The hidden Nash Equilibrium at the start of every Dota 2 game

[00:00:00]I'm a little nervous because I suspect we will see quite a few dissenting comments on this video. There will be some high-skll players and low-skll players throwing out edge cases, and I suspect some people might accuse me of even ruining their pubs.

[00:00:16]But nevertheless, I'm going to tell you what I discovered after an extremely deep dive using over 50,000 replays to analyze the impact of pregame strategies in Dota 2. The first thing your team should do is invade the opponent's jungle together in every game. If your team does not, you should go alone.

[00:00:38]Pregame strategy seems to be a much more complex decision tree, but it turns out to be very simple. You always invade. I found this from a detailed analysis of over 50,000 ranked replays. If you could always coordinate your team, there is a statistically optimal play that is always your best option. No matter what your opponents do before the horn, even if they know your general strategy because you both watched this video, their best response is just to do the exact same thing that you're going to do. Yet, only 15.2% of teams are using this majority invade strategy. Invading remains optimal even when controlling for team coordination, hero picks, player skill, and rank.

[00:01:27]Dota is way too complex for me to talk about an optimal strategy for the whole game. So, what we're talking about here is specifically the pregame, or the period after the draft ends, but before the horn. Dota is a strategy game where two teams of five try to destroy each other's base first. Before the game properly starts, there's about 90 seconds where there's no objectives on the map, and players are free to move around. Once the game starts, the first objectives spawn. These are four bounty runes, each worth 200 gold to the claiming team, so 800 gold up for grabs.

[00:02:00]During this pregame time, it is also possible to fight opponents and kill or die. Generally, each player on a team uses this time to focus on one of a few goals. They might contest the four bounty runes. They may position to place wards for vision, particularly around the mid lane, in order to give themselves an advantage into the early game. They may invade the opponent's side of the map, or they might sit under their own tower or in their own base doing nothing because they are dumb and nobody likes them. For this study, we're looking at 53,455 random ranked games, removing 1.2% because of fairness issues like bots or abandons. We labeled teams based on what their players were doing, either at the horn or two seconds before first contact, whichever came first. Strategy labels were assigned by merging all heroes that are clustered around the same objective or within 1500 units of each other. Then we take the centrid position for each group and use that to classify both their objective as well as their strategy label. So in this example, you can see Radiant has two heroes contesting each of the river runes and one hero invading the Dire Jungle Rune. Dire dots in red have all five heroes invaded past the river, but in two groups. One is pushed in around the jungle rune and one is contesting the river rune. What we end up with is a map of whether teams are contesting river runes, invading the enemy jungle, or defending their own jungle. So, you'll see that there's three main strategy labels. Either you are invading by crossing the river into opponent territory. You are contesting by hovering around the river, or you are defending by staying on your own high ground or farther back. We've also broken each group up into their nearest objective label. Don't worry about memorizing any of this. I just have it here for you to reference later. Getting a bounty rune also denies it to your opponents, which means a stolen bounty rune nets an advantage of 400 gold at the beginning of the game. Stealing a bounty rune turns out to be pretty good.

[00:04:05]For each net bounty rune a team steals, they get an increased win expectancy of 1.5%. That probably isn't fully causal, right? Better players probably know that they should be prioritizing bounty runes and know how to do it more effectively.

[00:04:20]But these are ranked games with evenly skilled players, so we'll assume it's mostly causal for now. I'm actually going to reel myself back and try to not get too distracted because our goal here is not to measure bounty runes. It's to measure opening strategies. Win rate is not the best method to use when talking about opening strategies. And that's because a lot happens between the pregame and the postgame. To get more direct measures of impact, let's instead look at which team has more gold 60 seconds into the game. Gold at 60 seconds is the most direct and valuable measurement for us because it also factors in the first two waves of creeps without factoring in the whole laning phase. Thus, we can tell if heroes are able to make it to their own lanes in time, if they have an advantage in those lanes. Not only did they get the bounty runes or kills, plus it gives us time for both teams to spend consumable items to regen health and mana after any initial fight. And those consumed items will be removed from their net worth.

[00:05:19]Now that we understand the method, before we talk about what does work, let's talk about what really doesn't work. A staggering 91% of games have at least one inactive player who just refuses to participate in the pregame strategy. I've labeled these null heroes because they have no observable opening strat. At 10 seconds to game start, they are away from all quantifiable objectives. These players like to hang out by a tower waiting to block creeps, or they might be placing wards in the side lane in preparation for the laning phase, or sometimes they're just AFK and Fountain because they ran off to take a [ __ ] before the game starts. In total, 73% of teams are impacted by a player like this. In fact, nearly 50% of teams have a player fully AFK in the fountain for 30 seconds or more at the start of each game with no movement whatsoever.

[00:06:12]Being completely AFK and just being a player who's not positioned near a rune are essentially the exact same thing when it comes to game outcomes. In fact, it's better to have a player who was AFK for 30 or more seconds at the beginning of the game just sitting in the fountain as long as they make it out to a bounty rune before the negative 10 second mark.

[00:06:36]Now, I'm positive that some of these players believe they're doing a huge big brain strat that blocking their creep wave or putting up just the right ward is the golden snitch of winning their laning phase. But the reality is I could find absolutely no positive relationship between any type of null positioning and game outcome. For each null hero, a team loses an average of about 140 net worth by 60 seconds into the game. There's also a 1.5% win expectancy loss per player, and these have huge zcores, meaning the correlation is beyond any doubt. In other words, by doing something other than going to a bounty rune, you cost your team the benefit of a bounty rune. That win expectancy shift is again probably not directly causal.

[00:07:28]But the net worth advantage is almost certainly causal, meaning that focusing on your own lane or your own vision before the horn is a bad overall strategy. Even for safe lane carries, even for mids, your team's outcomes are literally better if you invade the enemy jungle completely alone than they will be if you are away from objectives at the horn. Here's the expected gold gain from invading alone given your teammate strategies, where the red dot is the expected value for null heroes. four teammates. Contest means that they are at the river runes and hold means they are somewhere in their jungle, either high on the river high ground or near their defensive rune. The only situation where invading isn't noticeably better than being null is if four of your teammates are also invading. That's because four heroes is usually enough to get all of the value out of an invade and a fifth hero doesn't necessarily add much. Let's imagine you have one of these idiots on your team, as you probably often do. you're still better off invading with the remaining players who are active. The worst thing you can do is position yourself defensively around your own jungle. That sounds a little counterintuitive. You might be tempted to think that if you have fewer active players, playing conservatively is the stronger strategy, but in the pregame it isn't. If you defend with fewer active players, there's two real outcomes. First, maybe your opponents are not going to invade you. You grab runes that otherwise would have gone to your team anyway as you walk to your safe lane. So you have no real net gain over the alternative strategy in this case. Second, maybe your opponents do invade you, in which case the safe place to be is actually in their jungle where they aren't. And they'll get your runes, you'll get their runes, and you'll trade basically even. Here's an example game.

[00:09:20]This is a divine three ranked Slark playing with two AFK allies and two allies waiting to block creeps instead of participating in the pregame. This is normally a terrible situation because it basically guarantees that if the other team invades, they will get three or more runes. But Slark, as the only active player on his team, weaves into the enemy jungle and scouts. Seeing no immediate danger, he contests the Radiant Deep rune. His opponents have no idea how much backup he has and they back off. That leaves him to claim the Watcher and the offside river rune as well. Plus, nobody from Radiant actually invaded his jungle. So, his team is able to pick up their own jungle rune on the way to lane. Despite having four non-participating heroes in the pregame, Dyer ends up with a giant 694 gold lead at 60 seconds. Even if he died here while grabbing this rune, he still would have traded basically even. But that only happens in 9.7% of games where there is a solo invader. And him dying here does imply that Radiant has more heroes in this area, which might mean that his team is able to grab an additional river rune up on their safe side. So the worst case scenario here is basically breaking even. And the best case scenario is a huge advantage.

[00:10:40]Invading alone doesn't mean running blindly. It means scout and if it isn't safe, back off. So, out of all likely outcomes from playing down one or more players in the pregame, you are better off invading the opponent's jungle, even if you're playing completely alone and all four of your teammates are sitting in the fountain. This is where I briefly interrupt to say that liking this video, it's nothing to you. It's free. you you could have done it already, but to me it's an incredibly powerful signal that helps grow my channel and it gives me personal validation, which is super important for hobby channels like this.

[00:11:17]It's awkward for me to stop and ask for that help, but I do it because it is important. Please consider liking and subscribing. You can also help ensure that I'm able to do analysis projects of this size by supporting me on Patreon for as little as 75 cents a week. Link in the description.

[00:11:34]We will know if our teammates are AFK, but we can't know what our opponents are doing. For the rest of this analysis, I'm going to remove any games with null players to make sure all strategy comparisons are fair. If you end up playing against an opponent with null players, then your expected results will be even better. But you shouldn't plan around AFK opponents. Taking those games out leaves us with 14,188 fair games with all 10 active players.

[00:12:02]If we want to know what a good strategy is, we can start with a simple experiment. We'll make a payoff matrix between two all-encompassing strategies.

[00:12:10]Strategy one, the majority of players on the team invade the enemy side of the river. And strategy two, the majority of players on the team are positioned defensively. The map on the right will show a real world example of hero positions in the highlighted box. In this payoff matrix, each cell is Radiant's average gold advantage for each combination of Dyer and Radiant strategies. Dyer wants the most negative value, while Radiant wants the most positive value. It's pretty clear that Radiant is always better off with the top row, and for Dyer, the left column is always better. That means both teams are always better off with the majority invade strategy. This is an overly simplistic view of strategy, though.

[00:12:55]Obviously, there's a lot of ways to not invade your opponent, and some are going to be better than others. Let's expand this out to group more distinct game states. Here, we'll add conditions for if the majority of players are positioned toward the safe side of the river rune or the offside river rune or evenly split between the river runes.

[00:13:15]Defend here means in their jungle, closest to their safest rune, and invade means crossing the river. that encapsulates almost every meaningful strategy across the 14,188 games. For Radiant, invade is still completely dominant, always the best choice or tied for the best choice. For Dyer, invading into a majority defense is good, but a little worse than majority safe side river into that defense. Though the confidence intervals for those two options do overlap, meaning it is possible this is just a sampling error. In either case, the overall expected return for both teams on an invade is much better. Because Radiant has a dominant invade strategy, it means Dyer should also always invade.

[00:14:02]But strategies are not necessarily defined by where the majority of players go. So, let's expand. Again, I'm going to apologize because the table starts to get pretty small here. Most strategies used involve some form of stacking up and splitting heroes across the river runes. This is all the common strategies teams have used. Again, most of the time these are variations of sitting the majority of heroes either on the river or on your defensive high ground near the river. Definitions are in the bottom right. To save time, I'm not going to read them all. This accounts for a pretty detailed look of the wide majority of all strategies used by pub players. And even now, if we exclude the grayed out very rare openings as statistical noise, Radian is always better off with majority invade strategy. Dyer splits up a little less cleanly, and there are three cells where the full invade did not perform better, but it's still their best overall strategy. And finally, let's split up and look at every common combination, including how many heroes are invading and strategies involving 4:1 splits with single uncoordinated players around the map. The grid is starting to get pretty big, and what that means is we're seeing a lot more noise in some of the cells, mostly because there's just a ton of strategies that almost never pair off against each other. However, even with this clutter, invadebased strategies are still dominant. And you can see that Radiant is always best off doing a five-man invade, unless their opponents have a sole hero Ramboing around the map somewhere, in which case, Radiant is better off doing a three or fourman invade and holding the remaining hero or two back at the river to make sure that they can contest to runes. Dyer has a very similar layout. Now, we're hitting up against one of the limitations of this kind of buildup analysis. We're breaking invade success across so many statistically insignificant combinations that there are few cases where it just looks like it's worse than an alternative. For example, a dire invade against a radiant four on a river rune with one in the safe jungle. This is an artifact of sample sizes. It's essentially gerrymandering. What we've done is shove lots of the most successful invade outcomes into statistically insignificant cells, and that makes the remaining invade cells look weaker than they actually are. But even with this as the case, the most consistent overall strategy is still an invade. Of course, there is another possible explanation for why invades do so well, and that is because invading teams might just be better at working together. It might be a measurement of teamwork and not the power of the early game invade strategy. But if we only measure strategies where all five heroes are working together, we see that invade is almost always optimal for both teams.

[00:16:56]The only exception is if Dyer invades with five and Radiant defends with five.

[00:17:00]But the difference there is pretty marginal and is probably due to noise.

[00:17:05]So even if we control where both teams are working together as a pack of five, you can't meaningfully improve your outcome by doing anything other than invade. And just to be sure, we can also do a measurement to see if this is an artifact of how well coordinated a team is. Teams that communicate together, especially those in party or on microphone, have a much higher coordination than those blindly clumping together. By measuring the impact of this coordination, we can see if the invade advantage is simply because invading teams are better at working together. So, let's measure each team's compactness or how tightly together they stand and how coordinated they are or whether they are generally moving toward the same location at the same time. What we find is that invading teams are on average more tightly packed, which is what you would expect because the strategy necessitates it. Most other strategies involve spreading out either to contest multiple runes or to defend multiple high ground invasion points.

[00:18:05]But invaders are not more in sync. In fact, they're slightly less in sync overall. If the invade advantage were simply based on heavily coordinated teams doing better, then the invade strategy would not outperform other strategies. We can calculate the value of coordination and compactness by making OS regressions. This is a simple tool that finds the best straight line fit through data and then we use those lines to tell us the expected value of coordination or compactness for invaders versus non-invaders. In other words, this tells us the baseline value of having a synchronized team. For invading teams, being compact and coordinated contributes about 11% of the strategic advantage. But that means the positional advantage of invading is bringing 89% of the value. At least for invaders, coordination provides less value than compactness. This graph is showing how much better invade is than alternative strategies given the same level of compactness or synchronicity. The lead attributed to the act of invading does drop as coordination goes up, meaning well-coordinated teams do better in basically any strategy they choose.

[00:19:16]However, even in highly synchronized and compact teams, invaders do much better than those with other strategies. This shows the invade advantage is not just due to better teamwork. If we remove the value of teamwork from each invade, it has basically no average impact on the invade itself. The act of stepping into your opponent's territory is still extremely valuable.

[00:19:42]We could also look for dominant strategy through a thing called elimination of strictly dominated strategies. In this process, we start with every unique strategy possible. Every single thing we've observed, which is a huge grid of 341x 341 opening positions. This makes a distinction between the number of heroes closest to each rune, the number closest to the midtower, and which heroes are across the river. So, a team might be 050i, which means that five heroes are at the off lane rune, but they have not crossed the river yet. Or it could be 05i3, which means five heroes are at the offlane river rune, but three of them have crossed the river. Breaking up all of these categories gives us very small sample sizes. All of the dark patches are cells with no meaningful data. Let's merge similar strategies together until everything has at least 100 plays. So that might mean saying four off lane, one safe lane with two invaders is basically the same thing as four off lane, one safe lane with one invader.

[00:20:50]And we combine those. No combining a majority invade strategy with a non-majority invade strategy. And any meaningful results from strategies must be similar. We're not going to merge a strategy that wins 90% of the time with ones that win 10% of the time. All right, let's break this down until we have a grid where every row and column has at least one meaningful cell. Next, we can start eliminating strategies that are always negative or just break even.

[00:21:16]Even if your opponents were foolish enough to play one of these strategies, anything you do is favorable for you.

[00:21:22]That means they shouldn't pick it and you shouldn't try to counterpick it.

[00:21:26]We'll also take out dominated strategies. This is any strategy that is worse than a single other strategy in every remaining case. And finally, let's get rid of weekly dominated strategies.

[00:21:37]Those are strategies that are dominated only in cells where they have a favorable outcome. And we loop this process, continuing to remove strategies that are weak or dominated in the remaining game state. And that boils us down to this 2x two grid. Radiant should never pick the bottom option because it is overshadowed by the top option. Which means Radiant has only one rational option and you'll never guess what it is. It is play at one offlane river rune four push into the Dire jungle. And Dyier's best remaining response is the identical play. As a quick programming note, a group of heroes is defined together. So if you have five heroes all considered in one group, then all five will be considered invading, even if not all of them have crossed the river yet, which is what you're seeing in some of these samples.

[00:22:28]This is more honest because we can capture games with clear intent to invade, even if they aren't that wellcoordinated.

[00:22:35]These strategies are optimal over every other option according to this breakdown. There's no other option that remains viable against the field. This final grid or in this case this final cell is what we call a rationalizable strategy. This process of iterated elimination does not guarantee the only rationalizable strategy grid because the order that strategies are removed does matter. To ensure that we have a reasonable understanding, let's do the same thing about a thousand times, reducing the grid as much as we can by taking out failing options or merging similar neighbors. And what we find out is over half of these collapses, the grid reduces to a one by one set of choices. Far fewer than 6% have more than four choices available for each team. And of those rationalizable arrays, both sides have majority invade options remaining about 55% of the time with about 85% of games where at least one side has majority invade heavy options. In other words, basically all the time any non-invade option is only positive in one very unlikely scenario playing against a lowplay strategy. If we were a little less strict on how we eliminate, we would collapse down to all invade strategies really quickly.

[00:23:57]Interestingly, Radiant is even more motivated to invade than Dire. And for both teams, the single most common one by one equilibrium is this fiveman invade with one at the offside river rune and four pushing into the opponent jungle. This is consistent with the equilibrium we found when we built up from simple strategies, which means we can be pretty confident saying that in any normal circumstances, this strategy has the highest expected return for both radiant and dire. This is indistinguishable from a variety of similar strategies where one or two heroes go to the offline river rune and three or four heroes push into the enemy's jungle rune. I have a smart audience and I'm pretty sure there are already a few comments in the works about how I've missed something obvious.

[00:24:45]Teams with strong level one heroes may choose to invade because of that advantage. If that were true, invade strategies would look better because the heroes used to invade are better. To test for this, we'll train a statistical model to rank the chances that a team will invade using just the draft. If the model can predict the invade, it means players are invading conditionally based on their draft strength. However, what we find is that the draft has basically no impact on a team's decision to invade or not, at least in pub games. This is true at every skill level. The model is almost randomly guessing, so there's no clear pattern for which heroes are used to invade and which aren't. just to be sure we can use that model's fairly mediocre predictions to look at what happens as a team becomes more likely to invade. If invade advantage were draft dependent, we would expect to see this climb from lower returns on the left to higher returns on the right, but it's pretty much flat. That means invading is similarly strong regardless of which heroes are used. I also realized partway through this process that we already have the tools needed to score each individual hero based on their advantage in the pregame. We can make a linear regression to predict each hero's value to the team and then subtract this value out of each invade. In other words, we're normalizing every game by the expected value of its draft. If invade mostly does well due to being performed with really strong heroes, we will see the expected advantage of invade disappear or it could even go negative.

[00:26:23]But what actually happens is nothing.

[00:26:27]The invade strength basically does not change. So in summary, this is a fairly definitive proof that players are not broadly choosing invade based on their draft, at least not in any sensible pattern. It also means that invade strategies bring more value because the strategy itself is stronger, not because the heroes used to invade are better.

[00:26:51]Just for fun, here's a wall showing every hero's expected contribution to their team's advantage in the first 60 seconds of the game. The top five heroes all make sense to me. You have Lone Druid and Viper. Great level one damage output and last hitting in the first two waves of creeps. Bounty Hunter and Alchemist, both of whom generate extra gold due to abilities, and well, Pudge, the best pregame hero in Dota, but we'll come back to that. The worst five heroes mostly lack reliable stuns, slows, they don't have mobility, they don't really have damage before getting at least a few levels. These heroes don't contribute a ton to prehorn team fights.

[00:27:30]They can't zone opponents at level one, and they also struggle with lane pressures in the first couple of levels.

[00:27:37]In fact, Ancient Apparition and Enchantress both give up first blood in about one in six of their games. So, the only hero here who surprises me is Templar Assassin. TA players, let me know in the comments what about this hero makes her one of the least valuable contributors to the pregame.

[00:27:55]We can also take a look and see which heroes are good invade heroes. Like which heroes do better when they are invading. It turns out there is no such thing as a bad invade hero. Every single hero has better outcomes when invading.

[00:28:10]In fact, most heroes are break even or negative in impact for any option except invading where every hero is substantially positive. And for full team strategies, invading with three or more heroes leads to the best outcomes for all but four heroes. Doom, Dark Seir, Nyx Assassin, and Abden. And even for those heroes, invade is great. In many cases, it's statistically tied with some second option. So, we should envision these as four flexible heroes, not four no invade heroes.

[00:28:43]There is only one hero who has a positive pregame expectation no matter what strategy he does, and that is Pudge. For Pudge, invading is the least commonly chosen strategy, even though it is about three times more effective than other options. But he is also clearly the most flexible and most powerful pregame hero.

[00:29:09]Before we go any deeper, I really need to re-emphasize that what we're talking about here is a statistical edge, not an outcome guarantee. Invading won't suddenly mean that you win your lanes, and it won't even suddenly mean that you have better prehorn outcomes. That will all depend on how you play. When we look at basic openings, we see all options have the same basic distribution, a normal curve with a typical outcome range spread across about 430 to 450 advantage range at 60 seconds. But what invade has going for it is that the average is shifted very positively. The average for all the non-invade strategies is break even or negative.

[00:29:50]That means more of the range of likely outcomes for invade strategies are at least break even and a higher percentage of games played with those strategies will end up favorable at 60 seconds. A stunning 50% of all games with majority invade team strategies end up with a sizable lead at 60 seconds. That's more than double the chances of having a sizable deficit. That does not mean that I am telling you the main factor in success is whether or not you invade.

[00:30:18]The main factor in success is whether or not you execute whatever strategy you're using. Invading provides a real and fairly notable expected advantage of 160 gold, but that advantage can be much higher, as high as 1,000 or 1,500 gold when executed well. The key there is in the execution. Opening strategies only explain about 6% of the difference between first minute outcomes from game to game. 92% is unexplained by any of the factors we looked at. That's all execution and luck. But if you are making a decision about where you should go, you should always follow the optimal position. In this case, that means invading and contesting runes from your opponent's side of the map. On a playerbyplayer basis, the huge difference is between invading and not invading, not which rune you choose to contest once you invade. But if you are a farming carry, for example, you should not go sit in your own jungle, that is the lowest impact position you can stake out. I understand that it is easier for you to get to the first wave of creeps from there, and that makes it easy, but the overall results are much better if you invade with your team, split up for runes after looking for kills, and then return to the lane, either with a TP or through the gate portal.

[00:31:39]With the same skill, luck, and teamwork, your outcomes will be better if you invade, at least over the long run.

[00:31:46]Let's talk about skill. Just because a strategy is good does not necessarily mean good players use it more. But it does usually work out that way. If you watch good players and imitate them, you will generally find what they are doing is closer to the optimal strategy. Those of you who made it this far in the video and are still paying attention, didn't just leave me on to go do the dishes, you'll be unsurprised to find out that as players get better, invade strategies become more common. That's up until about legend rank, after which there's no statistical difference between ranks.

[00:32:22]But invade strategies are overall less effective at higher ranks. This doesn't mean what you might at first think it means. The reason you see a dip in value as rank goes up is because more teams use invade at higher ranks. Invade is still the best response to invade, but we already saw it is basically a statistical tie when two teams both use the invade strategy. If two teams both invade, they should generally trade even. And what that means is as more teams invade, the value of the invade strategy appears to go down. But it is still the optimal strategy. In a world where everybody always invades, you're just stuck with the close to zero early game advantage. Being stuck with a strategy and having no better option is quite literally the boring outcome of an equilibrium. Guardian players and ancient players both throw off the otherwise fairly linear downward value of invade strategies. I'm not entirely sure why Guardian makes sense to me.

[00:33:23]I've played with some Guardian players and they are lovely people who generally have no idea how to respond to even the slightest bit of surprise in a game. And for many Guardians, the idea of a fiveman coordinated assault in pregame time would be so foreign that it might as well be magic. But I am a little surprised by a similar bump at Ancient, a bracket I spent quite a long time playing in and I feel like I know pretty well. These are players who understand the game very well, generally have good instincts and reasonable ability to react to the unexpected. This bump at ancient very well could be statistical noise, but if you are a current ancient player and you have a different theory, please leave me a comment and let me know. Despite having fewer invades, Herold has by far the most early game contact. And that's probably because more players are wandering around the mid lane and the river runes very early.

[00:34:19]We've already removed games with obvious intentional feeders and AFK players. So, that's all I can really think of. If you're a Herold player and you know what this absolute insanity is about, please let me know in the comments. Once we get to more normal players buy around Crusader or Archon, there's a clear close to linear relationship between invading and pregame fights. Each skill bracket has about 3% more prehorn fighting than the prior bracket. And that's largely because of the increase in invade strategies. Hopefully by now I've convinced you that the only way to play Dota optimally is to get at least two of your teammates together and invade the enemy jungle every single game. And look, I'm playing the same pubs you are. I understand that that is harder than it sounds. But if you like, comment, and subscribe, it will increase the chances that your future teammate will have also seen this video. And who knows, that might help. Hey, this is me from the editing room. There's too much to say on this topic to fit into one reasonably sized video. I really have been trying. I've cut out tons of statistics, explanations on processes, and a whole section on game theory already, but we're only halfway through.

[00:35:31]Whoops, it happened again. So, I am once again going to have to split this topic into two videos. Next video, we'll talk about how to invade solo invades and why invading works so well. That means we're looking at blood grenades. We're looking at smoke of deceit. That means scoring different pathing options and checking out where opponents are most likely to be standing with more. And yes, I do realize this is also how I ended my last video, but then I made this instead. But this time, I already have all the data I need to make part two, so it should be just a couple weeks. If you made it this far, you can do me a huge favor by liking and subscribing. If you want to ensure these videos keep getting made, you can support me here on YouTube or over on Patreon for as little as 75 cents a week. Wow, so cheap. I'm also going to extol the virtues of these fine people who literally make it possible for me to take on these enormous projects. Fam of the cow tier supporters Dat Rose Sapphire von Jojo and Henry Elkington. Thank you friend of the cow tier supporters Adriel Moritz Debeir male B Svenge and anonymous Anna's hummingbird and St. Catfish plus all of the fan of the cow supporters you see going across your screen now. I also always put up a free blog on Patreon with these videos. They have additional data and more detailed graphics to make it easier to see some of the analysis stats.