Professional dual-mode Kelly criterion calculator — scenario preset buttons · negative-EV fail-safe warnings · Monte Carlo 500-path simulations · one-click copy of risk-control summary.
Kelly formula can be based on yourWin rate與Profit-loss ratioPrecisely calculate how much to stake on each trade or betOptimal capital fractionAvoid taking excessive risk that could lead to ruin, while also avoiding being overly conservative and missing out on profits.
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Full Kelly 在理論上能最大化長期資產成長率，但對參數估計誤差極度敏感。 如果實際勝率比預估值低 5%，Full Kelly 策略的資金曲線會出現劇烈波動， 甚至可能導致長期虧損。Half Kelly（使用 0.5 倍的全凱利比例）將波動降低約 75%， 同時保留約 75% 的成長率，被廣泛認為是實戰中最安全的選擇。 Edward Thorp 與 Bill Gross 等傳奇投資者均採用 Half Kelly 策略管理資金。
In stock/futures/cryptocurrency trading, the Kelly formula is transformed to f* = p/L - (1-p)/W，
其中 p 為勝率、W 為預期獲利百分比、L 為預期停損百分比。
例如：勝率 50%、停利 10%、停損 5% 的交易，
凱利比例 = 0.5/0.05 - 0.5/0.10 = 10 - 5 = 5 (i.e. 500%)。
這表示理論上應該使用 5 倍槓桿。但實戰中絕不能超過 100%，
因此通常使用 Half Kelly 將槓桿降至 250%，再根據個人風險承受能力進一步降低。
停損設定的重要性遠大於停利 — 停損越小，凱利公式允許的部位越大。
蒙特卡羅模擬透過隨機抽樣重複模擬數百次交易路徑， 幫助你了解在不同運氣條件下資金的實際表現。 Maximum drawdown (Max Drawdown) 是指從最高點到最低點的最大資產跌幅， 它是衡量策略風險的核心指標。如果模擬顯示 95% 的路徑最大回撤超過 30%， 即使凱利公式建議 Full Kelly，你也應該考慮降低至 Half 或 Quarter Kelly。 Probability of ruin 則是指資金虧損超過 80% 的路徑比例 — 如果這個數字高於 5%， 代表你的參數估計可能過於樂觀，需要重新評估勝率或調整止損策略。
本工具計算結果與蒙特卡羅模擬僅供數學模型推演與風險評估參考，不構成任何投資或投注建議。 投資有風險，請獨立評估並自負盈虧。過去的回測結果不代表未來表現。 凱利公式的準確性完全依賴輸入參數的真實性，錯誤的勝率估計會導致嚴重損失。
This page, its calculators, and examples are for education, research, and scenario estimation only. They are not personalized investment, trading, betting, tax, legal, or financial advice. Markets and local rules can change quickly; verify current primary information and take responsibility for your decisions. Past performance, model outputs, and simulations do not guarantee future results.