To double an account from $10,000 to $20,000 with a 5% risk per trade and different risk-reward ratios (1:2 and 1:3), we need to consider the number of winning trades required.

Here’s how to calculate it:

Initial Account Balance: $10,000 Target Account Balance: $20,000 Risk per Trade: 5% of account balance

1. Calculate the Risk Amount per Trade: The dollar amount risked per trade will change as the account balance grows.

2. Number of Doubling Periods (for a rough estimate): To go from $10,000 to $20,000 is one doubling.

3. Analyze with Different Risk-Reward Ratios:

Scenario A: Risk-Reward Ratio 1:2

• Meaning: For every $1 risked, you aim to gain $2.

• Win Rate for Break-Even: With a 1:2 risk-reward, you need to win at least 33.33% of your trades to break even (1 win for every 2 losses).

• Profit per Winning Trade (as a percentage of risk): If you risk 5%, a 1:2 win means you gain 10% of the risked amount.

• Approximate Number of Trades: This is where it gets more complex due to compounding. We’re not looking for a specific number of trades to reach a fixed percentage gain, but rather to double the account.

Let’s approach this from the perspective of overall percentage gain needed. To double your account, you need a 100% return on your initial $10,000.

Using the concept of “R-multiples”: If your risk is 1R, and your reward is 2R, then each winning trade nets you 2R. To make $10,000 profit from an initial $10,000, you need to gain $10,000. If 1R = 5% of $10,000 = $500, then 2R = $1,000. So, each winning trade (at 1:2) is approximately $1,000. You would need approximately $10,000 / $1,000 = 10 winning trades if each trade started from the initial balance.

However, since the risk amount changes with the account balance (5% of a growing balance), the profit per trade will also increase. This means you might need fewer winning trades than a simple division suggests.

Scenario B: Risk-Reward Ratio 1:3

• Meaning: For every $1 risked, you aim to gain $3.

• Win Rate for Break-Even: With a 1:3 risk-reward, you need to win at least 25% of your trades to break even (1 win for every 3 losses).

• Profit per Winning Trade (as a percentage of risk): If you risk 5%, a 1:3 win means you gain 15% of the risked amount.

• Approximate Number of Trades: If 1R = $500, then 3R = $1,500. You would need approximately $10,000 / $1,500 = 6.67 winning trades if each trade started from the initial balance. Again, with compounding, this number could be slightly lower.

Important Considerations and Nuances:

• Compounding: As your account grows, 5% of the new balance is a larger dollar amount. This means each subsequent winning trade (if you maintain the 5% risk) will yield a higher dollar profit, accelerating your progress towards the $20,000 goal.

• Losses: The above calculations assume only winning trades or a perfect sequence of wins. In reality, you will experience losses.

• Win Rate: Your actual win rate is crucial. A higher win rate will get you to your goal faster.

• Drawdowns: Even with a profitable system, you will experience drawdowns (periods where your account balance decreases). Managing these is key to reaching your target.

• Trade Frequency: How often you trade will affect the time it takes to reach your goal.

• Trading Strategy: The effectiveness of your trading strategy in identifying high-probability trades with your desired risk-reward ratio is paramount.

In summary, to double your account from $10,000 to $20,000 with a 5% risk per trade:

• With a 1:2 Risk-Reward Ratio: You would likely need around 6 to 10 net winning trades, depending on the sequence of wins and losses and the effect of compounding.

• With a 1:3 Risk-Reward Ratio: You would likely need around 4 to 7 net winning trades, again, depending on the sequence and compounding.

These are estimations. The actual number of trades will depend on your specific trading performance, including your win rate and the sequence of your wins and losses. It’s more about the accumulated R-multiples (R=Risk per tradeProfit​) needed to reach the target profit, rather than a fixed number of trades in isolation.