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> This simple example has the correct intuition, but the real way to formalize this intuition, and the way amount of randomness is usually quantified is in terms of entropy. This essentially gives the typical number of yes-or-no questions you need to ask to figure out what outcome I got. The concept of entropy is actually relevant, because it tells us the answer even in the case when all probabilities are not the same (say, a biased coin), and tells us how to actually maximize randomness (which is by maximizing the entropy).
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> The most important fact to know here is that if we have a set of outcomes that we can assign probabilities to, then the set of probabilities that maximizes the randomness in the system (the entropy) is when all probabilities are equal. Of course, the amount of randomness can also be increased by increasing the number of possible outcomes.
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> I’m not telling this just for the fun of it, but because in reality, players don’t play in such a way that every outcome is equally likely, and they can exert a lot of influence over the probabilities of various outcomes.
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> Your simplistic model of randomness in movement is essentially wrong for one simple reason: the opponent isn’t trying to guess the player’s speed, but their location. Therefore we need to look at not at what different speeds the player can move at, but given that they are at some location, where can they be after some amount of time T. Because that is the information the opponent is actually trying to obtain.
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> In that context, the answer is fairly simple: the player can be anywhere they can get to in the time T. Crucially, the set of possible locations only depends on the maximum speed the player can move at, because even if they only had two movement options: moving at maximum speed or standing still, they can always stop, loop back around, or do whatever they want to end up in the same location as if they had just walked slower. Therefore: the number of possible movement speeds doesn’t increase the number of possible outcomes.
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> Furthermore, of course needing only to get to the desired location, the player can arrange their movement patterns such that they can, in principle, always have an equal probability of being anywhere they can get to in time T. Of course there are many reasons in practice why they wouldn’t want to, but just that given a set of possible outcomes, the player can always maximize their randomness, regardless of the number of possible movement speeds.
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> So, as far as the amount of randomness is considered, the only reason Halo 5 does have more movement randomness than, say, Halo 3, is because it has a higher maximum movement speed. But if you were to increase the base movement speed in Halo 3, you could make it have more movement randomness than Halo 5. The important thing to understand is that the deciding factor is the maximum movement speed, not whether the player has to lower their weapon in order to move at said speed.
So i’m only answering this for fun cause your reply is actually pretty neat.
> This simple example has the correct intuition, but the real way to formalize this intuition, and the way amount of randomness is usually quantified is in terms of entropy. This essentially gives the typical number of yes-or-no questions you need to ask to figure out what outcome I got. The concept of entropy is actually relevant, because it tells us the answer even in the case when all probabilities are not the same (say, a biased coin), and tells us how to actually maximize randomness (which is by maximizing the entropy).
I like where your heads at. I’m assuming you you meant minimize randomness. But regardless entropy is still determined via probability. I simplified it for a reason. it removes all things that may make the argument unclear. My argument still holds. Regardless of whether eliminate specific things based on information obtained you will still have a greater amount of entropy in halo 5 than in halo 1 - 3.
> I’m not telling this just for the fun of it, but because in reality, players don’t play in such a way that every outcome is equally likely, and they can exert a lot of influence over the probabilities of various outcomes.
Your right players don’t play in a manner where every outcome is equal but because you are unfamiliar with a specific players play style you SHOULD treat it as if they are or risk losing the fight.
simple example: Say someone’s one shot. You could make a logical assumption that they will wait for their shields to recover or wait for help and play accordingly or you can treat everyone as if they will possible challenge you regardless. Choosing the ladder is usually the better option.
> Your simplistic model of randomness in movement is essentially wrong for one simple reason: the opponent isn’t trying to guess the player’s speed, but their location. Therefore we need to look at not at what different speeds the player can move at, but given that they are at some location, where can they be after some amount of time T. Because that is the information the opponent is actually trying to obtain.
Correct again But missing one small fact. A players position depends specifically on their velocity. Velocity being their direction and speed in which they are moving. the time T that you are referring to will be either larger or smaller based on the specific movement they decide to use. Bringing me back to a significant increase of randomness in H5.
> given a set of possible outcomes, the player can always maximize their randomness, regardless of the number of possible movement speeds.
Again not true.
These addition abilities affect way more than just speed. kneecapping allows trajectories that’s just not possible in other halos. which adds to your beloved entropy argument. Again these arguments of yours wouldn’t even come out of you if you actually played the game.
> So, as far as the amount of randomness is considered, the only reason Halo 5 does have more movement randomness than, say, Halo 3, is because it has a higher maximum movement speed. But if you were to increase the base movement speed in Halo 3, you could make it have more movement randomness than Halo 5. The important thing to understand is that the deciding factor is the maximum movement speed, not whether the player has to lower their weapon in order to move at said speed.
Again not true… read above…
And Finally i’m glad you agree that sprint makes H5 more random and allows for more challenging and fun gameplay. My goal is complete. The lowering of the gun to me is of no consequence. You can literally fire as soon as you press the shoot.
and again you wouldn’t say things like that if you played the game.
BTW increasing base movement speed in H3 wouldn’t result in more randomness it would result at the very best be the same amount if you put thrust in H3. But it wouldn’t because in all older halos the movement is a gradual increase making it harder to switch movement speeds. Which will lead to less people incorporating it in their gameplay which brings me back to your entropy example where not all players treat all options equally. most people will just opt for full sprint speed all the time since its easily accessible. Giving a clear break between crouch, walk, and run allows for an easier way for players to make the decision on which speed they’re gonna use and when.
