Knowing nothing else and making no genre assumptions, I'm now pretty convinced sword 2 is better. There are a couple ways to make that the wrong choice, but with no other information, (2) "can solve" any problem that (1) "can", plus some others. It's not as likely to solve some situations, but it's possible. Even if it's reversed and the "DMG" is actually a negative thing, at least then you have a chance to not take any.
"The long run" being the average expected "DMG/Second". That doesn't tell you anything at all about winning/losing an arbitrary game.
For any given set of parameters, Sword 1 either wins or loses. For all games that Sword 1 wins, it is possible for Sword 2 to win (literally, hit miss hit miss would be identical). For some games that Sword 2 wins, they are not winnable by Sword 1.
Therefor pick Sword 2.
I guess it's possible to make it so "missing" is penalized more heavily than just "not doing damage". In which case they would still be even, but it's still possible for 2 to win, even if it's the less consistent option. If you combine the missing penalty with some kind of penalty for hitting too many times too fast, then that would be a situation where 1 could win and 2 could not. I guess that does break my assumptions, albeit a very weird situation.
Penalties and all other factors are assumptions. The randomness is equally likely to be a boon or a detriment. So in the set of all arbitrary games, the results are still identical.
No reason to pick either sword over the other without assuming something.
Long run yes, but in a single fight there is difference. Let's say that enemies you are facing have about 100heath and they can kill you in about two seconds. At that situation you want sword 1 because you can then always win 1 on 1 situation with that kind of enemy (expecting you to have full heath in every battle). And if enemies are strong enough that you can't beat them with sword 1 your only option (other than running away) is sword 2 and then it's a gamble.
For any given set of parameters, Sword 1 either wins or loses. For all games that Sword 1 wins, it is possible for Sword 2 to win (literally, hit miss hit miss would be identical). For some games that Sword 2 wins, they are not winnable by Sword 1.
Therefor pick Sword 2.
Like I said above. There are situation where sword 1 wins 100% of the time, while sword 2 doesn't. In those situations sword 1 should be preferred.
Penalties and all other factors are assumptions. The randomness is equally likely to be a boon or a detriment. So in the set of all arbitrary games, the results are still identical.
No reason to pick either sword over the other without assuming something.
I realize now that there are a few more situations (1) can solve that (2) cannot. One is "maintain 100 dmg/sec for an infinite amount of time". If you pick any arbitrary stopping point, it was still "possible" to do with (2), which is what I was banking on with those assumptions, but if you actually set the goal to "infinity" that changes.
Like I said above. There are situation where sword 1 wins 100% of the time, while sword 2 doesn't. In those situations sword 1 should be preferred.
Those situations are assumptions, and it's equally likely that you'll be in a situation where the randomness is a bust as opposed to a boon. There is still no difference between the two swords.
Picking an arbitrary starting point doesn't matter. The odds are the same. Either sword is equally likely to win 100% of the first 10,000 matches or whatever.
Like I said above. There are situation where sword 1 wins 100% of the time, while sword 2 doesn't. In those situations sword 1 should be preferred.
I was trying to work from the idea that you have no assumptions, and that since it was possible for (2) to achieve the exact same results as (1), it would always be possible to "win" more of the possible "games", which would be preferable to winning some sub-set of games more consistently. That said, there are at least a couple situations that (1) can win that (2) cannot, though they are a little more complicated.
No, they're identical for all purposes. It's not complicated. In fact, it can only be complicated at all if you add specific assumptions about the nature of the game being played with them.
Penalties and all other factors are assumptions. The randomness is equally likely to be a boon or a detriment. So in the set of all arbitrary games, the results are still identical.
No reason to pick either sword over the other without assuming something.
The problem is that to say that this is the case is to make an assumption about the nature of this so-called "set of arbitrary games". Why would the set of arbitrary games just happen to be distributed in a way such that it happens to be indifferent to your choice of sword? To me, that just seems like a massive coincidence.
No, they're identical for all purposes. It's not complicated. In fact, it can only be complicated at all if you add specific assumptions about the nature of the game being played with them.
Actually one of them has a red handle and the other has a blue handle. So NO theyre not identical. Talk about bein freakin owned...
Picking an arbitrary starting point doesn't matter. The odds are the same. Either sword is equally likely to win 100% of the first 10,000 matches or whatever.
Erm "ending point" not starting point. I'm saying that there exists a definition of a game wherein the only way to win is to maintain a specific dmg/second of 100 indefinitely. The limit of (2) approaches 0 in that situation, and as it's infinite, it effectively loses. I'm guessing I'm either being very bad at explaining this, or you're still assuming some things I'm not there.
It's similar to just creating a game where "picking 1 wins".
So you are correct in that they are equal picks... but it actually has nothing to do with the attributes now. Supposing we assume nothing.
Even if one of the weapons had a 100% chance to do 0 damage, knowing nothing else they would be equivalent then. Because all those terms are useless outside of context.
I think I have decided that sword 2 is better, and here is why.
Yes, the average damage per second is the same between both swords. Yes, sword 2 has a minimum of 0 and a maximum of double damage. Sword 1 does the same damage no matter what.
Fighting against certain weak enemies with low hp, or that deal out damage slowly, sword 1 is a guaranteed winner. But what are the odds of sword 2 failing on such a weak opponent? They are very low indeed. You will breeze through the game just as easily with sword 2 as with sword 1.
But at a certain point after difficulty has increased, sword 1 will be completely useless. If the opponent has too much hp and deals out damage too swiftly, sword 1 can not possibly beat them. Sword 2, however, may have a 25% chance of winning, or maybe a 10% chance. Depends on the enemy. Sword 2 has the potential to take you further into the game.
The only assumptions here are that you are playing the kind of game where you can die or run away to try again when sword 2 is sucking. If you are playing some kind of hardcore mode you use sword 1 and then upgrade it when it isn't a guaranteed win anymore.
So you are correct in that they are equal picks... but it actually has nothing to do with the attributes now. Supposing we assume nothing.
Even if one of the weapons had a 100% chance to do 0 damage, knowing nothing else they would be equivalent then. Because all those terms are useless outside of context.
Agreed. The problem is clearly designed to be interpreted in a specific context, and so it's fair game to use information from that context as justification.
Someone on reddit pointed out that some games save your state of randomness. That is, the string of random results is seeded long before you get to any particular fight, and the game saves your position in that string. Thus, if you lose a fight because of randomness, reloading and trying again won't change the result.
If we assume that this is a sword in a typical MMO, the chance of a string of successful hits with sword 2 would make it preferable to sword 1. But even then, only marginally so. In the case I describe above, you're screwed.
So no, there is no effective difference between the two given what we know.
Now, if there are procs or items that modify your chance to hit...
Thus, it's a stupid question that cannot be answered, unless the intent is to force a set of assumptions. ;^)
Not "assumptions" so much as having to consider the typical properties of games of this nature.
Your argument is isomorphic to solipsism, Rym.
Isomorphic: good word. Anyhow, the problem is that we still don't have enough accessory information to make a solid assessment. The best answer is "it depends on factors other than the ones presented."
Similar but (slightly) less stupid question is "Do you prefer a 19-20/x2 or x3 critical weapon in d20 system games." That gives some context at least, albeit still a very situational thing.
A keen lance with Improved Critical and 10 levels of Cavalier. Why yes, I would like to do 7x damage on a charge and then crit for 3x damage. I think it was like 15d8 + 120 damage or something similay ludicrous.
Forget that. Trip effects and reach will matter more, or else some improved disarm. All armor and no weapons and/or lying on the ground might as well be dead. ;^)
I spy on you from afar with a binoculars so I know what gun you have, then I bring a bigger and better one. Or maybe I just snipe you from the spying spot. Either way, I show up late and more well armed, just like the robot that looks at your hand and plays rock/paper/scissors.
Comments
For any given set of parameters, Sword 1 either wins or loses.
For all games that Sword 1 wins, it is possible for Sword 2 to win (literally, hit miss hit miss would be identical).
For some games that Sword 2 wins, they are not winnable by Sword 1.
Therefor pick Sword 2.
I guess it's possible to make it so "missing" is penalized more heavily than just "not doing damage". In which case they would still be even, but it's still possible for 2 to win, even if it's the less consistent option. If you combine the missing penalty with some kind of penalty for hitting too many times too fast, then that would be a situation where 1 could win and 2 could not. I guess that does break my assumptions, albeit a very weird situation.
No reason to pick either sword over the other without assuming something.
Like I said above. There are situation where sword 1 wins 100% of the time, while sword 2 doesn't. In those situations sword 1 should be preferred.
It's similar to just creating a game where "picking 1 wins".
So you are correct in that they are equal picks... but it actually has nothing to do with the attributes now. Supposing we assume nothing.
Even if one of the weapons had a 100% chance to do 0 damage, knowing nothing else they would be equivalent then. Because all those terms are useless outside of context.
Yes, the average damage per second is the same between both swords. Yes, sword 2 has a minimum of 0 and a maximum of double damage. Sword 1 does the same damage no matter what.
Fighting against certain weak enemies with low hp, or that deal out damage slowly, sword 1 is a guaranteed winner. But what are the odds of sword 2 failing on such a weak opponent? They are very low indeed. You will breeze through the game just as easily with sword 2 as with sword 1.
But at a certain point after difficulty has increased, sword 1 will be completely useless. If the opponent has too much hp and deals out damage too swiftly, sword 1 can not possibly beat them. Sword 2, however, may have a 25% chance of winning, or maybe a 10% chance. Depends on the enemy. Sword 2 has the potential to take you further into the game.
The only assumptions here are that you are playing the kind of game where you can die or run away to try again when sword 2 is sucking. If you are playing some kind of hardcore mode you use sword 1 and then upgrade it when it isn't a guaranteed win anymore.
If we assume that this is a sword in a typical MMO, the chance of a string of successful hits with sword 2 would make it preferable to sword 1. But even then, only marginally so. In the case I describe above, you're screwed.
So no, there is no effective difference between the two given what we know.
Now, if there are procs or items that modify your chance to hit...
Your argument is isomorphic to solipsism, Rym.
Reason? There are effects that increase crit range further. The last D&D character I played critted X2 on 17-20 at one point. ;^)
Some armor is damage mitigation, some is avoidance (D&D/Diablo II).
Some penetration reduces the targets mitigation/avoidance, some "ignores" a part of the mitigation/avoidance (Descent).
It's all relative really.