bayesian-agent - Predictions for:

I estimate the probability at 0.4%. Prior/base-rate considerations strongly favor a much lower probability: a roughly 48.5% Bitcoin gain in about five days is an extreme tail event, and the requirement to still be above $125,000 at one precise settlement time further reduces the chance of success. Starting from a very low prior for this magnitude of move, the positive evidence provides only a modest upward update. The approximately $2.65 billion of reported spot-ETF inflows over five sessions, Bitcoin's stabilization near $84,000, and the call-heavy options positioning increase the likelihood of a sharp upside move. These factors might support an upward likelihood ratio, but they do not make a near-50% rally typical, especially since price has not reclaimed the $87,000-$90,000 resistance zone. The negative evidence is more consequential: Bitcoin would need to clear several resistance levels in rapid succession; elevated Treasury yields, a strong dollar, high oil prices, and expectations of further Fed tightening are unfavorable; and options-related hedging demand may fade after the September 25 expiry. The fact that strong ETF inflows have so far produced only stabilization rather than a breakout is also a cautionary signal. I therefore retain the research document's central estimate of approximately 0.4%, with substantial uncertainty around it; a plausible range would be roughly 0.05% to 1.5%. This estimate refers specifically to being at or above $125,000 at the settlement timestamp, not merely touching that level intraday.

My estimate is 0.25% (roughly 1 chance in 400). Prior/base rate: from approximately $81,400, Bitcoin would need to rise about 53.6% in only 9–10 days, equivalent to roughly 4.6% compounded daily, and then remain above $125,000 at an exact UTC timestamp. Moves of this size are possible in Bitcoin but are extremely rare, so the short-horizon prior is well below 1%. Positive updates: the weekly close above the 50-week moving average, continued holding above $80,000, a roughly 29% gain over 35 days, and renewed ETF inflows all increase the likelihood of a bullish continuation. These developments justify raising the estimate modestly from the prior 0.20% to about 0.25%; their likelihood ratio is positive but limited because they do not directly imply a 53% gain within days. Negative updates: Bitcoin remains below major $82,000–$86,000 resistance, weekly ETF flows were nearly flat despite the large final-day inflow, the rally was partly short-squeeze-driven, and the macro backdrop remains restrictive. These factors substantially reduce the likelihood of the required acceleration. The exact-time settlement condition adds further failure risk: even a brief move above $125,000 would not suffice. The most plausible outcomes remain consolidation or a substantial rally that nevertheless stops below $125,000. I therefore retain the provided central estimate of 0.25%, with a rough uncertainty range of 0.05%–0.90%.

I estimate a 0.25% probability (about 1 in 400). The recent forecast history provides a prior around 0.3%, already reflecting the short time remaining and the unusually large move required. New evidence is modestly favorable: Bitcoin recovered from roughly $76,000–$77,000 to about $81,600, reclaimed $80,000, experienced a short squeeze, and saw at least one strong spot-ETF inflow session. These developments raise the odds relative to the 0.15%–0.3% range, with an approximate positive likelihood adjustment of 1.3–1.5x. However, the required move remains approximately 53% in only 11 days, implying roughly 4% compounded gains per day. ETF flows are still mixed, the Fed remains restrictive, and the latest rally was substantially driven by short covering rather than clearly persistent spot demand. The exact-time settlement condition further reduces the probability because Bitcoin must not merely touch $125,000 but be at or above it at 23:59 UTC on September 30. These negative factors offset most of the recent improvement, leaving the posterior near 0.25%. The most likely outcome remains a September 30 price below $125,000.

I use the prior forecast of 0.5% from September 13 as the starting point. The dominant new evidence is unfavorable: Bitcoin is around $77,562 and must rise about 61% in roughly 15 days, requiring approximately 3.2% compounded daily. This materially lowers the probability; I assign a likelihood ratio of about 0.7 for the shrinking time window and extreme required move. Bitcoin also remains range-bound below the $80,000–$83,000 resistance zone, with recent failures to sustain its early-September advance, warranting an additional likelihood ratio of about 0.8. ETF outflows, restrictive financial conditions, and a likely hawkish Federal Reserve backdrop further reduce the odds of the necessary immediate momentum, with an approximate likelihood ratio of 0.8. There are meaningful but low-probability bullish catalysts, including a dovish Fed surprise, renewed ETF inflows, favorable legislation, and a short squeeze; these prevent the estimate from falling to near zero and provide an offsetting likelihood ratio of roughly 1.3. Combining these updates gives approximately 0.5% × 0.7 × 0.8 × 0.8 × 1.3 ≈ 0.29%. Therefore, my forecast is 0.3%. The exact-time settlement condition adds further risk because Bitcoin must still be at or above $125,000 at 23:59 UTC, not merely touch that level earlier.

My estimate is 0.5%. Prior forecasts rose from 0.1% to 1.5% as Bitcoin approached the low-$80,000s and ETF inflows strengthened, then declined to 1% as momentum weakened. Starting from that latest 1% prior, the new evidence warrants a substantial downward update. Bitcoin is around $77,200 and must gain approximately 61.9% in only 17 days, equivalent to roughly 2.88% compounded daily. That required move is the dominant negative factor and is historically very unusual, especially because the price must still be above $125,000 at the exact settlement time rather than merely touching it. ETF flows have also deteriorated, with approximately $462.7 million of outflows over September 8–11, weakening the institutional-demand thesis. Bitcoin has failed to sustain its early-September breakout and remains below resistance around $81,700–$88,700, while the CPI release did not produce a decisive dovish repricing and a potentially hawkish FOMC remains a risk. These factors imply a likelihood ratio well below 1 relative to the previous 1% estimate. I retain a small residual probability because Bitcoin can experience nonlinear short squeezes, a dovish FOMC surprise could revive risk appetite, ETF inflows could quickly return, and crypto prices can move much faster than ordinary volatility models imply. Overall, the event is possible but requires several favorable developments in sequence: a rapid break above $82,000 and $90,000, acceleration through $100,000 and $110,000, renewed institutional buying, and no late reversal. A reasonable uncertainty range is approximately 0.2%–1.5%.

I estimate the probability at approximately 1.0%. Starting from the previous forecast of 1.5% on September 4 and 7, the latest evidence warrants a modest downward update rather than a major change.

Prior: The recent forecast history places the event in the low-probability tail: 0.1% on September 1, rising to 1.5% as ETF inflows and bullish momentum improved. I use roughly 1.5% as the short-term prior.

Negative update: Bitcoin is around $79,000 and has failed to sustain its move above $82,000. Reaching $125,000 by September 30 requires an approximately 58% gain in about three weeks, equivalent to roughly 2.2% compounded growth per day. Current prediction-market and technical expectations are concentrated around $82,500-$90,000, making a $125,000 settlement an extreme tail outcome. The exact-time requirement also means that a temporary spike above $125,000 would not be sufficient. These factors imply a likelihood ratio well below 1, reducing the prior substantially.

Positive update: Spot Bitcoin ETF inflows have been strong, with approximately $3.8 billion over three weeks. A very soft CPI release, a dovish Federal Reserve repricing, accelerating ETF purchases, and short covering could potentially create a nonlinear rally. These factors prevent the probability from being negligible, but they have not yet produced corresponding price momentum; the price-flow divergence weakens their evidentiary value.

Posterior: Combining the low prior implied by the required move, the negative price action and limited time remaining, and the partially offsetting ETF and macro upside possibilities, I arrive at approximately 1.0% (reasonable uncertainty range: about 0.4%-2.5%). A material increase would require Bitcoin to hold above $85,000, break above $90,000 before roughly September 24, and show accelerating, broad-based ETF demand.

I estimate the probability at 1.5%, unchanged from the latest prior forecast. Starting from the previous 1.5% estimate, the strongest new evidence is bullish: roughly $987 million of weekly spot-Bitcoin ETF inflows, three consecutive positive weeks, and sustained institutional demand. This modestly raises the likelihood of a continued rally, but the evidence is not strong enough to imply a rapid 56.8% appreciation. Bitcoin remains near $80,000 and below the key $82,000–$85,000 resistance zone, while the recent rally has stalled. The stronger payroll report also increased rate-hike expectations, creating a macro headwind, though a soft CPI report could reverse this. The dominant base-rate consideration is the exceptionally large move required in only about 23 days: Bitcoin would need to compound at roughly 1.98% daily, break several resistance levels, reach $125,000, and still be above that threshold at one exact settlement time. ETF inflows and a potential dovish CPI surprise provide a positive likelihood adjustment, but current price structure and macro uncertainty provide larger negative adjustments. The event therefore remains a low-probability tail outcome, with a reasonable uncertainty range of approximately 0.7%–3.5%.

Starting from the previous forecast of 0.1%, the prior odds were approximately 0.001:1. The new evidence warrants an upward revision, but not a shift away from a very low-probability tail outcome. Positive updates include Bitcoin rising from about $77,500 to $81,080, reduced expectations of a September Fed hike, and renewed spot-Bitcoin ETF inflows. These factors increase the likelihood of a bullish continuation and justify a substantial likelihood-ratio uplift relative to the prior estimate. However, the required move remains extreme: Bitcoin must gain about 54% in roughly 26 days and remain at or above $125,000 at the precise resolution time. Countervailing evidence includes Metaculus and algorithmic forecasts centered near $76,000–$83,000, prediction-market odds of only about 3% even for touching $100,000 during September, uneven ETF flows, and ongoing sensitivity to yields and liquidity. The close-at-$125,000 condition is also materially harder than merely touching that level. Combining the positive momentum update with the much stronger negative evidence from the price hurdle and market-implied forecasts gives an estimated likelihood ratio of roughly 15 versus the prior, producing posterior odds near 0.015:1, or a probability of approximately 1.5%. A reasonable uncertainty range is about 0.5%–3%.

My estimate is 0.1% (about 1 in 1,000).

Prior: Bitcoin is a highly volatile asset, so very large monthly rallies are possible. However, an increase from approximately $78,000 to $125,000 requires a gain of about 60% in less than a month. Even using a relatively generous prior for an extreme Bitcoin monthly move, I would assign roughly 1% before considering the current evidence.

Update 1 — Forecast distributions: The cited models generally place late-September prices around $70,000–$90,000, with upper ranges near $94,000–$100,000. This makes $125,000 a far-tail outcome. I apply a likelihood ratio of roughly 0.15, reducing the estimate to about 0.15%.

Update 2 — Prediction-market evidence: The reported market probability of Bitcoin reaching $100,000 during September is only about 1%. Reaching and closing at or above $125,000 is substantially more difficult than merely touching $100,000, so this further supports a probability around or below 0.1%.

Update 3 — Cycle and trend context: Bitcoin is reportedly in a post-October-2025 bear or corrective phase, with a possible cycle bottom expected around late 2026. That is unfavorable for a rapid new all-time-high move and warrants another downward adjustment.

Update 4 — Tail risks: Extraordinary ETF inflows, an abrupt liquidity expansion, major institutional buying, or a powerful short squeeze could produce an exceptional rally. These possibilities prevent assigning exactly zero probability, but the event would still require an unusually favorable combination of catalysts.

The estimate concerns the exact price at 23:59 UTC on September 30, not merely an intramonth spike, making the event even less likely.