Citadel_Securities
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NOT FINANCIAL ADVICE DO YOUR OWN RESEARCH. THIS ACCOUNT AND ARTICLE ARE IN NO WAY AFFILIATED NOR ENDORSED BY THE ACTUAL CITADEL SECURITIES. I'M JUST A RANDOM MONKEY DOING KAW ECONOMICS RESEARCH.
Hey guyss, lets talk about how to actually make a ton of gold in KAW so you can actually finish your build and keep up with all the new lands.
Here's to all the dummies saying math isn't useful, jokes on you we're the ones making money IRL and in game.
RULES:
NO GLITCHES
NO EXPLOITS (such as volley transferring with 1000 alts)
and DEFINITELY NO USING YOUR WALLET LIKE A TOTAL FRICKIN LOSER
1 single account, just being smart with the game's mechanics
TIME VALUE OF GOLD AND INFLATION
First, lets define inflation, and talk about how that relates to the time value of gold.
Simply put, if you had 1T gold 10 years ago, that same 1T is not gonna be able to buy the same share of the total economy today. That's inflation. So the value of gold decays over time:
Decay = 1/(1+r)^t
where r in this case is KAW KAWWWW's inflation rate. This inflation rate is complex, and generally difficult to calculate without pulling tons of stats from the game (which I'm too lazy to do), so lets just run a rough estimate as a proxy. Total cost for full build has increased exponentially, stats increased, ally cost increased, etc etc, you get the idea. Lets say today's 1Q is worth 1T 10 years ago, so within 10 years we had a 1000x inflation, which gives us an estimate r of:
r = 0.9953 which is roughly a 99.53% increase in prices each year.
So that's the number we want to beat, if we will have any hope of completing the build and keeping up with constant updates.
HOW TO SPEND YOUR GOLD: USING MONEY TO MAKE MONEY
two main ways:
1. land and upgrades
2. ally stock market
Land and upgrades function as risk-free bonds, since they cant be stripped away by farmers
Ally stock market functions like risky assets since you can get stuck with an inactive, and/or they can be stripped and you can lose a lot if you get farmed while you have tons of gold out. This effectively functions similar to a market crash, but for your kingdom only.
THE RISK-FREE RATE
Lets evaluate the first option, to see if this beats inflation. Lets assume you LIVE FOREVER, the game LASTS FOREVER, and you play 24/7 FOREVER. This is the math of a perpetuity which has a present value of:
PV = CF/r
PV being present value
CF being the sequence of all future cashflows
and r being interest rate
Since there's no interest rate in KAWWW, lets just replace this with our 99.53% inflation rate as the number to beat.
So to rephrase, buying land and upgrading buildings only beats inflation if the cost in gold to open lands and upgrade buildings is less than PV. A concrete example, you upgrade a building and it generates you 10Q over the next year AND every year after FOREVER. The present value of that 10Q is actually 10Q/0.9953 = 10.05Q. So this upgrade is only worth it if the current cost of the upgrade is less than 10.05Q. And remember, we have frickinnn generous assumptions, you LIVE FOREVER, PLAY FOREVER 24/7, and the game LASTS FOREVER. From this we can create a rule of thumb:
ONLY UPGRADE YOUR LAND AND BUILDINGS IF YOU THINK YOU CAN GET THE MONEY BACK IN THE NEXT YEAR AND EVERY YEAR AFTER FOREVER FROM THE UPGRADE ALONE (so basically upgrade only with plates, and the cost becomes land opening cost).
Since most buildings past level 5 offer diminishing returns, it becomes increasingly likely at higher building levels that it's simply NOT WORTH the upgrade.
We have anecdotal evidence of this too, the current rank 1 player is not even build complete. That says a lot about how inefficient upgrading actually is to scaling your income!
THE ALLY STOCK MARKET
With any ally investment there is risk. Picking allies is like picking individual stocks, you have idiosyncratic risk, or the risk idiots take when they don't know how to diversify their portfolio. And of course market risk (risk of a crash). But luckily, the same portfolio diversification techniques IRL can be applied in game. Of course there will be differences, here we cant just buy an s&p500 index fund and go on vacation for 30 years. Here, the ally market works similar to a covered calls strategy IRL, and market risk works a bit differently too. Let me explain.
In covered calls, you sell call option premiums, and cover that sale by holding the underlying stock. The risk is if the stock goes down while you're holding. I think the colloquial phrase is picking up pennies in front of a steam roller.
In the ally market, every time you sell, you make 1.5%, but the risk is the ally becomes inactive or if you get strip farmed. So also... picking up pennies in front of a steamroller.
DIVERSIFICATION AND MARKET RISK
Luckily, there are mathematical models we can use to make this (in game) strategy statistically favorable for us in the long run.
We can also use the principles in factor investing to help us pick good allies. For example:
Good allies: Active, high growth rate, within exponential phase, good cost/stat ratios
Bad allies: inactive, been playing for years without growth, already grown so their future growth rate is poor, expensive cost/stat ratios
I ran a small experiment with the ally market, and found picking allies with the good characteristics pretty much mitigates all the risk of being stuck with a bad inactive ally, with about a 100% success rate. For the calculation below, lets just use 99%, because nothing in the real world is 100%.
Next lets talk about market risk, or the risk of being farmed while you have gold out. There's 2 main strategies to avoid a market crash in the ally stock market.
1. Avoid conflict
2. Stay small
Avoiding conflict while staying small stacks both probabilities in your favor, with the added benefit of avoiding high cost land and upgrades while using your gold more efficiently in the ally market. It's literally a win-win-win situation.
Believe it or not, this is already enough data for me to size my bets according to a partial kelly criterion. Here we use a half-Kelly.
f_partial = 0.5*(bp - q)/b
Where:
f_partial is the optimal bet size
b is odds received, in this case it's 1.5% or b=0.015
p is the probability of winning, so 99% or 0.99
and q is the probability of losing so 1% or 0.01
So our optimal wager becomes 16.17% of the total gold out, with a expected value (EV) of 0.48%
Oh boy... some rough numbers. This really does feel like picking up pennies in front of a steam roller. But let's see how profitable this strategy actually is below in the next section.
HOW PROFITABLE IS THIS STRATEGY?
Assuming you sell 3 allies a day (very generous, I typically sell about 20-30 a day with good factor loading), that's a profit compounding of:
Return per ally using 20% bankroll (rounded up from our 16.17% previously) we get:
yearly growth = [(1 + f·0.015)^p × (1 − f·L)^(1−p)]¹⁰⁹⁵
f = share of gold per ally = 0.2
p = success rate = 0.99
L = share lost if an ally gets stuck = 1 (total loss)
1095 = sales per year (3 a day × 365)
PROFIT = 123%
SO YEA, WE BEAT INFLATION. THIS ASSUMES 99% SUCCESS RATE.
LIMITATIONS
Skill plays a huge factor here, as just picking a few bad allies could cost you a lot. And there are also market bottleneck limitations. With huge amounts of capital, there may not be enough active, low cost, high growth allies to deploy your entire bankroll, so this strategy gets arbitraged away with more and more gold. It's also really time consuming to constantly be combing through clans to look for allies with theses specific qualifications.
Funny enough, we see similar things in the real world too. Lots of really good funds don't accept outside money, likely due to similar principles, in that lots of money makes a strategy less efficient.
CONCLUSION
We have essentially:
- Estimated inflation rate in KAW
- Found a way to use a covered call factor investing strategy to beat inflation
- Discovered the risk-free rate at higher upgrades does not beat inflation
- Found a way to reduce market risk by staying small and avoiding conflict
IN GAME AND IN LIFE. LOOK FOR THINGS THAT SCALE EXPONENTIALLY, INSTEAD OF LINEARLY.
AGAIN, NOT FINANCIAL ADVICE, NEITHER IN GAME NOR OUTSIDE OF GAME. INVEST AT YOUR OWN RISK.
Hey guyss, lets talk about how to actually make a ton of gold in KAW so you can actually finish your build and keep up with all the new lands.
Here's to all the dummies saying math isn't useful, jokes on you we're the ones making money IRL and in game.
RULES:
NO GLITCHES
NO EXPLOITS (such as volley transferring with 1000 alts)
and DEFINITELY NO USING YOUR WALLET LIKE A TOTAL FRICKIN LOSER
1 single account, just being smart with the game's mechanics
TIME VALUE OF GOLD AND INFLATION
First, lets define inflation, and talk about how that relates to the time value of gold.
Simply put, if you had 1T gold 10 years ago, that same 1T is not gonna be able to buy the same share of the total economy today. That's inflation. So the value of gold decays over time:
Decay = 1/(1+r)^t
where r in this case is KAW KAWWWW's inflation rate. This inflation rate is complex, and generally difficult to calculate without pulling tons of stats from the game (which I'm too lazy to do), so lets just run a rough estimate as a proxy. Total cost for full build has increased exponentially, stats increased, ally cost increased, etc etc, you get the idea. Lets say today's 1Q is worth 1T 10 years ago, so within 10 years we had a 1000x inflation, which gives us an estimate r of:
r = 0.9953 which is roughly a 99.53% increase in prices each year.
So that's the number we want to beat, if we will have any hope of completing the build and keeping up with constant updates.
HOW TO SPEND YOUR GOLD: USING MONEY TO MAKE MONEY
two main ways:
1. land and upgrades
2. ally stock market
Land and upgrades function as risk-free bonds, since they cant be stripped away by farmers
Ally stock market functions like risky assets since you can get stuck with an inactive, and/or they can be stripped and you can lose a lot if you get farmed while you have tons of gold out. This effectively functions similar to a market crash, but for your kingdom only.
THE RISK-FREE RATE
Lets evaluate the first option, to see if this beats inflation. Lets assume you LIVE FOREVER, the game LASTS FOREVER, and you play 24/7 FOREVER. This is the math of a perpetuity which has a present value of:
PV = CF/r
PV being present value
CF being the sequence of all future cashflows
and r being interest rate
Since there's no interest rate in KAWWW, lets just replace this with our 99.53% inflation rate as the number to beat.
So to rephrase, buying land and upgrading buildings only beats inflation if the cost in gold to open lands and upgrade buildings is less than PV. A concrete example, you upgrade a building and it generates you 10Q over the next year AND every year after FOREVER. The present value of that 10Q is actually 10Q/0.9953 = 10.05Q. So this upgrade is only worth it if the current cost of the upgrade is less than 10.05Q. And remember, we have frickinnn generous assumptions, you LIVE FOREVER, PLAY FOREVER 24/7, and the game LASTS FOREVER. From this we can create a rule of thumb:
ONLY UPGRADE YOUR LAND AND BUILDINGS IF YOU THINK YOU CAN GET THE MONEY BACK IN THE NEXT YEAR AND EVERY YEAR AFTER FOREVER FROM THE UPGRADE ALONE (so basically upgrade only with plates, and the cost becomes land opening cost).
Since most buildings past level 5 offer diminishing returns, it becomes increasingly likely at higher building levels that it's simply NOT WORTH the upgrade.
We have anecdotal evidence of this too, the current rank 1 player is not even build complete. That says a lot about how inefficient upgrading actually is to scaling your income!
THE ALLY STOCK MARKET
With any ally investment there is risk. Picking allies is like picking individual stocks, you have idiosyncratic risk, or the risk idiots take when they don't know how to diversify their portfolio. And of course market risk (risk of a crash). But luckily, the same portfolio diversification techniques IRL can be applied in game. Of course there will be differences, here we cant just buy an s&p500 index fund and go on vacation for 30 years. Here, the ally market works similar to a covered calls strategy IRL, and market risk works a bit differently too. Let me explain.
In covered calls, you sell call option premiums, and cover that sale by holding the underlying stock. The risk is if the stock goes down while you're holding. I think the colloquial phrase is picking up pennies in front of a steam roller.
In the ally market, every time you sell, you make 1.5%, but the risk is the ally becomes inactive or if you get strip farmed. So also... picking up pennies in front of a steamroller.
DIVERSIFICATION AND MARKET RISK
Luckily, there are mathematical models we can use to make this (in game) strategy statistically favorable for us in the long run.
We can also use the principles in factor investing to help us pick good allies. For example:
Good allies: Active, high growth rate, within exponential phase, good cost/stat ratios
Bad allies: inactive, been playing for years without growth, already grown so their future growth rate is poor, expensive cost/stat ratios
I ran a small experiment with the ally market, and found picking allies with the good characteristics pretty much mitigates all the risk of being stuck with a bad inactive ally, with about a 100% success rate. For the calculation below, lets just use 99%, because nothing in the real world is 100%.
Next lets talk about market risk, or the risk of being farmed while you have gold out. There's 2 main strategies to avoid a market crash in the ally stock market.
1. Avoid conflict
2. Stay small
Avoiding conflict while staying small stacks both probabilities in your favor, with the added benefit of avoiding high cost land and upgrades while using your gold more efficiently in the ally market. It's literally a win-win-win situation.
Believe it or not, this is already enough data for me to size my bets according to a partial kelly criterion. Here we use a half-Kelly.
f_partial = 0.5*(bp - q)/b
Where:
f_partial is the optimal bet size
b is odds received, in this case it's 1.5% or b=0.015
p is the probability of winning, so 99% or 0.99
and q is the probability of losing so 1% or 0.01
So our optimal wager becomes 16.17% of the total gold out, with a expected value (EV) of 0.48%
Oh boy... some rough numbers. This really does feel like picking up pennies in front of a steam roller. But let's see how profitable this strategy actually is below in the next section.
HOW PROFITABLE IS THIS STRATEGY?
Assuming you sell 3 allies a day (very generous, I typically sell about 20-30 a day with good factor loading), that's a profit compounding of:
Return per ally using 20% bankroll (rounded up from our 16.17% previously) we get:
yearly growth = [(1 + f·0.015)^p × (1 − f·L)^(1−p)]¹⁰⁹⁵
f = share of gold per ally = 0.2
p = success rate = 0.99
L = share lost if an ally gets stuck = 1 (total loss)
1095 = sales per year (3 a day × 365)
PROFIT = 123%
SO YEA, WE BEAT INFLATION. THIS ASSUMES 99% SUCCESS RATE.
LIMITATIONS
Skill plays a huge factor here, as just picking a few bad allies could cost you a lot. And there are also market bottleneck limitations. With huge amounts of capital, there may not be enough active, low cost, high growth allies to deploy your entire bankroll, so this strategy gets arbitraged away with more and more gold. It's also really time consuming to constantly be combing through clans to look for allies with theses specific qualifications.
Funny enough, we see similar things in the real world too. Lots of really good funds don't accept outside money, likely due to similar principles, in that lots of money makes a strategy less efficient.
CONCLUSION
We have essentially:
- Estimated inflation rate in KAW
- Found a way to use a covered call factor investing strategy to beat inflation
- Discovered the risk-free rate at higher upgrades does not beat inflation
- Found a way to reduce market risk by staying small and avoiding conflict
IN GAME AND IN LIFE. LOOK FOR THINGS THAT SCALE EXPONENTIALLY, INSTEAD OF LINEARLY.
AGAIN, NOT FINANCIAL ADVICE, NEITHER IN GAME NOR OUTSIDE OF GAME. INVEST AT YOUR OWN RISK.