The Perfect Bear Hunt Formation (Proven with Math)

Hey folks, have you ever wondered why formations in bear hunt are so confusing? Maybe you've seen a bunch of guides out there that absolutely swear that 10/10/80 or 1/1/98 or 10/30/60 or whatever combination is the best bear hunt. Or maybe you've even seen your alliance members swear that a particular formation works best for them. So then you excitedly go and try it out for yourself, and then you end up with worse results. How can this be? Or maybe you've just wondered more philosophically why, if the bear deals no damage to you and archers deal the most damage out of any troop type, you can't just always send 100% archers to maximize your score. Well, in today's theory crafting video, I hope to show you that bear hunt damage can be both predictable and optimizable. So, first, let me talk a little bit about how we can predict bear damage outcomes. You may remember in my other video about five lies that Kingshot developers tell about combat that these stats are completely made up. They're abstracted in such a way to present something to the player that's directionally accurate, but actually has a big implication on formations. Because despite what the attack and lethality stats actually read here, they always follow a predictable pattern between the troops of each tier. And for simplicity, I'll be talking about them combined as a total offensive factor since they get combined in the damage formula anyway. But basically, the combined offensive output for these two stats multiplied together is always going to equal one-third of the combined offensive output of the cavalry and one quarter of the combined offensive output of the archer. And again, this won't be reflected here in the numbers. I'm talking about the hidden numbers behind these that are actually used in the troop damage calculations for combat. Now, normally there are all sorts of percent chance based abilities firing between hero skills and troop abilities that are built in. Unless you use troops that do not have truegold bonus and are below tier six, where you have not yet learned the ones that have a percent chance to activate, then you only have the default static damage bonuses they come with. And if you were to lead a march or a rally with only blue heroes, such as Seth, you only ever have growth abilities and not combat abilities impacting your expedition damage output. So, what I'm going to show you on my farm account is that if you use those types of troops with blue heroes and you know exactly what your stat bonuses are going to be for the match, then there's actually nothing left up to chance for the battle outcome. Now, there is a small wrinkle in that you can't have a rally attack the bear without at least one other alliance member joining. So, what I'm going to do is add only a single joiner troop of infantry type which does not have any percent-based abilities that would deal damage to the bear or impact the damage of the main rally leader. And I'll just make sure I don't send it with any heroes and I kick out anyone else who tries to join. Now, I'm going to predict these outcomes independently from two separate sources. So, first I'll use Daryl's Kingshot simulator. And if you haven't used this tool, I would highly recommend it. I'll put a link to it in the description. But essentially, I'm going to predict the damage outcomes for a few different types of formations that I'm going to launch from my farm account. So, we'll start with an even split to baseline damage. Then, we'll use the same number of troops, but instead split in a 10/10/80 formation. We'll do a 1/1/98 formation and a 10/30/60 formation. And by now you might have noticed a bit of a limitation with this tool in that it requires you to input the formation and it will tell you the output score. But whereas there are many, many, many different combinations of formations you could put in, how do you know how to maximize your own damage? And this is where the bear formation tool for the Frakinator comes in handy. And I'm also going to link below to that in the description. In this case, the calculation flow works in the opposite fashion where I can put in the stats that I know I'll have and it will actually test all different formation combinations and give me a heat map of what will actually be the most viable formation for me to use in Bear Hunt. I know the chart can be a little bit confusing at first glance if you're not used to reading one of these, but it basically on each of the three axes gives you the percent of the formation that's made up by that troop type. And then you find the point of intersection and the corresponding color on the heat map tells you how close you are to an optimal damage amount. And in this case with the stats that I put in, my optimal amount should be a 3/28/69 formation. And to confirm, if I put this distribution of troops into the first simulator that I showed you, it actually gives me my highest score so far of all the combinations I've tried at 60,538. And using this heat map, we can find some predictions for other points that we're talking about using, such as the 10/10/80 formation. An even split of all three troop types will be just on this borderline here. So we'll call it something around 88 to 90%. A 1/1/98 formation would be just on the borderline of the 90% mark here. And a 10/30/60 split would be right on the bubble between these colors. So about 99% of the maximum damage I could do. So based off of these two calculators and using this distribution of stats and troops, I've put together a prediction logic for what the bear outcome should be. So I'll test the damage in game for each of them. We'll line it up against the battle simulation predictions as well as the Frakinator predictions. And I'll just say up front, I do expect these to be at least a few points off because of how the game handles rounding versus truncating under the hood. But we should definitely be close enough to make a conclusive prediction. So now all that's left to do is actually run the bear hunt itself. But in case you want additional proof, here is the Excel that I just showed you with the values blank. Bear hunt hasn't happened yet. And just so you can see, here's the time stamp. So I did it beforehand, not afterward. For the purposes of brevity of the video, I'll get rid of all the boring back and forth and just show the important screens if you want to take a look. [Music] All right. Well, that was a lot of fun, especially having to kick the same members from my rallies over and over again. Anyway, here you can see the timestamps of the five rallies that I ran today. So in order 1, 2, 3, 4, 5, and that corresponds to attacks 1 through 5 on this sheet. So now let's look at the results. And you can see after we've keyed those numbers in that the battle sim predictions were scarily accurate. And the Frakinator prediction also came in pretty close as far as I could observe through eyeballing the color codes on the chart. So I hope this dispels any notion for you that somehow bear hunt damage is not predictable or that we can't actually select an optimized formation in advance. And if you really want to get into the details of how the damage is actually calculated, that's all written up on that Frakinator website. So, this is all well and good for proving that we have predictive power in a nice, comfortable, controlled environment with only blue heroes and no RNG abilities. But what happens in the real world where all of these things are a factor? And what does that mean for you selecting your ideal bespoke formation to send for bear hunt? Well, let's talk about that. But first, a special thank you to my Sloth Squad channel members whose continued support helps make videos like this possible. And special thanks to the Play Smarter Community who've made a way for serious spenders to invest smarter and support my channel by leveraging your in-gam

swear that a particular formulation works best for them. So then you excitedly go and try it out for yourself and then you end up with worse results. How can this be? Or maybe you've just wondered more philosophically why if the bear deals no damage to you and archers deal the most damage

out of any troop type, you can't just always send 100% archers to maximize your score. Well, in today's theory crafting video, I hope to show you that bear hunt damage can be both predictable and optimizable. So, first, let me talk a little bit about how we can predict bear damage outcomes.

You may remember in my other video about five lies that Kingshot developers tell about combat that these stats are completely made up. They're abstracted in such a way to present something to the player that's directionally accurate, but actually has a big implication on formations.

Because despite what the attack and lethality stats actually read here, they always follow a predictable pattern between the troops of each tier. And for simplicity, I'll be talking about them combined as a total offensive factor since they get combined in the

damage formula anyway. But basically, the combined offensive output for these two stats multiplied together is always going to equal one-third of the combined offensive output of the cavalry and one quarter of the combined offensive output of the archer. And again, this won't be reflected here

in the numbers. I'm talking about the hidden numbers behind these that are actually used in the troop damage calculations for combat. Now, normally there are all sorts of percent chance based abilities firing between hero skills and troop abilities that are built in. Unless you

use troops that do not have truegold bonus and are below tier six, where you have not yet learned the ones that have a percent chance to activate, then you only have the default static damage bonuses they come with. And if you were to lead a march or a rally with only blue heroes, such as Seth,

you only ever have growth abilities and not combat abilities impacting your expedition damage output.

So, what I'm going to show you on my farm account is that if you use those types of troops with blue heroes and you know exactly what your stat bonuses are going to be for the match, then there's actually nothing left up to chance for the battle outcome. Now,

there is a small wrinkle in that you can't have a rally attack the bear without at least one other alliance member joining. So, what I'm going to do is add only a single joiner troop of infantry type which does not have any percent-based abilities that would deal damage to the bear or impact the

damage of the main rally leader. And I'll just make sure I don't send it with any heroes and I kick out anyone else who tries to join. Now, I'm going to predict these outcomes independently from two separate sources. So, first I'll use Daryl's Kingshot simulator. And if you haven't used this

tool, I would highly recommend it. I'll put a link to it in the description. But essentially, I'm going to predict the damage outcomes for a few different types of formations that I'm going to launch from my farm account. So, we'll start with an even split to baseline damage. Then,

we'll use the same number of troops, but instead split in a 10/10/80 formation. We'll do a 1/1/98 formation and a 10/30/60 formation. And by now you might have noticed a bit of a limitation with this tool in that it requires you to input the formation and it will tell you the output score.

But whereas there are many, many, many different combinations of formations you could put in, how do you know how to maximize your own damage? And this is where the bear formation tool for the Frakinator comes in handy. And I'm also going to link below to that in the description.

In this case, the calculation flow works in the opposite fashion where I can put in the stats that I know I'll have and it will actually test all different formation combinations and give me a heat map of what will actually be the most viable formation for me to use in Bear Hunt. I know

the chart can be a little bit confusing at first glance if you're not used to reading one of these, but it basically on each of the three axes gives you the percent of the formation that's made up by that troop type. And then you find the point of intersection and the corresponding color on

the heat map tells you how close you are to an optimal damage amount. And in this case with the stats that I put in, my optimal amount should be a 3/28/69 formation. And to confirm, if I put this distribution of troops into the first simulator that I showed you,

it actually gives me my highest score so far of all the combinations I've tried at 60,538. And using this heat map, we can find some predictions for other points that we're talking about using, such as the 10/10/80 formation. An even split of all three troop types will be just on this border

line here. So we'll call it something around 88 to 90%. A 1/1/98 formation would be just on the borderline of the 90% mark here. And a 10/30/60 split would be right on the bubble between these colors. So about 99% of the maximum damage I could do. So based off of these two calculators

and using this distribution of stats and troops, I've put together a prediction logic for what the bear outcome should be. So I'll test the damage in game for each of them. We'll line it up against the battle simulation predictions as well as the Frakinator predictions. And I'll

just say up front, I do expect these to be at least a few points off because of how the game handles rounding versus truncating under the hood. But we should definitely be close enough to make a conclusive prediction. So now all that's left to do is actually run the bear hunt itself. But

in case you want additional proof, here is the Excel that I just showed you with the values blank. Bear hunt hasn't happened yet. And just so you can see, here's the time stamp. So I did it beforehand, not afterward. For the purposes of brevity of the video, I'll get rid of all

the boring back and forth and just show the important screens if you want to take a look.

[Music] All right. Well, that was a lot of fun, especially having to kick the same members from my rallies over and over again. Anyway, here you can see the timestamps of the five rallies that I ran today. So in order 1, 2, 3, 4, 5, and that corresponds to attacks 1 through 5 on this

sheet. So now let's look at the results. And you can see after we've keyed those numbers in that the battle sim predictions were scarily accurate. And the Frakinator prediction also came in pretty close as far as I could observe through eyeballing the color codes on the chart. So I hope

this dispels any notion for you that somehow bear hunt damage is not predictable or that we can't actually select an optimized formation in advance. And if you really want to get into the details of how the damage is actually calculated, that's all written up on that Frakinator website. So,

this is all well and good for proving that we have predictive power in a nice, comfortable, controlled environment with only blue heroes and no RNG abilities. But what happens in the real world where all of these things are a factor? And what does that mean for you selecting

your ideal bespoke formation to send for bear hunt? Well, let's talk about that. But first, a special thank you to my Sloth Squad channel members whose continued support helps make videos like this possible. And special thanks to the Play Smarter Community who've made a way for

serious spenders to invest smarter and support my channel by leveraging your in-game spend when checking out with creator code "sloth". If you want a trustworthy concierge-like approach to buying packs at a discount that follows you from game to game and treats you like a VIP,

then check out the link below in the description for details. So before we go down the road of abilities further, let's limit the scope of the problem. Yes, abilities that are going to increase attack or lethality by a certain percentage or even straight up damage increasing ones aren't

as big of a deal as you might think because the damage formula is multiplicative of all of these factors and because they impact all troop types equally. Yes, they will definitely impact the total amount of damage being dealt to the bear. But in terms of simply selecting the ideal

proportion of troops to send for your formation, the effect actually cancels out. In fact, the only abilities you have to be mindful of are those that will affect a specific troops ability to deal damage. So archers that have already hit T7 or specific true gold levels, as well as some

cavalry true gold levels will impact the ideal fraction of troops you should send. And hero abilities from generation 4 onward that affect troops disproportionately also will change that.

Well, fortunately with testing, once we've properly captured these abilities in the code, this can actually all be reduced to an expected value. And at least as far as troop abilities are concerned, we've already captured the main break points for archer and cavalry abilities. And if I

apply this to the real battle stats from my main account, you can actually see that the resulting graph isn't really that different when you account for these troop abilities. So, even though we haven't coded in the hero abilities from the Gen 4 or Gen 5 heroes yet, you can still consider this

to be pretty directionally accurate. This is also true, especially when you consider the spread of the heat map. So, even though this is the ideal point, anything within this swath over here is still going to get you within 90% of the total damage output. What's actually most important is

that you don't go too far to the edges and send no troops of a particular type. I mentioned this in the troop count portion of that battle myths video, but there's a multiplier in there that's the square root of the minimum number of troops on each side of the battle. And for whatever reason,

we've been able to back into some sort of validation that bear has 5,000 infantry troops, which means if you're sending troops that are below 5,000 of a particular troop type, there's potential for those to scale linearly as you add more of that troop type. Well,

anything over 5,000 troops is going to suffer from diminishing returns due to the way that square root function works. So, this explains the reason why we've observed that if you send no troops of a particular type, you start to see a drop off in the total damage output. So, overall,

if you want to make the most of your bear hunt, I recommend coming here, plugging in your troop stats, and seeing what your own rally should look like, and then possibly doing it with the stats of one or two of the big whales in your alliance to help you set some ideal formations to send

to their marches. And as long as they don't have any unusual stat investments, you'll probably see that 90% of the damage is going to come just from getting something roughly in this spot, no matter who you're sending it to. So feel free to min-max this as much as you would like. But

remember, formations are only one aspect of the bear hunt you have to get right. To see the rest of the pieces of the puzzle you need to get right to maximize your score, check out my guide to bear

hunt, also linked below in the description. Thanks again for watching and happy gaming out there!