Thanks so much! I learned from none other than the best: @Flexoo, who perfected this art far earlier than I did. As for the algorithm, it's a (tree) recursive algorithm in Python. Recursion is a concept that is usually introduced with introductory programming courses but is quite hard to grasp the first time (as experienced in the intro programming course - many, including me, still treat this as a class that teaches a language instead of concepts). The idea behind a recursive algorithm like this is the following: Perform an action on the current level. (i.e. writing out bullet points to describe a topic in mind) Run the algorithm on the sub-structure. (i.e. analyzing each bullet as if it were a topic, repeating the above step) Stop the algorithm given a certain condition, or base case. (i.e. when a topic's description is sufficiently descriptive) That's probably enough as a high-level description, and it just barely scratches the surface of the world of programming. If you want to learn more and begin to think more like a programmer, I would highly recommend taking a look at the course I took this year; you can find the current website here (append sp22 as a subdomain if you want to see the previous semester's slides).

Unsolicited Advice: Crafting Top-tier Articles with Outlines Hey all! I haven’t been writing for a while, but rest assured - I still know how to write (hopefully). Just recently, I was hovering around the forum and went to an idea rabbit hole of giving unsolicited advice, and from there, the idea of writing about outlines was born. As a young and inexperienced writer, I once wrote an editorial claiming that the main points to gain popularity as a writer were title, format, and images. Poor past me - I had it all backwards. While those points boost article appearance and make it more reader friendly, it’s not the main reason an article would gain traction. The true reason some works of writing rose to the top and not others was all in the way it was created and the flow. Leaps of logic and confusing side tangents confuse readers; clear points of reasoning and logical, smooth flow makes something a breeze to read. And the fastest and easiest way to write a piece to check all of these boxes is with none other than a simple outline. The Birth of an Outline Enjoyer Here’s some backstory: I definitely wasn’t and still am not the best writer, but I’ve built up some respectable work over time. My beginnings were quite terrible - I remember one of the first essays I wrote as a grade schooler earned me a C. Showing the paper to my parents was truly an embarrassment. My dad screamed at me for my poor writing and then proceeded to tear apart my work. As a young and restless student, I was quite bad at writing - I had a short attention span and jumped from idea to idea, and so the essay was truly incomprehensible and unacceptable. That’s when I was taught the idea of main ideas and a thesis - a sentence summarizing the purpose of the work. I was confused at the time, but I just followed along out of fear, writing and re-writing until it passed my dad’s inspections and earned me a solid A-, barely passable in the eyes of parents who expected straight As. And as expected, my parents weren’t satisfied - I created one good paper, but it was evident that I continued to struggle as a writer. That’s when writing class came in and I was introduced to an outline. Definition 1.1: Outline A bulleted list of ideas used for your paper, I think. Being introduced to a concept to construct work and the idea of forcing yourself to write outlines and continuous drafts definitely helped shape my work up from “completely unacceptable” to “somewhat passable, just because you write too much and no one wants to read that”, but at that point, I just didn’t understand what an outline was for. I’d write an outline and proceed to write a paper without even thinking of the outline I had written moments ago, going back to my old ways. This continued on for years - I just struggled as a writer, barely earning passing marks in papers (side note: many of my classes often curved their paper grades up to mid/low 80 marks as long as you wrote for the correct prompt, hence why an 85 is ‘barely passing’ instead of ‘decent work’) and writing to little success as an AWS writer, taking months to craft something somewhat usable. And then it hit me. In my last year of formal high school education, I got a bad case of Tanki-influenced senioritis - I just didn’t have the motivation to do classwork since I was so hyper-focused on improving things in my Tanki helper position. It didn’t help that I had an English teacher who made us write tons of papers and writing prompts. As an indifferent student, I often begged for extensions and speedran papers in the mere hours before deadlines, writing up a bare-bones outline and filling it out with fluff words to make the word count. Surprisingly, instead of being greeted with poor grades, my teachers loved my work, which was a pleasant change for once. At first, I wasn’t sure if it was just my classmates’ senioritis dragging them down to the position of middle school writers or if I had actually improved, but as I began to write some more papers and prompts, I realized while the grade curve certainly was easier, my writing had also become much more coherent and organized - I could write much more complex and work far better and faster than I did back in my early AWS days (though my word choice and writing execution are still awful, but that’s not something I can easily solve). Now, I’ve reached a point where outlining and quickly writing something up is second nature, and it’s just one simple process. Here’s how it all works. Outlining: An Art and an Algorithm I’m completely kidding about the art part - fortunately, outlining is analytical and algorithmic; I just wanted to put that in since all my professors keep calling all the math we do “an art”. In fact, you can think of outlining as a computer algorithm; something like this: Well, now that I threw these lines of code at you, it’s time to explain what they mean. The first thing is turning your paper idea into an outline, or what I defined as “write_outline”. It’s a pretty simple idea that fits nicely into a recursive algorithm: Step 1: List out main points - things like an introduction, background story, big ideas, comparisons, and conclusions, to name a few. These will serve as the main “paragraphs” or “sections” of your work. Step 2: Within each main point, there will probably be additional points you want to cover. Under each of these main points, add some more bullet points covering your additional topics. Step 3: This continues again - within your additional points, you can scour out more points, and so on. Keep outlining additional points as needed, indenting and writing little fragments and ideas. It’s a good point to stop indenting and bullet pointing when your bullet point indentation reaches more than half the page you get into too much detail or if your bullet points start looking like paragraphs and sentences rather than short ideas. Likewise, writing out your paper from an outline is also a recursive algorithm - you reverse the process of creating bullet points from a topic and turn them into full sentences. Whereas you started with the big ideas from a topic, you now start with the small details and write your way up: Step 1: Go through your smallest subpoints and construct them into coherent sentences. Step 2: Go back to the next point that surrounds the subpoint and join the subpoints into one sentence. Step 3: Again, we repeat - creating coherent bits from subpoints until we have a full body paragraph or large topic, and before you know it, the paper has written itself. This algorithmic approach allows me to really buckle down when I lack the ability to write something or am in a time crunch - it simplifies writing into just following short steps by building an outline, then unraveling it and adding fluff to create your work. By implementing this technique, the changes were like night and day - whereas before, it took long hours (days, even months) of toiling away to write something coherent, it was now effortless. In fact, the other day, I crafted up a short 5-paragraph essay in just a few minutes. The time saved leaves plenty of space to spruce things up and format it to your heart’s desire. Hypocrite PR, what about format? And yes, while outline creates solid structure and flow, you can’t forget about format. Format first is still backwards - it’s like believing that fancy footwear is the main way of making you faster versus training - but it’s also a factor to consider. A nice way to think of outlines and format is like function and form. Outlines provide the main function of the article, making your work readable and actually usable instead of a page of fluff that no one will ever be able to decipher. On the other hand, format is the form, something that shapes the article into something presentable and easily digestible. With that in mind, let’s revisit my three main claims of title, genre, and images with the outline model in mind. Title: A nice title is like a hook for your work and definitely something that needs to be at least usable and marketable. By defining your main points, a title is easy to generate. Genre: I don’t agree with my old points anymore; a few tips and tricks for genre here and there work, but all in all, it comes down to outlining and planning things. With that in mind, here are some sample structures to constructing hot guides, reviews, and interviews. Images/Media: Still relevant, if not more so. Images can complement your work and provide fast and insightful ways to consume information. Now, with an outline, you can add bullet points with a note to insert images and pinpoint the best places to add these bits of information to best fit your work. Having this planned ahead also reduces the unfortunate rookie PR mistake of adding images after every other paragraph. And that’s a wrap! I’m aware that I might’ve wasted your time gushing about outlines, something you already learned in grade school and implemented in your daily life. I’m just slow, alright? *sobs unimportantly* Or maybe I’ve also wasted your time by telling you about outlines as you don’t care in the slightest about writing. *sobs importantly* Anyways, regardless of your enjoyment or perceived usefulness out of your article, I hope you found something interesting and can apply it to your life. Thanks for reading, start writing (more) outlines, and catch you later! (if I hop on the forum ever again)

tragically unfortunately, i'm also part of the late train, and it makes me so sad to have missed out on this post. i've been doing things such as probability (lots of it, much to the dismay of neckbeards), getting covid, and being stared down by phd students (im a trash bag but yes) but one thing i do is that i always pay respects (hopefully) and be a nice person (depending on my focus state). Enough of my rambling; it's time to say what I really wanted to say. After all these years, I'm so glad to be blessed by so many writing legends who have taught me so much, and it hurts each time when they leave one by one, especially the ones that had such huge impacts and people I've actually been able to interact with. I just remember reading your stories as a young child at church (how scandalous breaking the rules) and feeling so inspired by the breath of fresh air, so much so that it made me want to get up and start writing again. Your writing has always been an inspiration and something I constantly look up to - I always feel like there's something I can learn from it, and it was great working with you as colleagues in the AWS and in various projects since. And as kaisdf mentioned, we were all anticipating the day that you would join us in the (arguably super cool and amazing) reporter team, but alas, things are not how they were. However, as the doors of reportership close, there are many more opportunities ahead in real life, and I know that your talent will bring you success there. I wish you nothing but the best in the next stage of your life. also rude man my typos are made with style don't diss them ?

Hey all! Made a quick app that tracks the Tanki Fund at intervals (excuse the first few messy ones as I haven't set up many features yet). Note that it does not update live but rather is intended to update every 15 minutes once I sort out the details. You can find it here.

Yes, This is possible by taking advantage of conditional probability. I have a simulator for that - simply input the number of turns you've taken, the max energy you can attain, and it should give you a final distribution. Anyways, some interesting facts: Starting at 0, P(C3) ~= 0.95 (almost certain) One Meteorite: If you hit the first meteorite and then get shot back 5, then P(C3 | M1) ~= 0.88 +/- 0.01 Two Meteorites: If you then hit the second meteorite and then get shot back 5 again, then P(C3 | M1, M2) ~= 0.71 +/- 0.01 Three Meteorites: If you hit all three of the first meteorites, then P(C3 | M1, M2, M3) ~= 0.48 +/- 0.01 (a bit of a critical point - this is where we hit under 50%) Four Meteorites: If you hit 4 meteorites, then P(C3 | M1, M2, M3) ~= 0.11 +/- 0.01 P(C3) - No conditions applied. P(C3 | M1) - Start with 600 energy, hit one meteor at 8, get sent back to 3: (chose a random set of integers ranging from 1 per move to 1.5 per move) P(C3 | M1, M2) - Start with 600 energy, go all ones, hit one meteor at 8, get sent back to 3, go up to 14, get sent back to 3: P(C3 | M1, M2, M3) - Start with 600 energy, hit all first 3 meteorites. P(C3 | M1, M2, M3) - Start with 600 energy, hit all first 4 meteorites. Note that this also means, getting pushed back -5 with each meteorite.

Yes. I just created something new on my local config that will calculate about how much additional energy you need to spend. As I don't know how much energy can be earned through buying, I'll just list raw energy values (on top of default of 600 energy).* Checkpoint 4: Checkpoint 5: *Note that the probabilities of reaching the goal may be very slightly off since I am using two different simulations - one calculates the final steps and the other one overflows to account for additional energy. I could fix that, but I'm kind of lazy. Bonus Note: you could just use the averages for Checkpoint 3, 4, 5 that I listed previously and subtract the energy you have to obtain the additional energy you need to spend. It might require a fair bit of mathematical maturity to make these connections though.

Yes. If you follow my simulation code, I have clearly stated the meteorite positions: Upon running one of the simulations with infinite energy up to the end of the game (with modifications to display current steps, etc.), we get the following output: In the output, each time you hit the meteorite, it is removed. As a result, in the later stages, where the meteorites are more spread out, the more common path trajectory is in a bit of a zigzag shape (i.e. the backwards moves are more frequent).

Yes. Suppose you missed some missions while out on holiday and only ended up with 2/3 of the energy, or only 400 instead of the total rounded possible 600 energy. Your total would come out to the following: This gives you a pretty certain chance of reaching Checkpoint 2 and a smaller but still plausible chance of reaching Checkpoint 3. By the way, you could just simulate the following yourself using the notebook I linked here. ? Simply just change the values (your maximum number of energy you can earn after this point, current step in the game, and goal) as desired: Then you just run this cell: and voila - you now have the end distribution that I was talking about! Even better, you can customize your current scenario to see how the game will work out for you. Happy tinkering!

The distribution of Checkpoint 3 mentions that the energy needed is between 400-600; the latter number is the upper bound for F2P energy requirements - meaning most people will get to Checkpoint 3. Since Checkpoint 2 is behind Checkpoint 3, this means that most all players who play enough will reach Checkpoint 2. (i.e. the probability of reaching Checkpoint 3 is nearly 1; as Checkpoint 2 is about half of the steps of Checkpoint 3 and has a smaller distribution of meteorites, you are pretty much guaranteed to hit Checkpoint 2 if you have the full potential energy as F2P. If you are interested, here are the statistics: Turns Distribution: Note that this is far below the full potential F2P energy soft limit of 600 energy. Distribution of end steps (starting at 600):

Hello all! I'm back with a probability simulation post. NOTE: the following were based on priors thanks to the wonderful @emrakul and may not guarantee correct results. If you would like, here they are: So the most viable method was simulation. Based on the priors from above, I created a function to essentially "play" the game multiple times. Here it is: From there, I made some simulations on how much energy you needed to reach the last three checkpoints, and here are the results: I've also created my own simulator that you can use. Simply input the amount of energy you have, your current steps, and your goal, and it will calculate your end steps and likelihood of reaching your goal. (You can use checkpoint[index] zero-indexed to reference the checkpoint you want to reach, i.e. to reach checkpoint 4, you can put GOAL = checkpoint[3]) An interesting simulation deals with the amount of energy a F2P player can possibly earn. For most F2P players, checkpoint 4 is nearly impossible to reach, so if you wanted Crisis and Armadillo, you had better make a wish to be part of that 0.2% to reach checkpoint 4 without spending a single dime. You can find the notebook simulation here.

The more time to TeX up my probability write-up about this game then ?

Two Three questions: 1. How many units of energy can be obtained through playing daily missions? 2. At which steps are the checkpoints located? (How many steps are required to reach each checkpoint?) 3. (edited) Can chain-reactions occur? Something like if you hit a meteorite and are sent back but then land on another meteorite, you are sent back again.

Words cannot express how much I'll miss you. Thank you for always being a reliable and humble helper and friend - always there to lend a helping hand on short notice or send me a reassuring message when I was blinded by my own limited perspective, not to mention being a fun and amiable person to chat with through the ups and downs. You were always there to help when I needed someone to check work or add a little extra contribution for the paper and you were always willing to learn from others and find something to improve and I have always been impressed by your attitude and outlook. I cannot express how grateful I am to have had the opportunity to work with you and learn from you. With your solid morals and values as well as the work ethic you have shown, I am sure you will see success wherever you go. Best of luck in real life!

Sounds like a good idea, especially if you post specifics. That would help find conditional probabilities, e.g. the probability of paints given an epic drop, or P[Paint|Epic Drop]. I'll make a form to submit results.

Well, by making a probability post, that's how. A tale of two expectations, Part III Now, we want to find how many expected supplies you will get and how many expected legendary augments you will get before and after the change. We can't do this perfectly, but we can do so with the following assumptions: Modeling the previous drops of legendary augments with current Ultra Container probabilities assuming the upper tier rewards are still about the same in terms of augment rewards. Scale the model accordingly for a F2P player playing without Premium over a 2-week challenge period. (e.g. compare current containers to old containers AND compare current # of containers you can earn to current # of containers you could earn) We then assume the player completes all missions for 2 weeks and completes the challenge completely without the battle pass. We also assume there are 2 ultra weekends, each offering 7 UCs and 5 regular containers. We also assume the mission rewards to be 3000 crystals and 15 of 3 types of supplies each day just for simplicity. Add in shard passive income and assume the player earns an additional 50 shards to generate 2 containers per day. Assume that all the rewards are according to my sheet - that is, all the rare rewards are unlocked so there are more chances of supplies. Assume the players don't rank up. It would make little difference. This yields the following: Pre-update: Player earns 14 UC and 24 Containers, 2 of which are shard containers and not to mention an additional 42000 crystals and 630 supplies for completing missions. Post-update: Player earns 14 UC and 25 Containers. Earning Supplies: To simulate earning supplies, we make the following assumptions: The prize pool for tiers with multiple prizes is a bag with all rewards listed. (e.g. for common tier for old containers, you would have 3500 crystals, 125 of each supply excluding repair kits/batteries/golds in a bag and you draw one if you get a common prize). I hope this makes sense. Group all supplies as one "general supply" for simplicity. Generalize the supply kits as 125 for old containers (there were kits with more but we can ignore those as they do not have a large impact) and 100 for new containers (there are kits with less but we can ignore those as they do not have a large impact). Now, let's simulate how many supplies you would expect to earn with each prize pool. You just simply look through the prize pool to see how many entries there are for supplies as opposed to other entries, get the proportion of those (listed in each Supply Share Column) and then multiply that with the overall probability to get the EV of supply kits per rarity group. Then once that's done, you add the EV of supply kits per rarity (as getting a common is independent of getting an epic, so the expected values can be added together) to get the end result, or the expected number of supply kits you get when opening a container. Then add any bonus supplies from challenges and weekly/daily missions, and the final values of supplies you earn throughout the week are obtained: Assuming you use about 25 supplies in a 15-minute battle and that a player plays about 70 battles a week (total of 140 battles) on average to complete all their missions (including Ultra Weekend and possibly arduous weekly missions). It's easy to see that you end up with a lot of supplies, and for players who play a lot, they will be constantly lacking supplies. Additionally, I also assumed that all supplies were the same under a pretense of a general supply to make it easier to calculate; however, in reality, often there are fewer repair kits and batteries, which are more crucial and more used, so players can often be in a shortage of supplies from there. Earning Augments: This one is a bit easier. You now have 39 chances (14 UC + 25 new containers) as opposed to 14 chances to get legendary augments. Now, let's see how many legendary augments you can expect to earn (assuming you have 35 augments to unlock out of 140 for even 25%): To get EV Augment, you multiply Augment Share by Chance (0.01 for regular, 0.02 for UC) and then multiply by number of containers through linearity. Then you sum them up as they are independent variables. This yields the following chances, which do show that your chances of getting a legendary augment is higher. However, you would expect to only earn 1 legendary augment after 1/0.1325 weeks, or about 7-8 weeks, as opposed to the old 1/0.07, which is about 14 weeks. Despite it being better, it doesn't really give you a great chance at getting a legendary augment, much less one that you'll want to use. Bottom Line: Earning supplies is going to be a lot harder, and players who lack crucial supplies like repair kits and batteries will be at a disadvantage. There is still consistent supplies income (from challenges and weekly containers) and players will need to be able to manage their supplies very well to stay afloat. You do have more chances to get legendary augments; however: The chances are still very low, so you will need to open a lot of containers to get your hands on one special augment. On top of that, you cannot select which augments you prefer - you could end up with something like rubberized rounds, which could be completely useless.

So after the V-LOG, I've just gotten the values for previous container valuation and current container valuation, and setting all other values equal, the value of a container was slashed by over 50%.* Do note that these are just my personal valuations (which may be different from yours); feel free to make a copy of the sheet or play around with the numbers here. Additionally, container rewards for missions seems to defeat the purpose - I feel like getting supplies and crystals was a bit better as the rewards were more practical, consistent, and scaled depending on rank. This is not practical nor consistent as rewards are just values listed on a roulette, and furthermore, they do not scale as ranking up does not mean you get more containers per mission or better chances. I feel like some sort of scaling like with weekly containers (or perhaps the previous method with shards) would definitely be a better option for mission rewards. *Yes, this might be a high number, but again it is my own number - it may be even higher or lower of a change depending on what you value.

Updated the sheet to support new vs. old container comparisons!

Hi all! I looked through the questions and comments about personal container valuation and how it's not the high value I put in as a placeholder and for the benefit of the doubt. To resolve this, I created a spreadsheet that allows you to input personal valuations to each (type of) item and how many you have to give you a custom valuation on how much your container is worth. To use this, simply go to the sheet and change the values for personal valuations in the Valuations column and update the (approximate) number of each item you have in the Quantity column. It will then calculate your expected value for you. There are valuations for the Ultra Container and regular Container. In the future, hopefully I can support a version of the old container vs current container if the stats are released for those. Check it out here! Notes: You might want to make a copy so that you can add extra items - e.g. if you really want a specific paint, you can set a custom valuation for that paint and a different valuation for all other paints. However, I have left it editable in case you want to play around with it as is. Please let me know if there is any error or issue and I will try to maintain it before I go back to school.

Yes. It is for multiple variables. If you would really like to get into the nitty-gritty, the x-axis is the reward valuation in crystals and the y-axis is the percent per unit, though if I were to draw a true graph, it would be a discrete graph as opposed to a smooth continuous graph. It is just a reference to what I mean.

Yes, you are absolutely correct. However, I do not have the rarity group chances of old containers so I cannot compare them with new containers. At least not right now. Hopefully that data is released soon and we can then calculate it ? As for Ultra Containers, I find that there are just generally fewer use cases and again I do not have a fair comparison so I decided to omit it. That's true - I forgot to consider Premium account as well as the implications behind removing supplies. The post I made was more of a math based post describing the changes of two specific situations and definitely should not be taken into account for everything - it's just there to calculate if the new container rewards for ranking up and premium bonus were fair changes. The intention of the post was not to directly critique the update (as I have posted my general thoughts on the update and the direction of Tanki as a whole elsewhere) but rather to just show some math. I feel like having all things considered would definitely be a more update-based review I could have written had the Newspaper still been around. I would assume so. This is why there are the following assumptions: We want to assume a generous bound. It's definitely true that players might not value things like paints and shot effects and it's up to their personal utility (and I definitely understand why it would be 0 for some if not all players). However, I wanted to put a higher value to give the game the benefit of the doubt. It's a "best case" scenario - each player has a different situation and you cannot tailor it very well to each of them (at least not yet; I could definitely make a EV calculator sometime this weekend) I've noted this in the disclaimers and mentioned that you need to take personal utility into account as well as those are just specific examples and valuations I have. And yes, if you replaced all the 100ks/500ks with 0 values, you would actually end up tanking the value below 5689, the lower bound - which is definitely not great. Hopefully that clears it all up. In no way do I mean to sugarcoat any changes or updates but rather just take a look at the valuation of a container right now with very generous assumptions. Perhaps with the V-LOG or future announcements we will able to obtain the previous drop rates and then I can make a better comparison as well as a valuation chart.

Some people like math okay

Hi. I'm back. Looking through new container rewards has inspired me to prepare the following: A tale of Two Expectations, Round II Is a container truly a better reward when ranking up? Or as a premium reward? Of course, I'd hope by now most of you have developed some sense of mathematical intuition on how this works, but if not, we're here to get to the bottom of it. So let's work with the given: Previously, you earned 2500 crystals per day as well as 10 of each supply (except repair kits, which were worth 3x as much, so you got 10//3 = 3 of those). You also earned a crystal amount for ranking up. This would range from 10 - 40000 crystals from Private to Legend. For both of these events, you now receive 1 container. Now, this means we need to calculate the expected value of a container as well as the values of the previous two events. For Premium Bonus: This is fairly simple. We can just convert the supplies to their crystal values and then add to 2500: 4*(10(50)) + 3(150) + 2500 = 2000 + 450 + 2500 = 4950 crystals. For Ranking up: If you're a Legend, it's a flat rate of 40000 crystals per rank up. If not (and you're making your way to your first Legend rank), it's a value according to the following chart. For fun, that average is around 11067 crystals - you get more than the average once you reach Major. For Containers: *sigh* You know how physics questions always come with a ton of assumptions - e.g. assume this is an ideal op-amp, assume this is an inertial frame of reference, assume air resistance is negligible, and so on? Well, it's time to buckle up our seatbelts and play the assumption game. So for today's episode, we will have 2 scenarios: 1. The complete newbie - this player will have no rewards unlocked except the turrets and hulls as I've looked across accounts and it seems a bit complex (e.g. one account had different rewards as compared to the other) and plus it will not affect the results too much. 2. The whale - honestly, this guy should more about paying his rent than getting container rewards, with all the rewards unlocked except pure repeatable rewards. Of course, these are a bit on the extreme end, but you can tell where you lie approximately and then be able to assess your expected value from there - just note that your expected values should decrease following a logarithmic pattern (starting at a high value and losing value little by little). We then try to convert everything into crystal value with the following assumptions: Supplies and augments are converted into their crystal values. That means for the core 4 supplies (BD, BA, Speed Boosts, Mines) that should be 50 crystals, 150 crystals for repair kits, and 300 crystals for batteries. And as for turret augments, it's 149 and 245k or something like that. The following items don't have an "assigned" crystal value, but I will make a broader assumption giving Tanki the benefit of the doubt: Rare Tier Paints: 100000 crystals (it would be unfair to overlook 10 crystals paint and replace that with maxed 500k paint, so I settled for a more fair medium bound) Epic/Legendary Paints: 500000 crystals (as per highest value, plus it caps out in price) Shot Effects: 100000 crystals (lower value in my opinion - similar to a paint) Hull Augments: 500000 crystals (It's a bit more valuable than some basic turret augments) Legendary Augments: 500000 crystals (to be fair, it really caps out as no augment is a permanent meta buff forever) So, with that all done and dusted, aha, you thought we were done here. Nope. First, we need to compute the expected value of each tier, then combine that expected value to compute the total expected value. For this, we make another few more assumptions: We assume that all rewards are drawn at an equal probability - i.e. you have the same probability of getting mines as getting 1000 crystals at the uncommon tier. (To visualize this, just think of a bag and put all the rewards in each tier in the bag, then draw one out and replace it for the next container if it is a repeatable item). Just kidding, it was just one assumption. I just wanted to add bullet points because it looks really cool. Now, it's time to do the math. Let's get the expected (crystal) value for each tier. I went and smashed these into TeXit: Note that I decided to use approximations since it was far too difficult to smash calculator for a difference on the order of 1-2% and I just completely stopped caring about epics for Scenario 1. But here are your values. Note: Don't forget about utility! I used crystal values because that is the most neutral way of calculating these. However, keep in mind that utility is also in play. As a very basic example, if you really want an augment and get it, your utility for the reward is high; conversely, if you really didn't want the augment and get it, your utility is low. The perceived value for a reward definitely plays a role, and you'll need to keep that in mind when making your decisions. Bottom Line The resulting expected value of containers (in crystals, with a generous upper bound) is between 5689 and 32064 crystals. This makes a rank-up container somewhat valuable in lower ranks as a container's reward is far more than 10 crystals for ranking up to private, but this value decreases as time goes on and considering utility. Again, with all things considered (e.g. utility), the premium reward stays about the same in value. However, utility does play a role here. I would rather have a constant supply of same rewards as opposed to putting my reward luck on the roulette. Additionally, the distribution of container rewards is right skewed - i.e. the chances of getting something more common (to the left of the EV bar) is higher and vice versa, the chances of getting something less common (to the right of the EV bar) is lower. The implications of this is fairly simple - for right skewed distributions, the mean is higher than the median. This means even though the EV is higher, you often get a lower valued reward as there are simply more values that fall under the mean (I hope you already knew this). Here's a visual explanation. In the end, your expected earnings are higher for lower-ranked rankups, lower for higher-ranked rankups, and a coin toss for Premium rewards. But it all depends on your perceived utility of these items (of which I've inputted generous values as placeholders) as only you can determine that. P.S. I won't comment much on shards vs. mission containers. Basically this update only gives containers for playing MM as opposed to some passive income and some active income - again, that depends on your preferences and play habits to see if you win or lose on this one. Note: Fixed the math, the resolution might be fuzzy because PDF -> png.

This is intended to be neutral and free from sharp criticism and I hope I come across like so because I truly don't mean to hate or critique, but rather just asking the game about its vision and values. I don't really understand what direction the game is trying to develop into and what it wants to be known as anymore. Before, I perceived it as a fun tank game that was a bit different than most of the other games that I played and the unique graphics, mechanics, and strategies really drew me in. Each change seemed to be developing the mechanics of the game and reinforcing this vision of a game; at least this is what I thought. But now, it really seems like there are just changes done here and that sort of fit with the trends [of current/popular games] at the moment (e.g. mobile developments like hover hulls to give mobile gamers a better game experience, battle pass sorta mechanic that went with the MM update cause that seems to be a popular game design model at least in a lot of games, containers/dropboxes as it's also a popular game and business model, these are just a few examples I could come up with off the top of my head) and not as many changes that really define Tanki as a unique game. As I'm writing right now, Tanki seems to lack a clear future roadmap and identity - what is the game and what do we want it to be seen as? Is it supposed to be a tank game? Is it supposed to be a general fun game that uses tanks as opposed to players? Is it a top the Play Store charts game? Is it [fill in the blank cause I'm out of ideas]? That's what I'm not sure of - I'm not sure what exactly the game wants to be, what the game's core values are, and how each update drives the changes needed to reach their vision. I feel like some sort of transparency into the game's future development plans would definitely help us understand the reasoning behind these changes and possibly provide our feedback better to work together and improve the game. Hopefully we are able to understand more of an idea of what the game is and what it wants to become - key components to its identity I (and maybe others) just can't seem to grasp. That's my $0.02; feel free to let me know if I'm completely wrong or don't make sense or anything at all.

Jeez, and I thought I wrote text walls.... Though as a point of critique as a part of the writer in me, I'd definitely appreciate some insight as to why you feel the way you do about these complaints. Some, if not most, of your complaints just go [equipment item/feature/noun] is too [OP/expensive/pointless/unfair/negative adjective] without any justification. Anyways, to write a complaint to antipurge the comment (and provide an example), uh, I'm also not a huge fan of 15 minute MM battles - I feel like MM hit the sweet spot with 10 minutes. I feel like the shorter battles were always a bit too short and didn't allow me to warm up to my full potential, and the long battles just feel like there's a little bit too much time/effort to be put in them and I don't like putting effort.

That's because the newspaper isn't here anymore ? /s but also not /s