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 | Optimum 1v1 sniper battle strategy for 2fortsniper | |
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I've attempted a thorough analysis, which I'll share here to see if anyone can find flaws. I didn't do it for 2fort because the optimum 2fort strategy would involve crossing over to the enemy base, which is silly for a sniper battle. (But when the players silently agree not to cross over in 2fort, the 2fortsniper strategy then applies since, as I will show, the barrels in 2FS aren't a factor.)
First, observe that speed-sniping is a bad strategy because the enemy will win by walking out with a charged shot. Even if you hit first, your hit won't kill (not even a head-shot) and theirs will. (I'm known as a speed-sniper, but I only SS if my opponent does too, or if my opponent's wall-sniping isn't good enough to force me to WS.)
Definitions
camper - a player who is at least partly exposed, waiting at one spot for the enemy to come out.
walker - a player walking out from full hiding to at least partial exposure.
guess - The camper's guess is the possible walk-out location the camper holds their dot near. The walker's guess is the location the walker begins their dot at when walking out.
bail - to run to hiding after seeing that you've guessed wrong
I'll split my analysis into 3 posts. In this first post, I'll show how a camper can best exploit a walker whose strategy lacks a crucial element. In my 2nd post I'll reveal what that crucial element is and outline how a walker beats a camper. That 2nd post will imply that the optimum strategy for both players is, broadly speaking, to never camp (ie it's a walker-vs-walker battle). In my 3rd post I'll go into the specifics of the walker-vs-walker strategy.
The preamble is almost over but now I want to clarify in advance a couple things you may or may not find obvious.
In my discussion I'll be mentioning random choices. When I say "random", I don't mean a human's feeble attempt at being random. Rather, I'm talking about something like using the seconds hand of your watch, or using a random number generator. For instance on a TI calculator you can enter randInt(1,4 and that will pick a random number from 1 to 4.
Next point is that whether you're walking or camping, you must guess a spot your enemy can be at, as opposed to holding your dot between 2 spots thinking you'll be able to make a sick shot the instant you see them. If the enemy is making specific guesses and you're not, you'll get crushed. Sadly, there's no way around the fact that wall-sniping is largely about luck-of-the-guess (until the players battle each other long enough so that their scores can't be attributed to luck anymore).
Now for part 1 of the analysis:
Assumptions
1. If camper & walker both guess right, camper kills walker.
2. If a player guesses wrong, the other player has time to bail.
Here is the strategy our sub-optimal walker will use:
- Randomly pick one of the 4 places to walk out from.
- Randomly pick one of the places to aim at.
- If walking from a bottom door, keep walking toward the side wall within the base) until the camper is visible when camping at one of the 2 the opposite side camping locations. (Otherwise, the camper can always be hidden from a bottom walker, always guess top andbe correct 100% of the times walker becomes visible.)
Thanks to Assumption #1 from before, the camper can easily exploit the above strategy (not because any of those bullet points are wrong, but because something is missing). Here is what we'll do as the camper:
> Ranomly pick a spot to camp from. We only need to camp from 4 spots. On the bottom we'll camp near the side wall (inside the base).
> From those spots, we'll have 2 walk-out spots in our visibility (one top, one bottom). Randomly guess one of them.
> When aiming at the top, be completely hidden except to someone barely sticking out from the wall (that way if they walk all the way over from the other side instead of that wall, you're equally ready). When aiming at the bottom, come out a little further and aim at the center wall next to the door.
> If we guess wrong, we'll bail (and hope the enemy guessed wrong too). If the enemy responds by picking a random spot (without camping), we'll choose a random camping spot (but we'll be sure not to give the enemy info based on how long it took us to get to the spot). If the enemy responds by choosing a random camping spot, see next post. For now, let's assume they won't camp and that we'll get to camp before they walk out.
So how does that all play out?
Each player will always have a choice between 2 possible guesses.
25% of the times the walker becomes visible, Camper guesses right and Walker guesses wrong = kill for Camper.
25% of the time it's the other way around = kill for Walker
25% of the time they're both right = kill for Camper (by Assumption #1)
25% of the time, both guess wrong, both live and they restart
That means overall, of the times there's a kill, 2/3 of the scenarios favor the camper. So against this walker, we'll camp whenever given the opportunity. (We won't always have the opportunity if they also camp whenever we die. But then we'll punish them with the strategy of next post, so we'll be at an advantage whether we're camping or walking.)
If you're wondering what happens when the enemy's choices are biased or non-random, nothing changes except for the fact that you can exploit the enemy even more by adjusting your choice percentages. If you don't adjust, you'll still win 2/3 of the time as the camper. By adjusting you can win more often, but the risk of that is, if you adjust and they adjust in response (or if they started the pattern on purpose to trick you into adjusting so they could switch it up), you'll win less often. So if you wanna be safe, make each choice randomly and with equal weight.
Stay tuned for part 2 :) | |
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Wisdom
Super Regular
Dizzy Capper
|  | | P: | 10/06/2015 17:23 EST |
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Alternative strategy: faster reflexes. | |
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Yes, but if your opponent is equally lightning-fast, the player with the strategical advantage will win. Or if their strategy is superior enough to yours, they can be a slower aimer than you (up to an extent) and still win.
For instance, if you strategy is to always camp from the top-right and hold your dot on the center of their wall, and your opponent knows that and decides to walk out and blind-shoot exactly where you always stand, you're going to lose if they're half-decent. Your dot has to move all the way over whereas theirs doesn't have to move at all, all they have to do is release their mouse button. | |
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Part 2: how to exploit a camper.
This time we're the walker. We'll do what the previous walker did, but we'll add an element to it that will turn the tides in the walker's favor. The camper will have no good response except to not camp anymore (I think camping is flawed precisely because of what I'm about to discuss here).
When the camper is aiming at the top or bottom door, they're exposed not only to an enemy who places themselves into one those spots, but also to an enemy standing outside altogether. We, as the walker, will enter a visible outdoor spot far from the door (somewhere in front of the ramp). Once there, we'll have 2 possible guesses as usual. The camper's dot, even if held toward the bottom door, will be far from us compared to the distance of our dot to them. Therefore, we will win that battle whenever our guess is correct. If our guess is wrong and the camper guessed top, we again have the advantage (for the same reason) so the camper will bail (then we'll pick a random walk-out spot as before so it's like a do-over).
The camper can't guess that floor spot because then their dot would be visible to us so we'd never walk there (and it would be far from our other walk-out spots). But even if that weren't the case, they'd have 3 guesses to choose from whereas we'd only have 2, meaning we'd guess right more often.
But that's not all, it gets better -- once we're outdoors, we'll be able to see where the enemy is aiming because if they're smart, they're holding their dot on an exterior wall. So if we see they're aiming at the bottom door, we'll simply go back inside and walk out from the battlements. Their guess will be wrong 100% of the time, huge advantage to us. On the other hand, if they're aiming at the top door, we'll see that too and stay on the ground level. The camper can prevent this info by periodically re-guessing (randomly so that we don't know when they'll move their dot or how long it will be gone for), but that would suck even worse for them because they'd have to re-guess very often so that we can't exploit them by walking out the moment they move it). The problem with frequent re-guessing is they're vulnerable at the moment they're moving their dot to another spot. The more time spent doing that, the more likely it is we'll walk out at one of those vulerable moments for them.
If the camper doesn't re-guess, here's how often we'll kill them: .5(1/3) + .5 = 2/3
Half the time, the camper will be visible when we walk out. When that happens, we only win 1/3 of the times someone guesses correctly.
Half the time, the camper won't be visible, in which case we'll always win that battle.
Let's pretend the camper wrote a script to move their dot from location to location in nearly no time, so that re-guessing isn't a problem for them. They're still at a disadvantage, just not quite as big of one. To calculating our advantage in that case, we'll use some game theory.
The camper has an incentive to aim at the bottom door, because if we sneak onto the outdoor spot and we guess wrong, we'll die. For that reason, we'll want to walk out from a top door more often than a bottom door.
How often, x, should we walk out from a top door?
We're looking for the unexploitable percentage, aka Nash equilibrum. It's the percentage that makes our enemy indifferent to guessing the top or bottom. In other words, it's the percentage that causes their kill probability to be equal with either guess, ie:
P(enemy kills us when guessing top) = P(... bottom)
Call those P1 and P2. Their equations are below (if someone asks, I'll explain how I got them).
P1 = x/(1+x)
P2 = 1.5(1-x)/(2-x)
Setting P1=P2 and doing some algebra, we end up with a quadratic equation with one positive solution: x = √(7) - 2 ≈ 64.575%
So almost 13/20 of the time, or almost 2/3 of the time, we wanna walk out from the top.
What will be our kill % by doing that?
1 - x/(1+x) ≈ 60.76%
Summary: if the enemy perfectly utilizes re-guessing, we win 60.76% of the time. If the enemy does not re-guess, we win 2/3 of the time.
Since camping sucks (if the stuff in this post is correct), in part 3 I'll discuss the optimum walker-vs-walker strategy. | |
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I take it back, camping is good. There's a way to negate the walker's outdoor ground tactic.
Instead of re-guessing, the camper should re-camp. That is, pick another random camping spot (with the possibility of repeating the same one). Just often enough so that the walker can't use the tactic, which seems to be about every 10 seconds. So you stand in one spot for 10 seconds then re-pick a spot.
The enemy's logical response is to do the same thing: when they walk out and see an empty side, instead of going toward the bridge they'll just camp (in hopes that when you pick a new spot, it will be on their visible side, meaning advantage them).
So each player will take turns camping and walking out (sometimes at the same time) until you're in each other's visibility.
If the enemy tries to gain an advantage by camping longer than 10 sec (or whatever the magic number is, we can find out by experimentation), you'll implement the tactic of last post. If they camp for shorter periods than that, advantage you because you'll spend more time camping than them (hence you'll be in an advantageous position for more time per match, which will lead to a better score for you in the long run).
And there it is. Can anyone think of flaws? | |
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 | Can anyone think of flaws? | |
Concing medics, and pill spamming spies. | |
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-[IBSC]-iLluSiON-
Daycare Manager
Killer Scout
| | | P: | 10/07/2015 17:08 EST | | E: | 10/07/2015 17:10 EST |
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Good analysis.
Now, how about one on obtaining and capturing the enemy flag? (in regular 2fort) :D | |
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Wisdom
Super Regular
Dizzy Capper
| | | P: | 10/07/2015 18:50 EST |
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| Ignorant_Florist wrote:
| Can anyone think of flaws? | |
Concing medics, and pill spamming spies. | |
Neither of which are available in 2fortsniper | |
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| Can anyone think of flaws?
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Wisdom | |
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It's pretty cool somebody has attempted to breakdown sniping systematically (which has probably been tried a million times in the past), and in this case even mathematical formulas are being used.
There are far more than just 4 places for camping, however. Sometimes I will camp in "awkward" places, like next to a dead body or at a place where a sniper might not be expected to camp. It's definitely not a flawless tactic, but I think it can sometimes allow you to mess with your opponent's mind, especially if they are approaching a sniper match with the mindset that everything can fit nicely into a box.
Overall, your thread was very enjoyable from the conceptual standpoint. Yet, I have doubts about its real-world application when it comes playing against high-level snipers.
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| Jesus_is_King wrote:
Yet, I have doubts about its real-world application when it comes playing against high-level snipers. | |
The strategy assumes your opponent will play at a high level. If your opponent were a noob, you could do almost whatever you want and still win. But if you mean you doubt whether the strategy I found is in fact flawless, well so do I since I've only just thought of it. As time passes, myself or someone might notice things I overlooked.
| ...I think [fill in the blank] can sometimes allow you to mess with your opponent's mind, especially if they are approaching a sniper match with the mindset that everything can fit nicely into a box. | |
An opponent playing with a cold and calculated approach is not susceptible to psychological tactics. The topic here is a two-player zero-sum game, and it has been proven that there exists at least one unexploitable strategy for any game in that category. A player who has found such a strategy will not care what their opponent tries. In fact, if the enemy's strategy differs from ours in any way, that only opens the enemy up for exploitation if we choose to take advantage (but if we don't, we're safe by sticking to our original strategy).
However, already I see that my strategy is incomplete. In order to be truly optimum, it would have to be a Nash equilibrium. My strategy is not an equilibrium because the enemy has an incentive to deviate which I even mentioned yesterday: if they camp longer than 10 seconds they gain a slight advantage if we don't adjust. If my strategy were an equilibrium, we would never have to adjust and the enemy would have no incentive not to copy our strategy.
Therefore, I think we have to sometimes camp longer than 10 seconds and sometimes try the counter-tactic I mentioned in "Part 2". If we never camped long, we'd never gain a cheap tactical advantage and the enemy would never have to try the counter-tactic. If we never tried the counter-tactic, the enemy could camp as long as they wanted. For each, there should exist a percentage of how often to do it so that your opponent can't gain a stragical advantage regardless of how frequently/infrequently they try each. The question now is to figure out those percentages, which I'll attempt another time.
Also, I haven't given the barrels enough thought. I concluded that they're a bad camping spot, but I haven't weighed the pros/cons of walking out from them (given the opportunity). I think that probably will change things, but my analysis of it will have to wait.
| There are far more than just 4 places for camping, however. | |
Most spots are out in the open, and the problem with that is as follows. You have to guess between 4 possible walk-out locations. That's more uncertainty than the enemy has regardless of where you're standing, so the enemy will guess right more often and therefore kill you more often. In some spots they'll only have 1 guess to make. In a couple spots they'll have 3. In most they'll have just 2 (they'll sweep their dot high or sweep it low). The barrels are bad too (as a camping spot) because when the enemy walks out from the far side, you have 2 guesses to make whereas they only have 1 since they see the barrels before the doors, meaning you'd only get 50% of the kills (Assumption #1 would be the equalizer). 50% sounds fine, except that I said from the 4 good camping spots you get 2/3 of the kills. If you mix between the barrels and a spot behind them so that the enemy has 2 guesses, that actually hurts you because at that other spot they can see you from all 4 walkout spots, and overall you end up getting only 40% of the kills.
If you disagree with anything in that last paragraph then I welcome your thoughts. I hinted at there being a few more than 4 good camping spots, but from what I can tell, they're only optional because they wouldn't theoretically add to the strategy (though I can't rule out that they might add to it psychologically). | |
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| yousnoozeyoudie wrote:
| Ignorant_Florist wrote:
| Can anyone think of flaws? | |
Concing medics, and pill spamming spies. | |
Neither of which are available in 2fortsniper | |
We don't play that here. NEXT! | |
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Wisdom
Super Regular
Dizzy Capper
| | | P: | 10/08/2015 17:13 EST | | E: | 10/08/2015 17:13 EST |
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| Almond_Bread wrote:
[stuff]
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I sniped competitively for around a decade. The factors that seemed to matter at the highest levels of TFC sniper-only matches were the following:
1. Reflexes - It doesn't matter how well you plan if the other sniper has faster reflexes than you, because at this level everyone knows how to camp, how to blindshoot, etc.
2. Style - Most snipers are only really good at one style of sniping, be it wall sniping or speed sniping. In the case of wall sniping, you have campers and you have anti-campers. A lot can wall snipe and speed snipe, but not equally well. It also depends how well you can handle sniping against different styles. I knew wall snipers that could decimate speed snipers easily, but also the other way around. That isn't often the case though.
3. Networking - This factor is one that many of us don't have much control over. I have a very good connection via my ISP but, due to the way my traffic is routed to Drippy's, I shoot through players at varying rates. When the server is full, it is about 30-35% of shots that I take. It doesn't matter how awesome you are if you can't hit what you're shooting at. I saw this a lot in competitive sniping. | |
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I agree that psychological tactics wont work very well against certain people, and I do not propose it to be the deciding factor in winning/losing. But, it will force your opponent to realize that you can be anywhere in the map at any time. In that case, trying to predict your opponent or make some sort of statistical assessment becomes more impractical. "reflexes" will probably be the deciding factor.
Maybe martial arts can make a good analogy. All styles that I know of will emphasize quickness. If a kick-boxer who knows every kick an punch in the book is fighting a ju-jitsu guy who only knows a few takedown moves and an arm-bar... the latter can win that match if he has faster reflexes.
I still think your thread offers a valuable outlook on things. In gaming, or in life in general, success or failure can come down to all the little details.
Just for the record, though, I'm a bigger fan of team-based sniper matches than 1v1.
Hey!!!... I'm guessing we may as well kick off a plan for sniper league 4
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