FOMO3D — Game-Theoretic Equilibrium
A game based on Ethereum called FOMO3D has recently stolen the spotlight — it has become the world’s most popular smart-contract-based game since CryptoKitties.
The rules of the game can be read on the official website. Below is a brief summary:
“Each round of the fast version kicks off with a short ICO phase, during which all players will be able to buy keys for the same average key price, determined by the total amount of ETH invested during this phase. Once the ICO phase ends, then the normal round begins with the timer set and starting to countdown.
During a round, a timer is constantly counting down to zero (hard cap is 24h). Every time a key is purchased, the buyer becomes the new “holder of the private keys” and additional time (of 30s) is added to the countdown. The price of the keys will now start to get slightly more expensive with each purchase. When the timer reaches zero, the last person to have bought a key wins the round!”
At the end of the round, the ETH in the pot is divided up: the winner receives half of the pot, with the rest split between all F3D players as well as to P3D holders. P3D work like security tokens that earn you dividends on every buy and sell on the entire ecosystem (including future games). Since we don’t know what future games will look like, we focus our analysis only on F3D.
One can invite others to become buyers and earn 10% of any investment made by their invitees. Once a round ends, 48% of the Active Pot goes to the final winner. 2% goes to the team’s community fund. The remaining 50% gets distributed to F3D players, P3D holders, or gets carried over into next round based on the final winner’s team.
When a new key buyer enters, he/she chooses one of the four teams to associate their keys with. The investment then gets allocated across the pot, existing F3D key holders, and P3D holders depending on which team you pick:
Team Snek shares the highest dividends from new players. Let’s assume that all players choose team Snek. This is largely the case currently, as it represents 80–90% of the total pool.
The key price increases by a square root function to the total amount in the active pot. The best scenario for F3D players is one where:
1) all newcomers choose team Snek — this would distribute the most to existing F3D players
2) Team Bull wins the game, this would distribute the most to F3D players from the final Active Pot
We can analyze the expected reward for F3D players under this optimal scenario.
If you buy n0 key now, at price p0, it will cost you n0 x p0 ETH at present. Below we calculate the final return you get assuming the round ends with total investment reaching Yt.
Solving the above formulas, we get:
Further, we can get C = 0 based on the current key supply, total investment and key price:
We add the final pay at the end of the round, which is:
The total return will be:
In summary; assuming no referrals, in order to break even, you need the total investment pool to grow 7x versus against the pool size at your time of entry. With referrals this number is 6x.
At the time of writing (5:35pm HKT July 22nd 2018), the total pool is currently at 91,613 ETH. If you enter the game now, you’ll need to wait for the investment pool to grow to 6 x 91,613 = 549,678 ETH before earning back your principal.
Notes/Assumptions:
1. All newcomers join team Snek (best case for F3D players)
2. Team Bull is the final winner (best case for F3D players)
3. The key price increases by a sqrt function to the active pot (currently true)
4. You don’t expect to be the final winner, or to get paid by airdrop
There is 100mm ETH in circulation. If we expect the final total investment to reach 1mm ETH, then we would expect the game to stop before 1/7.23 = 0.138mm. But if everyone stops before 0.138mm, you should stop before 0.138/7.23 = 0.019 mm. If everyone stops before 0.019 mm, you should… In summary, you should never enter.
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