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Betkyo Research

Posted on AI-assisted

The denominator problem: pricing an hour of a fixed-pool airdrop

#crypto #math #python #web3

Every "play-to-airdrop" game has the same hidden variable, and it is not the token price. It is the number of other players.

Here is the arithmetic with one real example. Hamster Kombat announced 300 million players on 30 July 2024 and a whitepaper giving 60% of its token to them. The airdrop landed on 26 September 2024: 131 million accounts qualified. Sixty percent of a 100 billion supply is 60 billion tokens, so the average share was

60_000_000_000 / 131_000_000 ≈ 458 tokens
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At the listing price (about $0.011) that is $5.04. The token fell about 30% on day one and reached $0.0025 by 1 November, which makes the average share $1.15. If a player tapped ten minutes a day for the six months between launch and airdrop, that is 30 hours, so:

5.04 / 30 ≈ $0.17 per hour at listing
1.15 / 30 ≈ $0.04 per hour six weeks later
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The part people miss is the direction of the growth term. In a casino game the payout rule is per bet and does not depend on how many other people are playing: a dice roll that pays 1.98× at a 50% chance pays that whether a thousand people or a hundred million are rolling. In a fixed-pool airdrop the payout is pool / N, so every announcement of "more players" is an announcement that your share got smaller. A player who tapped twice as much did not double their hourly rate; they raised the denominator for everyone, themselves included.

A small function makes the comparison concrete:

def per_hour_fixed_pool(pool_tokens, players, price, hours):
    return pool_tokens / players * price / hours

def per_hour_fixed_edge(edge, stake, hands_per_hour):
    # expected cost (negative return) per hour, known before you play
    return -edge * stake * hands_per_hour

print(per_hour_fixed_pool(60e9, 131e6, 0.011, 30))   # 0.168
print(per_hour_fixed_pool(60e9, 131e6, 0.0025, 30))  # 0.038
print(per_hour_fixed_edge(0.01, 1.0, 600))           # -6.0  (1% edge, $1 bets, 600 rolls/h)
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Neither number is a recommendation. The second one is negative, as every house-edge game is. But the second one is known before the first roll, and the first one is known only after the pool, the headcount and the price are all fixed, which in this case was six months after people started playing. The mini-app's own monthly counter, readable by anyone, went from over 100 million in late September to about 41 million by early November. That curve is what "finding out the price of an hour" looks like at scale.

I work on the Betkyo Journal, where we publish this kind of derivation for casino games with the engine source as the reference. The full write-up, with the sources (Decrypt, Cointelegraph, ForkLog, BitPinas, CoinGecko), is here: https://betkyo.com/en/blog/hamster-kombat-300-million-players-a-60-billion-token-airdrop-and-the-month-they-left/

18+. Not financial advice.

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