kelly-criterion

Name: kelly-criterion
Author: agiprolabs

243installs53forks

How to install kelly-criterion?

agiprolabs/claude-trading-skills/kelly-criterion

$npx -y skills add agiprolabs/claude-trading-skills --skill kelly-criterion

Installs into the current project.

Summary

Kelly criterion optimal sizing with fractional variants, edge estimation, and practical application for crypto trading

Files · 1

View on GitHub

SKILL.md

1	# Kelly Criterion — Optimal Bet Sizing
2
3	The Kelly criterion is the mathematically optimal bet size that maximizes long-term geometric growth of capital. Developed by John Kelly at Bell Labs in 1956, it answers a precise question: given a known edge, what fraction of your bankroll should you risk to maximize the compounding rate?
4
5	Core insight: Betting too small leaves growth on the table. Betting too large increases ruin risk and actually reduces long-term growth. Kelly finds the exact optimum between these extremes.
6
7	Practical insight: You should almost never use full Kelly. Estimation error in your edge means full Kelly will overbets in practice. Use fractional Kelly (0.25x to 0.5x) for real trading.
8
9	---
10
11	## The Kelly Formula
12
13	For a binary outcome (win or lose):
14
15	```
16	f* = (p * b - q) / b
17	```
18
19	Where:
20	- `f*` = optimal fraction of bankroll to bet
21	- `p` = probability of winning
22	- `q` = probability of losing (1 - p)
23	- `b` = payoff ratio (average win / average loss)
24
25	Equivalent forms:
26
27	```
28	f* = p - q / b
29	f* = p - (1 - p) / b
30	f* = (p * b - (1 - p)) / b
31	```
32
33	Edge = `p * b - q` = expected value per unit risked. Kelly only makes sense when edge > 0. If edge is zero or negative, the optimal bet is zero — do not trade.
34
35	### Quick Reference
36
37	\| Win Rate \| Payoff 1:1 \| Payoff 1.5:1 \| Payoff 2:1 \| Payoff 3:1 \|
38	\|----------\|-----------\|-------------\|-----------\|-----------\|
39	\| 40% \| -20% \| -6.7% \| 10% \| 20% \|
40	\| 45% \| -10% \| 3.3% \| 15% \| 25% \|
41	\| 50% \| 0% \| 16.7% \| 25% \| 33.3% \|
42	\| 55% \| 10% \| 18.3% \| 27.5% \| 35% \|
43	\| 60% \| 20% \| 26.7% \| 35% \| 40% \|
44
45	Values are full Kelly fraction. In practice, use 0.25x to 0.5x of these numbers.
46
47	---
48
49	## Why Use Fractional Kelly
50
51	Full Kelly assumes you know `p` and `b` exactly. You never do. Here is why fractional Kelly is essential:
52
53	### 1. Estimation Error
54
55	Your win rate estimate from 100 trades has a standard error of roughly ±5%. If your true win rate is 55% but you estimate 60%, full Kelly will overbets by ~50%, which reduces long-term growth below what half Kelly would achieve.
56
57	### 2. Variance and Drawdowns
58
59	Full Kelly has extremely high variance. Expected maximum drawdown for full Kelly is roughly 50-80% of account. This is psychologically devastating and practically dangerous (margin calls, inability to continue trading).
60
61	\| Kelly Fraction \| Relative Growth Rate \| Approximate Max Drawdown \|
62	\|---------------\|---------------------\|-------------------------\|
63	\| 1.0x (full) \| 100% \| 50-80% \|
64	\| 0.5x (half) \| ~75% \| 25-40% \|
65	\| 0.25x (quarter)\| ~50% \| 12-20% \|
66	\| 0.1x (tenth) \| ~25% \| 5-10% \|
67
68	### 3. Asymmetry of Over vs. Under Betting
69
70	Overbetting by 2x (betting at 2f) produces zero long-term growth — the same as not trading at all. Underbetting by 2x (betting at 0.5f) still captures ~75% of the optimal growth rate. The penalty for overbetting is catastrophically worse than for underbetting.
71
72	### Recommended Fractions
73
74	\| Fraction \| When to Use \|
75	\|----------\|------------\|
76	\| 0.10x Kelly \| Very uncertain edge, new strategy, < 30 trades in sample \|
77	\| 0.25x Kelly \| Moderate confidence, 30-100 trades, reasonable Sharpe \|
78	\| 0.50x Kelly \| High confidence, 100+ trades, consistent performance \|
79	\| 1.00x Kelly \| Never recommended in practice \|
80
81	---
82
83	## Estimating Your Edge
84
85	Kelly requires two inputs: win rate (`p`) and payoff ratio (`b`). Both must be estimated from data.
86
87	### Minimum Data Requirements
88
89	- 50 trades minimum for any Kelly calculation. Below this, estimation error dominates.
90	- 100+ trades preferred for half Kelly sizing.
91	- 200+ trades before considering aggressive fractions.
92
93	### Calculation from Trade History
94
95	```python
96	wins = [t for t in trades if t > 0]
97	losses = [t for t in trades if t < 0]
98
99	win_rate = len(wins) / len(trades) # p
100	payoff_ratio = mean(wins) / abs(mean(losses)) # b
101	edge = win_rate * payoff_ratio - (1 - win_rate) # should be > 0
102
103	kelly_full = (win_rate * payoff_ratio - (1 - win_rate)) / payoff_ratio
104	```
105
106	### Conservative Estimation
107
108	Use the lower bound of a Wilson confidence interval for win rate rather than the point estimate:
109
110	```python
111	import math
112
113	def wilson_lower(wins: int, total: int, z: float = 1.96) -> float:
114	"""Lower bound of Wilson score interval (95% confidence)."""
115	p = wins / total
116	denominator = 1 + z**2 / total
117	centre = p + z*2 / (2 total)
118	spread = z * math.sqrt((p * (1 - p) + z*2 / (4 total)) / total)
119	return (centre - spread) / denominator
120	```
121
122	Using the lower bound of the confidence interval for win rate automatically builds in conserva

agiprolabsPublisher · 61 listings

Preview

agiprolabs/claude-trading-skills

# Kelly Criterion — Optimal Bet Sizing

The Kelly criterion is the mathematically optimal bet size that maximizes long-term geometric growth of capital. Developed by John Kelly at Bell Labs in 1956, i

**Core insight**: Betting too small leaves growth on the table. Betting too large increases ruin risk and actually *reduces* long-term growth. Kelly finds the e

**Practical insight**: You should almost never use full Kelly. Estimation error in your edge means full Kelly will overbets in practice. Use fractional Kelly (0

Repoagiprolabs/claude-trading-skills

LicenseMIT

TypeSkills

CategoryFinance

UpdatedJun 2026

Repo stars235

First seenJul 22, 2026

People who liked this also viewed

6 picks

Type

kelly-criterion

243installs53forks

View on GitHub

How to install kelly-criterion?

agiprolabs/claude-trading-skills/kelly-criterion

$npx -y skills add agiprolabs/claude-trading-skills --skill kelly-criterion

Installs into the current project.

Summary

Kelly criterion optimal sizing with fractional variants, edge estimation, and practical application for crypto trading

Files · 1

View on GitHub

SKILL.md

1	# Kelly Criterion — Optimal Bet Sizing
2
3	The Kelly criterion is the mathematically optimal bet size that maximizes long-term geometric growth of capital. Developed by John Kelly at Bell Labs in 1956, it answers a precise question: given a known edge, what fraction of your bankroll should you risk to maximize the compounding rate?
4
5	Core insight: Betting too small leaves growth on the table. Betting too large increases ruin risk and actually reduces long-term growth. Kelly finds the exact optimum between these extremes.
6
7	Practical insight: You should almost never use full Kelly. Estimation error in your edge means full Kelly will overbets in practice. Use fractional Kelly (0.25x to 0.5x) for real trading.
8
9	---
10
11	## The Kelly Formula
12
13	For a binary outcome (win or lose):
14
15	```
16	f* = (p * b - q) / b
17	```
18
19	Where:
20	- `f*` = optimal fraction of bankroll to bet
21	- `p` = probability of winning
22	- `q` = probability of losing (1 - p)
23	- `b` = payoff ratio (average win / average loss)
24
25	Equivalent forms:
26
27	```
28	f* = p - q / b
29	f* = p - (1 - p) / b
30	f* = (p * b - (1 - p)) / b
31	```
32
33	Edge = `p * b - q` = expected value per unit risked. Kelly only makes sense when edge > 0. If edge is zero or negative, the optimal bet is zero — do not trade.
34
35	### Quick Reference
36
37	\| Win Rate \| Payoff 1:1 \| Payoff 1.5:1 \| Payoff 2:1 \| Payoff 3:1 \|
38	\|----------\|-----------\|-------------\|-----------\|-----------\|
39	\| 40% \| -20% \| -6.7% \| 10% \| 20% \|
40	\| 45% \| -10% \| 3.3% \| 15% \| 25% \|
41	\| 50% \| 0% \| 16.7% \| 25% \| 33.3% \|
42	\| 55% \| 10% \| 18.3% \| 27.5% \| 35% \|
43	\| 60% \| 20% \| 26.7% \| 35% \| 40% \|
44
45	Values are full Kelly fraction. In practice, use 0.25x to 0.5x of these numbers.
46
47	---
48
49	## Why Use Fractional Kelly
50
51	Full Kelly assumes you know `p` and `b` exactly. You never do. Here is why fractional Kelly is essential:
52
53	### 1. Estimation Error
54
55	Your win rate estimate from 100 trades has a standard error of roughly ±5%. If your true win rate is 55% but you estimate 60%, full Kelly will overbets by ~50%, which reduces long-term growth below what half Kelly would achieve.
56
57	### 2. Variance and Drawdowns
58
59	Full Kelly has extremely high variance. Expected maximum drawdown for full Kelly is roughly 50-80% of account. This is psychologically devastating and practically dangerous (margin calls, inability to continue trading).
60
61	\| Kelly Fraction \| Relative Growth Rate \| Approximate Max Drawdown \|
62	\|---------------\|---------------------\|-------------------------\|
63	\| 1.0x (full) \| 100% \| 50-80% \|
64	\| 0.5x (half) \| ~75% \| 25-40% \|
65	\| 0.25x (quarter)\| ~50% \| 12-20% \|
66	\| 0.1x (tenth) \| ~25% \| 5-10% \|
67
68	### 3. Asymmetry of Over vs. Under Betting
69
70	Overbetting by 2x (betting at 2f) produces zero long-term growth — the same as not trading at all. Underbetting by 2x (betting at 0.5f) still captures ~75% of the optimal growth rate. The penalty for overbetting is catastrophically worse than for underbetting.
71
72	### Recommended Fractions
73
74	\| Fraction \| When to Use \|
75	\|----------\|------------\|
76	\| 0.10x Kelly \| Very uncertain edge, new strategy, < 30 trades in sample \|
77	\| 0.25x Kelly \| Moderate confidence, 30-100 trades, reasonable Sharpe \|
78	\| 0.50x Kelly \| High confidence, 100+ trades, consistent performance \|
79	\| 1.00x Kelly \| Never recommended in practice \|
80
81	---
82
83	## Estimating Your Edge
84
85	Kelly requires two inputs: win rate (`p`) and payoff ratio (`b`). Both must be estimated from data.
86
87	### Minimum Data Requirements
88
89	- 50 trades minimum for any Kelly calculation. Below this, estimation error dominates.
90	- 100+ trades preferred for half Kelly sizing.
91	- 200+ trades before considering aggressive fractions.
92
93	### Calculation from Trade History
94
95	```python
96	wins = [t for t in trades if t > 0]
97	losses = [t for t in trades if t < 0]
98
99	win_rate = len(wins) / len(trades) # p
100	payoff_ratio = mean(wins) / abs(mean(losses)) # b
101	edge = win_rate * payoff_ratio - (1 - win_rate) # should be > 0
102
103	kelly_full = (win_rate * payoff_ratio - (1 - win_rate)) / payoff_ratio
104	```
105
106	### Conservative Estimation
107
108	Use the lower bound of a Wilson confidence interval for win rate rather than the point estimate:
109
110	```python
111	import math
112
113	def wilson_lower(wins: int, total: int, z: float = 1.96) -> float:
114	"""Lower bound of Wilson score interval (95% confidence)."""
115	p = wins / total
116	denominator = 1 + z**2 / total
117	centre = p + z*2 / (2 total)
118	spread = z * math.sqrt((p * (1 - p) + z*2 / (4 total)) / total)
119	return (centre - spread) / denominator
120	```
121
122	Using the lower bound of the confidence interval for win rate automatically builds in conserva

agiprolabsPublisher · 61 listings

Preview

agiprolabs/claude-trading-skills

# Kelly Criterion — Optimal Bet Sizing

The Kelly criterion is the mathematically optimal bet size that maximizes long-term geometric growth of capital. Developed by John Kelly at Bell Labs in 1956, i

**Core insight**: Betting too small leaves growth on the table. Betting too large increases ruin risk and actually *reduces* long-term growth. Kelly finds the e

**Practical insight**: You should almost never use full Kelly. Estimation error in your edge means full Kelly will overbets in practice. Use fractional Kelly (0

Repoagiprolabs/claude-trading-skills

LicenseMIT

TypeSkills

CategoryFinance

UpdatedJun 2026

Repo stars235

First seenJul 22, 2026

People who liked this also viewed

6 picks

Type