Numb3rs-A Mathematical Gunfight

[@devondevon4366]

One of my favorite shows

[@The3nlightened0ne]

Guys this is simple. We don't need to over complicate it. -The worst shooter shoots the second best shooter because it would be irrational to shoot the the best shooter -The second best shooter shoots the best shooter because it is irrational to hit the worst when there's a greater threat -Thus, the best shooter reasons the same way, shooting his greatest threat; the second best shooter Moral of the Story: There's an advantage to being the weakest.

[@FalconFlyer75]

problem is even going by that logic still doesn't make any sense, - lets say 1/3 shooter fires at 2/3 and hits, then he's dead since 3/3 is certain to kill him - lets say 1/3 shooter fires at 3/3 and hits, probably still dead but there's a chance 2/3 could miss - lets say 1/3 shooter fires at 3/3 and MISSES, outcome is the same as the video, 2/3 still goes for 3/3 and vice versa lets say the video said the 1/3 shooter was BETTER OFF missing the 3/3 shooter that would make more sense

[@MrBraddles3128]

FalconFlyer75, if #1 hits #3 and kills him, chances are that he's finished when #2 shoots at him. The game is about limiting your risk in the best possible way. The best possible way to do it is how they said in the video. You want #2 and #3 shooting at each other so that when it's time for your second shot, you have a 50% chance of killing your opponent as opposed to having only a 33% chance.

[@br41nb0x7]

There are a few assumptions that may not be visible. It's based on the assertion that with each shot, their accuracy increases: "I hit the target once every three tries". In a hard case of probability, each individual shot is going to operate with its likelihood of success. So, for example, every time #1 shoots, it would always be a 1/3 (33%) chance for each shot. Implicit in the scenario is that their chances sequentially rise: after the first shot, #1 would go from 1/3 to 2/3, and if #1 ever got to use a third shot, it would be 3/3. The order of firing is important, then, because if #1 shoots with 1/3 accuracy, he reduces his following threat risk if he misses #2. Since #2 is likely to survive, he serves as the best target for #3's shot (assuming #3 survives). Whomever is left, #1's odds on a second shot are better. However, despite this false assumption of probability, #1 would still be better off shooting at #2 first, though this modified scenario wouldn't give #1 any better odds surviving subsequently.

[@EarthSurferUSA]

@@br41nb0x7 No, it is not an assertion that their accuracy increases. All three have a different amount of skill, and that is fixed, (stick with me here, I know). This is so easy to understand, let me explain. The first shooter, (the worst shot), is betting he will miss the second best shooter, or he would be taken out by the best shooter next, (since the 2nd best would be down). Of course the second best shooter shoots next, and of course has to pick the best shooting guy, or he is dead at the next shot, (by the best shooter if he is still standing). The best guy now goes down, (66% chance), and the worst shot now has the next shot with a 66% chance of hitting him, (there is where you are wrong),---and you know he is going to take his sweet azz time aiming this time. :) I think it would have worked out the same if the first 2 shooters shot at the best shooter first. The first would probably miss, the second would probably hit the best shooter,--and it is the worst shooters shot next, (since the best is down), with the same 66% chance of hitting the same guy. The best guy only had a 33% chance of not getting hit in both cases, because he shot last. Your quote sir: "So, for example, every time #1 shoots, it would always be a 1/3 (33%) chance for each shot." Yes, but that does mean 1 of 3 shots will hit the target, (law of averages I think), so the probability of a hit actually increases with each shot, but only to 3 shots. Then the probability starts over again at 33%. If by very low probability, he took 30 shots and missed the first 20, he would be 100% for the next 10 shots, or his initial 33% chance would not stand. It has been 25 years since I had 3 stats classes for engineering degrees, but I got pretty good at it. I was usually able to see the concepts before I put numbers to it. This is an easy probability problem that we can see in our heads. I don't remember how to figure out tough ones anymore, but I don't think you can prove me wrong here. But there is always a chance. :)

[@EarthSurferUSA]

@@FalconFlyer75 Nope, the best shooter is down when the 2nd shooter shat at him with a 66% chance of hitting him. It actually works out the exact same way if shooter 1 and 2 took their first shot at the best guy. The best guy only had a 33% chance of not getting hit, because he shot last.

[@michaeluphoff4749]

It is just crazy how much math I learned from watching this show.

[@CSIAddict]

great moment loved David and Colby too funny

[@JohnSmith-kf8mv]

Probably said somewhere in comments: 3rd shooter should fire in the air. 2nd shooter will shoot at 1st cos 1st hasn't shot yet. And 1st shooter, if alive, will shoot at the guy who shot at him, 2nd. If, as in the show, 3rd shooter at 2nd, he could hit him and kill him. This leaves 1st to shoot, and he might decide to shoot 3rd and kill him rather than shooting in the air .

[@jasonpinson8755]

Good to see numbers again.💯

[@libalchris]

Yeah I don't know how they came up with that idea. I just ran the calculations and got 13.8% chance of survivlal if (1/3) guy shoots (2/3) guy first, vs about 31.3% odds of survival if he shoots (3/3) guy first. (This assuming all the players make logical moves.

[@katymvt]

But, if he misses on purpose, then he almost has 100% of survival. Because if 2 shoots 1, 3 has nobody else to shoot at but 2. If 2 shoots at 3 and hits him the game is over. If he misses, 3 will automatically shoot 2, because he's mad that 2 shot at him.

[@parijat99]

all said and done.... we still use the different algorithms as shown in Numb3rs .... in our day-to-day lives.. even if we don't realize it... I use set theory, game theory and probability ratios in our line of work! Thanks to #Numb3rs

[@callanightshade8079]

In the intro to the show you even hear Charlie say "We use math every day" which is true. Even something as simple as putting a box in between two other boxes is math. Our brain is measuring if it'll fit or not, it may be off by a bit but it's still math

[@onoakposehaefekodha3974]

Math students watching Numb3rs be felling like superheroes, "Everything is numbers" 😀

[@claytonwade3570]

bc it is lol

[@lich109]

Exactly, even if you have one shot, you shoot at the best shot, if you miss, the second best shoots at the best, at that point he can kill whoever he wants, you are at the same disadvantage the other guy is, if you shoot at the second best and kill him, you are screwed.

[@The3nlightened0ne]

dude, it is just an analogy for the actual event. The 1/3 shooter engages the 2/3 shooter to prompt a fight, but realizing that the 3/3 shooter is a real threat, the 2/3 engages the 3/3 gunner, thereby causing the 3/3 to shoot back, leaving the 2/3 dead, and then suposedly leaving the 3/3 gunner dead leaving both, the 2/3 and the 3/3 shooters dead. This is simply a way for a lesser unit to turn a situation to its advantage. 1/3 is metaphorically the F.I.B in this context.

[@coolgalstatus]

what if he purposely misses charlie when he shoots?

[@mangonauts6464]

But why shoot at the 2/3 shot? Assuming you miss your first shot, (and can't deliberately not hit anyone) it's in either of the two's best interests to shoot each other first no matter what anyway. So you might as well shoot the 3/3 shot. And if you shot the 2/3 and somehow hit, then you're guaranteed to be shot by the 3/3.

[@lich109]

all of these percentages are averages, the percentages I took were based if the bullet hit the person you were aiming for with dying given a negative, so for the first example it was -33 (you hit him you die so negative number), 66, 50, and the second example was 33, 66, 50. If you killed the deadshot the numbers would be 33 (you hit) and 33 (second best misses) that scenario has a 33% chance of happening, which is still better odds.

[@scottzvidzo5564]

"If I'm still standing I'm gonna shoot you and I don't miss" Granger is a cool ass agent and I mean way cooler than David. 😂

[@spinnerrogers]

The preferences of the shooters could've been more clear. It seems the shooters want 1st to live and 2nd to get back at who shot them. Also, they must shoot with intention to hit. This makes it rational for the 2nd shooter to shoot the 3rd always (cuz if he hits the 1st, which he will more often than not, he's dead). The 1st shooter knows what the 2nd will do and actually hopes to miss the 2nd (if he hits he's dead): if he misses he guarantees his safety, assuming the others act rationally with regard to their preferences.

[@lich109]

If you aim at the second best shot you have a 33% chance of dying (the hit), the a 66% chance of not dying (second best shooting best) then a 50% chance of dying, if you shoot at the best you have a 33% chance of not dying, then a 66% chance of not dying, then a 50% chance of not dying. In percentages that translates to 27.66_% chance that you will survive (if you shoot at the second best shot), and if you both shoot at the best (if both miss) the chance you survive will increase to 49.66_%

[@The3nlightened0ne]

Well, we must consider that these mathematical concepts are factual. I simply was aluded by game theory during my high school days because it seemed unrealistic, but stuck with it and the elementary concepts began to make sense. I dont watch this show, but in order to understand this fully, I'll have to know the exact context that fits with this metaphorical "gun fight"

[@IIoWoII]

A duel... between 3 people.

[@lich109]

One thing to think about that isn't around percentages, there is no possible scenario where you are the survivor, if you want to live, there will always be somebody else there, let's examine the outcomes, 3 shoots at 2, kills him, then dies, 1 is left, three shoots at 1, kills him, 2 might or might not kill 3, if he doesn't then both are fine, if he does, then 2 is left, if 3 misses, then only one more person can die because a dead man can't fire his gun, so 2 kills 1 or 1 kills somebody.

[@rajatroy1138]

Shooting at 2 by 3 makes his chances of getting a shot higher the next time. Missing leaves 3 with higher chance of survival, Shooting at 3 by 2 increases risk since 3 only gets one shot correct he can be shot later. Shooting 2 makes perfect sense by for 1 since 2 is better shot than 3 and 3 can be shot later as chances are he will miss both of the first 2 shots.

[@SG1Mitchell]

what is THAT you mean? Season 5, Episode 10 Frienimies.

[@gorgolyt]

I don't know why you're talking about analogies... I know this isn't real life? Anyway, what I meant to say is, why would you ever shoot at the 2/3 guy if you're guaranteed to die if you HIT him?

[@animusmon]

Season and episode?

[@rishi4]

loved the intro, and the gunfight looked cool but to me it didnt make a lot of sense because if Marhshall shoots at Charlie and hits well then he's done since Colby never misses and it would be his turn If Marshall Shoots at Colby and hits then he would have to face Charlie, while Charlie would have the advantage, Marshall still would stand a chance since Charlie has a possiblity of missing and if he shoots at Colby and misses then Charlie still shoots Colby and the same result as the clip

[@sheepzification]

imagine a DUEL between 3 people:D

[@libalchris]

I didn't notice that. In that case the problem is flawed. It would in fact be impossible to determine what is the best choice for each player to make in a given scenario without knowing the motivations of player 3. Since his survival does not depend on it, how does 3 determine who to shoot if he's still alive when it's his turn? Does he take into account which players shot at him? If so does he flip a coin if both or neither players shot at him? Without knowing that the problem is unsolvable.

[@lich109]

At that point he would have been shot at by both of them so he would still go after the better shot.

[@lich109]

So how is Gastrophetes wrong? If there is a round two you are at a massive disadvantage, and if both people aim at the dead shot, then the odds are against him surviving, not to mention you have a higher chance of living in the next rounds.

[@juld55]

Travis Marshall, the Doomsday Killer.

[@gorgolyt]

rofl why would you shoot at the guy when you're guaranteed to die if you miss him?

[@warbacca1017]

Ah, so The Good, The Bad, and The Ugly...gotcha

[@EarthSurferUSA]

It would work out the same if shooter 1 and 2 both took their first shot at shooter 3, (the best shot who never misses). The best shot only had a 33% chance of not getting hit because he shot last in both sequences. The first shooter, (the worst shot) shoots at the best shooter and misses, (66% chance he will miss). The second shooter shoots at the best shooter, and takes him down with a 66% chance. Now it is the worst shooters turn again, (because the best is down), and he again has a 66% chance of hitting the same guy he missed on his first shot. And you better bet, he is going to take his sweet azz time aiming this time. :)

[@EarthSurferUSA]

Correction: "and he again has a 66% chance of hitting the same guy he missed on his first shot." should be: "and this time, instead of a 33% chance, he has a 66% chance of hitting the same guy he missed on his first shot."

[@Nk7289]

.....Travis.......Marshall!!

[@CreatingPulsars]

Colin is such epic win

[@didoberte3475]

frensh please

[@libalchris]

This is completely inaccurate. shooting at (2/3) is the absolute worst option (1/3) could make. His best bet would be to shoot at the ground assuring he hits nobody (this would actually make him statistically the most likely person to survive), but if that isn't allowed he would be much better off shooting at (1).

[@amenaghawonoyegun3028]

It's 👍🏾

[@Bella26111]

Where Charlie lost his hair? hehe Where are the curls? Well, that in the next episode he has grown a little. :P hahhahaha

[@robertlewisvazquez]

But this depends on who go's first

[@kijuuki]

lol @ the tumbleweed

[@tommymiddlefinger1283]

Proving once again that 5 out of 3 people are bad at math. 😄

[@The3nlightened0ne]

Isnt this a mexican stand off?

[@eataneraser]

This is so stupid.