this game
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Sometimes it’s not a matter of learning but UNLEARNING. E.g. a lot of players fall into the gambler’s fallacy; they erroneously think if something has not happened yet then it WILL happen more likely; also true randomness pulls all kinds of bizarre things like 10 bad draws in a row even when the expected is to be only 50% bad draws.
I admit I don’t trust the black box of this game’s code to be perfectly fair; e.g. I currently suspect they “yo-yo the MMR” in order to lose too easily on a small win streak so they can keep you playing; but that’s besides the point and it doesn’t negate the fact you can improve even if unfairness exists in a system.
Why didn’t you admit that in the other thread when SwampFace accused of you being a thin-foiled hatter who pretends they’re not one?
It’s a normal functioning of the MMR system, as it seeks to find the most fair match for you. Yes, they DO want you to win 50% of the time, not just because then you should be playing more, but also because that’s what balance looks like. But the way it’s accomplished is quite logical.
When you’re on a winning streak, you get matched against either:
a) similar opponents who’re also on a highroll streak, or
b) better opponents who are on “normal” or lowroll streak.
If the probability of winning against a) is 50%, as it should be, and the probability of winning against b) are lower than 50%, then the expected winrate in those situations will be an average of the two, which means less than 50%. If a system is working exactly as it’s intended and described, as MMR system does, can it really be called “rigging”?
If the same “unfairness” is shared between every player, can it really be called “unfair”?
I mean, it’s literally the definition of fairness xD
You are incapable to have a rational discussion. You demean others on the first chance you get by misrepresenting what they said.
It’s my mistake to give you a chance.
No, the mistake is not recognizing the point I was trying to convey.
The point was not that I’m calling you that. It’s the excerpt from Swamp’s reply to you where he said you admitted many times of being like them, but don’t want to do it anymore because you get called “tin-foil hatter”.
I just made the point shorter hoping I wasn’t talking to someone with negative comprehension skills, but apparently I am. No amount of sugar coating can change a fact like that. You really need to go back in the elementary school and hone up on reading comprehension.
After your recent bullying I don’t expect any rational response from you but since others are reading, to make it clear: I meant there it’s a completely disingenuous interpretation of what the MMR is if it works that way; I meant it may ACCELERATE how easily you win if you had a loss streak and how easily you lose if you had a win streak in order to maximize time played; hence the “yo-yo’ing / fair but rigged” idea.
And again for the record because bullies like to systematically lie: I never said I’m sure about it: I’m saying I don’t trust black box code to be as people assume it is for certain.
Where do you even pull crap like this from? Can you quote me a scientific research with such a discovery?
Anyway, I see you’re having an episode, so no point in talking. Nice projections, btw:
It’s too bad I was being 100% rational and you weren’t at least 50%.
I repeatedly said, I don’t believe it; I suspect it; I never said I’m sure and I explictly say that every time. You are either lying or you need to learn to read end of.
I wasn’t talking about that. I asked you to quote me a research claiming “bullies like to lie systematically”, because you stated it as a fact, and I’m in the crap-cleaning mood, and you’re full of it. Can’t let you go around “correcting” smarter people than you and fabricating “facts” in the same time.
EDIT: Oh Goodness, it seems I’m literally arguing with a hallucinating, out-of-date version of chat gpt
Then clean your misconceptions. Someone telling you they don’t believe something but they consider it a chance because the code is black box they don’t do “tin foil”; they literally do good scientific rigor; the code is literally unknown to you to be that sure.
It’s literally the most unreasonable stance here to say that you’re EITHER sure it’s rigged OR not rigged by 100%; e.g. currently I think it’s NOT rigged but I’m not 100% sure; even if it is I would suspect more that they try to maximize game played only.