The Luckiest GoldenEye Speedrun Explained

speedrunners take on the most brutal challenges and optimize them to a level never thought possible before they come up with the most insane tricks and can not only pull them off over and over like clockwork but even make it look easy but there is one thing that speedr Runners Fear One untameable Beast three words that strike fear into their hearts random number generation this is the luckiest golden eye speedrun frig double O agent explained quickly before we go on right now in my life I'm in the situation I'm sure a lot of you are familiar with I'm trying to save up to purchase my first home and today's economy is doing its best to make that dream impossible well today's sponsor rocket money is here to help it's easy to fall into the Trap of signing up for recurring subscriptions and forgetting about them rocket money identifies recurring charges and allows you to cancel these unwanted subscriptions with just a tap but here's something even better you can monitor and categorize your 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greatest golden eye and Perfect Dark player of all time perfect Ace his current world records in both games are shown here in green he set the record in May 2023 with a time of 1 minute and 3 seconds despite the timing method being in-game time which only shows times rounded down to the second this is an untied world record four players tie for 104 frig has four mission objectives objective a rescue hostages there are six hostages being held in various parts of the ship and you need to free two on agent four on secret agent and five on the double agent difficulty objectives B and C are similar disarm the bridge bomb and the engine room bomb they require selecting the diffuser in the inventory and using it on these C4 explosives stuck to consoles finally objective D is to plant a tracking bug on a helicopter at the back of the ship Bond plants tracking bugs by throwing them at full force directly at the object so why is this relatively simple Mission so special well because for the hostages to count as being rescued freeing them is not enough they need to escape as well as soon as the hostage taker is out of commission hostages pick an Escape Route at random out of six possible destinations this is at the heart of the randomness of this Mission the time a hostage takes to escape can range anywhere between 7 seconds and well over a minute based on multiple factors but more on that later in fact I'm going to dedicate the whole second half of this video to dive into that matter for now let's get into perfect Aces world record immediately there are a few things to note AC is running diagonally while looking down running diagonally is about 30% faster than simply running forwards this is because Bond speed is a combination of his forwards and sideways speed adding up to a diagonal Vector so by pressing C up and C left or right ace is able to move around faster he plays with the 1.2 control style instead of the default 1.1 the default is to use the stick to move and turn and the C buttons to look up and down and strave sideways 1.2 uses the stick to look around and turn and the C buttons to move in all four directions the reason 1.2 is faster is because it allows bond to keep top speed while turning in 1.1 you would have to sacrifice some speed to turn using the control stick at the top level there's also an increasingly popular control style called 2.x usually 2.4 where runners hold two controllers and control Bond using one joystick to move and one to turn it's marginally faster in most levels because of an oversight with the second controller and cut scenes that allows bond to start the level running at full speed frigate is an exception though you don't W start the level by moving forward so 1.2 is the best choice looking down is done for lag reduction this is straightforward less stuff on screen easier for the console to render golden eye can be very laggy at times so it compensates for lag by factoring movement based on the length of each frame this process is a bit imperfect though so bond does run slower under heavy lag than he does in lagless conditions as a rule of thumb the difference between looking down and not is about 1 second per minute of run time finally Ace is running on the jack Japanese version of the game this version is usually preferred to the North American release not because of faster text but because of more lenient auto aim and extra body armor in some levels there's no body armor in frigate but the auto aim is useful the path Ace stes through the level is optimized so that the hostage that takes the longest to escape is freed as early as possible he goes down to the lower deck and frees these two hostages the second one takes the longest path out of the ship for the hostage to start Escaping The Taker needs to be dead and faded out Simply injuring the guard will cause him to go after Bond and the hostage will stay put indefinitely until that specific guard dies from this point the fastest route is to go disarm the engine room bomb then get back up to do the rest of the [Music] objectives the sixth hostage is in the engine room but because theow agent only requires five hostages to be freed Ace doesn't free him it seems like freeing all six hostages would improve the odds of success but it's actually not really the case while it does improve the odds of hostages escaping it comes at the cost of several seconds and the risk of guards blowing up the bomb so it actually makes it harder to set a world record time to go back up to the other side of the ship Ace performs What's called the pipe warp instead of being a full wall the pipe's actual shape matches their visual shape somewhat well this leaves a clear gap between them that's too small small for Bon to fit through however it is possible to go through anyway thanks to lag Bon has a collision radius around him that is checked on every frame for walls objects and guards but when calculating if his movement is valid between frames the game simply draws a line and checks if it crosses a wall or another boundary if that doesn't hit any obstacle bond is moved at the end of it if his new position is clear of any walls he moves and if it isn't he doesn't unlike Bond though this line has no width so the thetically it can fit through a gap of any size with the right position and angle any size but the problem is even full running speed plus strafing is not enough to clear a wall in a single frame until lag comes into play like I said earlier the game compensates for lag by factoring Bond's Movement by the length of a frame the refresh rate of the N64 is 60 HZ but in reality the game basically never runs above 30 frames per second or 260th of a second per frame so with a base speed of about 13.5 and a factor of two Bond runs at roughly 27 units of distance per frame when switching weapons the game experiences a pretty big lag Spike as it loads the model of the next weapon which often causes the next frame to be delayed by about 2 to three extra 60s of a second this causes bond to move by several times his speed in that frame which turns out to be enough to clear the wall and clip through so long as the line drown between the frames actually fits in the gap between the pipes this is how not only the pipe work but basically every warp in the game works including every slow to Open Door in Depot in Jungle and so on now Ace frees two more hostages you can see the Japanese auto aim at work here Ace tries to aim for the head to take out the guards faster the auto aim corrects towards the middle of the body so he deliberately aims way up so that the auto aim corrects towards their heads he completes objective d by launching the tracker bug into outer space it somehow lands on the helicopter Ace keeps looking towards the helicopter to keep it loaded otherwise the bug would go right through in the mission would fail throwing the bug from this far is actually fairly easy to get consistently for top runners finally Ace heads to the bridge for the final hostage rescue in the second bomb diffusal the guards in this room are gone because by shooting as he ran across the boat at the start Ace alerted them and caused them to run out he Sprints to the boat and the level is complete in 1 minute and 3 seconds note that we don't see the text objective a complete that's because it completes during the fade out at which point the text doesn't appear on screen because the game checks for Mission completion at the very end of this Fade Out hostages can escape up to about one full second after the level is finished now I overlooked a bit of a key detail let's talk about how the hostage is escaped and why this Speed Run is so lucky the approach we're going to take is to set a Target time for example 103 and try to find out the probability of hostages escaping before this time first we're going to figure out when each hostage is released an average run then we'll assign a probability function for how long a hostage is escape takes independently for each one of them finally we'll calculate the probability that all five of them Escape at or before the target time on any given run the first part is quite easy we can take one of A's runs and simply measure the time it takes for him to reach each hostage it's made a little more complicated by all the pausing to select the bomb diffuser and tracker but it's relatively easy to factor them out the result we get is this Ace usually reaches each hostage around 14 16 38 40 and 54 seconds into the Run respectively we will revisit these numbers further down the line but for now this is what we're going to use as our Baseline before we go any further though there's a tiny annoyance we need to get out of the way how do we refer to each hostage how about we give them names these two will be Francis and Chuck and the two downstairs freeden's secret agent and double agent will be Sam and eler for completeness his sake let's call the engine room hostage Eugene and of course under Bridge we find Bridget now to find out how long they take to escape here are the six Escape points again you would think that hostages would take the shortest path to every Point like this for example of course they don't that would be too complicated the reality is actually a lot simpler than that because of the host's navigation graph in any level of golden eye a navigation graph is a set of interconnected nodes that defines where non-playable characters or NPCs can move in frig the hostages navigation graph is well a bit incomplete so for instance hostages will never go through this door this one or that one to go from here to there they will go that way instead now as you may have noticed to exit the ship there's basically a single option therefore no matter what Escape point they pick everyone is going to first head to this area then head over to their chosen location this simplifies calculating their path by a huge amount and it also means that no matter who we're talking about Escape points can be ordered from the fastest to the slowest all you need to do is find out how long each hostage takes to run to here and then how long it takes from there to every Escape Point note that the upper deck favors the back of the ship slightly and the lower deck favors the front but the difference is very small there's just one exception how does Bridget make it all the way to there in about 5 Seconds the answer is quite simple they don't have to this zone is not a circle it's the crosssection of a sphere centered above the ship at this elevation the circle is rather small but at higher elevation its radius reaches into the ship while it also being the optimal Escape point for everyone else is just a coincidence for Bridget the best escape point is better than the others by a much wider margin as a side note these two Escape points are actually so high their radius doesn't touch the ship so hostages need to be unloaded to reach them but more on unloaded movement later now that we know how much time each hostage takes to reach every Escape Point what is the probability of them being fast enough first we need to look at the probability of choosing each Escape point when they choose their escape Point hostages call the random number generation or RNG to get a number from 0 to 255 and they check if it's above 40 80 120 160 or 200 the slightly imbalanced distributions skes the odds towards this point giving the optimal point a 15.6% chance of being selected however it's possible to improve those odds hostages like scientists can surrender if threatened if you shoot near a hostage after they've chosen their destination they will stop what they're doing and surrender as they start to put their hands up though they immediately pick a new Escape point and start running but why is rrolling a good idea if you don't know which point they picked in the first place well because thanks to a bug in their code when they choose their new destination this time the probability for the best escape Point improves to 33.8% the problem with this strategy though is that it takes a bit of extra time to make the hostage surrender so it's quite impractical to go for in a run while it would be useful for both Oliver and Bridget only Bridget can realistically be made to do this since you hang around a bit longer for the bomb diffusal there are more factors at play guard death animations hostages only begin their escape when their taker has fully faded out there are 16 possible death animations with variable lengths and probabilities to complicate things even more a guard will pick from a different set of animations depending on where they took lethal damage be it the head torso gut thigh or somewhere else in the limb generally generally Runners will aim for the body or the head so to simplify things a bit we can look at the animations for those two body parts they're actually quite similar with the head having two more possibilities both terrible for the speedrun the bad animations are about 5 Seconds slower than all the other possibilities every animation has an equal chance of being chosen so that's simple to that we need to add the time it takes for the guard to fade out which thankfully is a fixed 1.61 seconds and now we have the time it takes from the moment the guard is taken out until the moment the hostage picks an escape Point as well as the time it takes for the hostage to reach that escape Point except the time it takes to run to an escape point isn't just one simple number many more things can throw a wrench in the process the biggest one is guards getting in the way hostages need to path around obstacles including guards and other hostages and they're not always great at it one annoyingly placed guard can easily completely erase any chance at completion a run might have had on top of that NPCs can be unloaded when Bond is far enough in looking away from them an unloaded hostage has a much simpler way of moving they stay at a node on the navigation graph and check the distance to the next one they wait until they would have run that distance if they were actually running and then snap to the node if it's free they no longer calculate collisions or path around obstacles even including doors they warp right through them however they do check if their position conflicts with another inpc and that's where the trouble lies if the node they're trying to get to is already occupied the hostage is loaded back at the start node and manually runs the segment again pathing around obstacles this time also since they snap directly to their target node this is how hostages can escape at these points in fact it's the only way they can reach the Escape Zone this is why Runners avoid looking towards the back of the ship at the end of a run they make sure not to load any hostage that's trying to escape there another potential issue is lag caused by a couple dozen guards being alerted at once it can be mitigated with lookdown by only making noise when strictly necessary and by eliminating as many guards along the way as possible of course that also reduces the chances of them impeding hostages guards can also sometimes throw grenades or blow up consoles and the explosion kills a random hostage we'll gather all of these issues into one group called the outside factors no matter how hard we try factors like these are impossible to model accurately there are two ways one could go about this the first and the simplest is to assume that the conditions are ideal every time and only focus on the probabilities that can actually be calculated we call these the base odds no matter what happens the probability of success cannot go higher than the base odds from there one could make an educated guess on the estimated probability that outside factors cause problems and Factor the base odds by this amount this is an overly simplistic way to look at it though because Sam has a lot more leeway than Oliver for instance the second is to do a statistical analysis based on empirical data in this case it's too impractical it would require a tailor made roh hack that logs data on each hostages Target Escape point and precise Escape time you would need worldclass Runners to run hundreds of runs at or near world record pace and record each one accurately so let's first take the easy path and calculate the base probability Sam who we free 14 seconds in takes this path to leave the ship and can then go to one of the six Escape points leading to this Escape time distribution to determine when exactly Sam starts escaping we need to factor in his taker's death animation and Fade Out times assuming there's an equal chance to hit the head or the body this is the probability distribution for the death animation thankfully the Fade Out is a constant 1.61 second so we can simply add it to every possibility to get the Escape start probability distribution now we need to somehow combine these two together how do we do that the answer is simple what's the probability that we get both the best animation and the best escape Point since both of these events are independent of each other it's just like rolling two di trying to get double sixes to to get a double six you have a 1 in six chance of getting a six here and another 1 in six chance of getting a six there to get the probability of both of them at the same time you simply multiply the probabilities together the chance of a double 6 is 1 and 36 in this case the probabilities are different but the idea is the same therefore the probability of getting both the fastest animation and the fastest Escape is the product of both which is 1.2% thankfully we don't need the absolute best case scenario we simply need it to be good enough the second shortest animation length is only a sixth of a second slower and is shared by three animations so this one has a probability of 3.7% since either one of these results is fine getting one or the other doesn't matter so what do we do with the probability let's go back to di let's say I want a diet to land on either a five or a six it has a one in six chance of landing on a five and a one in six on landing on a six to get the probability of it landing on a five or on a six you simply add the two probabilities together there's a two in six chance or a 1 in three that the die will land on a five or on a six therefore in our case the probability that we get the fastest or second fastest animation and the fastest Escape point is 1.2% Plus 3.7% or 4.9% now all we need to do is to repeat this for every possible combination of Escape points and animations considering we have every possibility if we add up all of these probabilities we should get 100% and indeed we do the next thing we need to do is filter every combination of animations and Escape points that result in the hostage escaping too late for the objective to complete once we do this we get 100% is there a mistake no it's actually because we free Sam so early in the run that no matter what animation or Escape point he uses he will always make it out in time theoretically in the worst case though it gets very close so in practice with lag and guards getting in the way Sam doesn't escape in time on every run Oliver is even deeper into the ship he takes this path out which can take well over 40 or even 50 seconds as a result once we combine the animations and the Escape point we find that basically only the best possible Escape Point has even a chance of being fast enough while theoretically the worst animations can just barely make it in time in practice this is very dubious because Oliver has a higher chance of getting stuck if he leaves late this time he will escape quickly enough only 21.7% of the time Francis and Chuck are close to each other the first one we free Francis also has the shortest path so his probability is significantly better than Chuck's 97.7% compared to 65.8% regardless both have a decent chance of making it out in time as you can see here getting the worst animations throws a wrench and their odds of making it out in time finally Bridget is Freed at the very end and because of the Quirk with the trigger area they absolutely have to choose the best escape Point slow death animations also won't cut it so they have the lowest chance of any hostage of getting out at a meager 14.5% so what do we do with these numbers remember that if you want to know the probability that two independent events happen at the same time you have to multiply their probabilities together the same principle applies regardless of how many independent events you have the probability of objective a completing in time is the probability that all five hostages Escape in time we need to multiply 100% by 21.7% 97.7% 65.8% and finally 14.5% and we get a total probability of 2.0% that's it now I mentioned before that Bridget could potentially have better odds of choosing the best escape path if we make them surrender it's clunky and costs a bit of time but assuming that someone managed to pull it off consistently they could improve their chances to a slightly less brutal 4.4% but remember these are the base odds this is the best it could possibly ever get in reality hostages have plenty of occasions to get slowed down by guards lag being loaded at the wrong time anything unfortunately we can't know for sure what happens in reality because we simply don't have the data as cool as it would have been to do hundreds of trial runs in a special rum hack it's simply unrealistic so we went ahead and did it wh Ted made the custom rum hack and testing was conducted by Perfect days in Shan Johan time to do some real trials on a real console [Music] perfect day since Shan John played 200 trial runs all near world record Pace to obtain this data the slowest run logged is a 106 and Ace even managed to get 159 second run that's right 4 seconds faster than his current world record thanks to White dad's rum hack they carefully logged each host's path in Escape time the resulting data gives us a ton of insight on what kind of odds to ECT when going for frig double O agent first to improve the quality of data Whit head removed the ability for a hostage to pick a doomed Escape point this means that Oliver and Bridget always pick the best and Chuck cannot pick the worst this improves the odds of completion of trial runs by a factor of about 50 or in other words we're looking at a sample of the 2% of runs that even could have a chance to complete in the first place of their 200 attempts they saw one run complete in 101 two runs complete in 102 one run complete in 10 3 and four runs complete in 104 remember that because hostages can escape during the fade out an objective a complete in 104 can still be valid for a 103 run but what about specific hostages let's look at Bridget first assuming they pick the best escape Point their escape is pretty much secured then you have Francis and Chuck which are subject to some wild time losses from time to time Oliver unsurprisingly can easily lose over 10 seconds when trying to get out but perhaps more surprising is Sam who despite having what should be an easier route has just as hard a time getting out more specifically even Sam's fastest measured Escape times were several seconds slower than the predicted times in theory therefore and again only looking at the viable Escape points we find that in practice hostages have a much lower chance of escaping in time than is theoretically possible Bridget completes 76% of the time because despite being pretty consistent the timing window is very narrow Francis and Chuck complete 77 and 44% of the time they're subject to guards getting in the way and Chuck gets his name from what Runners call the chair stuck Sam benefits from being freed first but his Escape can get so bad that despite that he still only completes 62% of the time although keep in mind that every Escape point was made available to him Oliver is by far the worst even when choosing the best escape point every time what should be 100% success rate in theory turns into 27% because not only is his path the longest and one of the most inconsistent he also has one of the narrowest windows to get out in time now we can run a Monte Carlo simulation to model the real probability of hostages escaping before any Target Time based on the known probabilities and the empirical data on outside factors how does the Monte Carlo method work well it's pretty simple you take all your variable factors and assign them a random value based on their respective probability function for example if I want to calculate the sum of 10 dice I can randomly assign a number from 1 to six to each of them and sum them now the result I get is meaningless it's just one random result but if I repeat this thousands of times millions of times and tally the results I will end up with a representation of the probability of each sum from 10 to 60 the more random trials the more accurate this model will be on average in this case the probability function gives us a distribution of the range of time a hostage can take to run to their given Escape Route the probability of each point in that distribution is estimated using the data in the 200 trial runs this analysis was done by onslot with a bit of my input we took several different approaches that yielded slightly different results every simulation went through each of these steps first select a subsample of Hostage release times in a way that filters the slowest trials and randomly draw from this group to get a typical run with worldall record potential then for each hostage draw a random running time from the distribution measured into the 200 trials add this running time to the release time and take the maximum across all five hostages to get the time at which objective a completes repeat this a few million times and what you get is a probability distribution of the time of completion of objective a the results will be displayed using a CDF a cumulative distribution function the way it works is simple for any value on the time axis this is the probability that by finishing the mission at this time objective a will be completed as time goes on the cumulative distribution function can only ever go up since it represents the cumulative probability that objective a completes at or before this time this includes the possibility of the objective completing during the Fade Out the first approach was to select the fastest 50 release times to draw from after 1 million simulated runs for 7.8% objective a would complete in time however and this is a huge caveat this number is assuming that no bad Escape points were chosen which is itself only a 2% chance we need to paint the whole picture the probability of objective a completing in time is equal to the probability that a completes and all chosen Escape points are good which we'll call E plus the probability that a completes and not all chosen Escape points are good which is e Prime the probability of events A and E is equal to the probability of a given that e happens multiplied by the probability of e itself we know these values 7.8% * 2% or 0.16% we can do the same on the other side the probability that not all Escape points are good is simply the opposite of 2% or 98% but what is the probability that a completes given that e does not happen well of course that's zero if at least one Escape Point can't allow a hostage to escape in time objective a will never complete in time therefore the result we get is 0.16% or 1 in 628 chance that all five hostages Escape fast enough to allow for a 103 run to complete this is several times less than the 2% we found theoretically which makes sense given how we found it in practice most hostages run into obstacles when trying to escape the theoretical calculations didn't account for the second approach is perhaps the most optimistic instead of taking the fastest 50 it looks at the fastest Five release times the result is essentially the ideal time for when a hostage starts to escape to get the odds of completion for a best case scenario can of run here here we find the 10.6% of runs completed in time for a 103 which translates to 0.22% or 1 in 463 after factoring the choice of Escape points now because these two approaches filter out the slowest release times while they do serve to eliminate slow runs they also tend to favor the faster death animations over the slower ones which is something that Runners don't have control over for the most part this is why another approach was also looked at here instead of taking random release time times we took a fixed reference time to reach every hostage sampled from one of AC's runs at a 102 Pace as you can see these times are slightly faster than the Baseline we used earlier since they were measured on one of A's faster runs even better than the current world record in his4 trial runs Ace clocked in at an average of 102.4 so it's not unreasonable to use as a benchmark I do need to point out that because they were measured using video footage and not the actual in-game time they are to be taken with a grain of salt as they could deviate by up to half a second or so with this standard run we randomized the death animation of the hostage taker to get a random release time and then we randomize the escape with the data sample from the 200 trial runs the result is a 6.9% completion rate or one in 700 once we factor in the choice of Escape points slightly worse than the other two methods this is most likely due to the fact that this approach considers all death animations equally again with the assumption that the runner has a 50/50 chance of hitting the head or the body on the other hand in reality runs are bound to vary a bit more than the Benchmark times we chose finally we looked at one last possibility what if Ace was on the Run of his life what is the fastest possible time he could get on the level for this one I dissected his fastest recorded completion ever a 59sec run and extracted these splits from it this is the absolute best case scenario for when each hostage taker could be killed using this route from there the process is the same randomize the animation randomize the Escape time using the sample data and this is the result for 103 we get an 11% completion rate or 1 in 443 chance when factoring in the Escape Point choice for a 102 a 5.6% rate or one in 864 for a 101 this drops to 2.1% or 1 in 2200 for a 1 minute flat 0.7% with all the correct Escape points or one in over 7,000 without and finally we do find that yes a time of 59 seconds is indeed possible but the odds of it happening are on the order of 1 in 25,000 at this point this trrain is put in Oliver because he's freed early in the Run improvements to the run time don't change his release time much and his minimum Escape time of about 39 seconds means he basically never escapes faster than 1 minute flat it's reasonable to assume that a run at to 58 or even 57 pace could be done but the probability of hostages escaping would be next to zero that being said there's a tool assisted speedrun of this level by Whited which uses some rather unconventional strategies that I sadly don't have time to dive into and gets a final time of 51 seconds in this one our buddy Eugene is freed because Bon throws a grenade that perfectly takes out the engine room hostage taker this frees up the need for Oliver to escape and allows this faster time so the question has been answered to the best of the speedr running community's ability the probability of AC's world record r run is on the order of 0.2% or 1 in 500 given that one plays a level at this blistering Pace again I want to emphasize that this entire analysis made possible by whad Ace Shan John and onslot is the best we have but it's not perfect many assumptions were made along the way it only looks at the current world record strategy but other routes were developed to maximize the overall Prospect of getting a good run sometimes sacrificing the ability to get a 103 in order to make 105 or 106 more likely not unlike in other fields of scientific research this experiment furthered our understanding of key buttl necks and it could be the Catalyst of new discoveries that make the presents impossible the future is [Music] reality [Music]

Channel: Bismuth

Views: 204,342

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Id: hsyXjZ09OFI

Length: 35min 6sec (2106 seconds)

Published: Fri Dec 01 2023