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A discrete Markov chain is basically a random walk on a graph, where each outgoing edge has a fixed probability. Cool fact: any initial distribution on a sufficiently nice* Markov chain converges to its stationary distribution after many steps—because it's a contraction mapping.

Keenan Crane

38,804 subscribers

181,771 просмотров • 1 год назад •via X (Twitter)

Наука и технологии Новости и политика Образование

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One of the simplest algorithms for sampling from a probability distribution is Random Walk Metropolis-Hastings. It proposes new samples by taking Gaussian-distributed steps, accepting or rejecting them to maintain the target distribution. I call this pdf the "fidget spinner".

One of the simplest algorithms for sampling from a probability distribution is Random Walk Metropolis-Hastings. It proposes new samples by taking Gaussian-distributed steps, accepting or rejecting them to maintain the target distribution. I call this pdf the "fidget spinner".

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Most agents track price. Ours track how information propagates through markets. That difference is where the edge comes from. The visualization below is a Shannon entropy field: a model of how uncertainty collapses and spreads as new information enters a market. Each trade, liquidity shift, or derivatives flow updates a probability distribution. When information arrives, entropy collapses locally as the market incorporates it. But that update rarely happens everywhere at once. Different venues, liquidity pools, and derivative layers incorporate signals at different speeds, creating measurable information gradients across the system. One of the analytical tools in our agents’ stack models this directly: > Entropy quantifies uncertainty embedded in each probability market > KL divergence reveals conflicting distributions across venues > Information gradients show where signals have propagated—and where they haven’t yet Prediction markets and DeFi make this particularly powerful because price already represents probability. Mapping how those probability distributions update across venues turns the market into a measurable system: a live field of information flow showing where uncertainty remains—and where probability is likely to adjust next

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Math quant bot on Polymarket made over $457K PnL in 20 days - he turned $7,387 → $457k profit it uses Markov Chains to find "mispriced" windows on BTC and ETH up/down markets - made 14,200+ predictions, with ~$22,850 avg. daily profit by exploiting gaps humans miss at 3AM strategy: a 1h BTC/ETH up/down market is a binary contract it pays $1 if event happens → $0 if not Markov Chains give you the probability of the next market state based on: > current state of the market (up / down / flat) > transition matrix built from live price data > diagonal persistence value - how stable the current state is formula: p̂ − market_price ≥ 0.05 AND P(j, j) ≥ 0.87 bot profile: - read article below to understand how Markov Chains are used to extract edge from prediction markets

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