### Strategy Analysis and Grouping Calculation
#### Strategy One: Fixed Daily Investment of 20 Yuan
- Rule: Divide 600 yuan evenly over 30 days, investing 20 yuan each day, profit-loss ratio 1:1, win rate 90%.
- Daily expected revenue:
\[
(0.9 \times 20) + (0.1 \times -20) = 16 \ \text{yuan}
\]
- Monthly total expected revenue:
\[
16 \times 30 = 480 \ \text{yuan}
\]
---
#### Strategy Two: Grouped Compound Interest Strategy
- Rule: Divide 600 yuan into several groups, with equal principal for each group. If there is a loss on any day within a group, stop immediately and lose the principal of that group; if profitable, roll over the profit + principal into the next trade.
- Key Logic:
- Each group trades for \(n\) days, success requires continuous profit for \(n\) days, failure probability decreases exponentially with days, but profit increases exponentially with days.
- Expected revenue formula (each group \(X\) yuan, for \(n\) days):
\[
\text{Expected Revenue} = X \cdot \left[ (1.8)^n -1 \right]
\]
Where \(1.8 = 0.9 \times 2\) (win rate 90% + profit-loss ratio 1:1).
---
### Group Optimization and Revenue Comparison
1. Grouping for 3 days:
- Initial principal for each group \(X = 60\) yuan (divided into 10 groups), expected revenue:
\[
60 \cdot \left(1.8^3 -1\right) = 60 \cdot 4.832 = 289.92 \ \text{yuan/group}
\]
- Total revenue: \(289.92 \times 10 = 2,\!899.2\) yuan.
2. Grouping for 5 days:
- Initial principal for each group \(X = 100\) yuan (divided into 6 groups), expected revenue:
\[
100 \cdot \left(1.8^5 -1\right) = 100 \cdot 17.896 = 1,\!789.6 \ \text{yuan/group}
\]
- Total Revenue: \(1,\!789.6 \times 6 = 10,\!737.6\) yuan.
3. Grouping for 6 days:
- Initial principal for each group \(X = 120\) yuan (divided into 5 groups), expected revenue:
\[
120 \cdot \left(1.8^6 -1\right) = 120 \cdot 33.18 = 3,\!981.6 \ \text{yuan/group}
\]
- Total revenue: \(3,\!981.6 \times 5 = 19,\!908\) yuan.
---
### Conclusion
1. Strategy Selection:
Strategy Two (Grouped Compound Interest) significantly outperforms Strategy One. Taking a 5-day group as an example, the expected revenue reaches 10,737 yuan, far exceeding the 480 yuan of Strategy One.
2. Optimal grouping:
- Recommended to divide into 6 groups, each group for 5 days, initial principal 100 yuan.
- Reason: Achieving a balance between revenue and risk (highest expected revenue with reasonable grouping).
- Extreme grouping (e.g., 1 group for 30 days) has a higher mathematical expectation, but the actual success rate is only 4.2%, making the risk uncontrollable.
---
Answer:
1. Choose Strategy Two, the expected revenue is much higher than the fixed strategy.
2. Best grouping: divide into 6 groups, each group for 5 days, initial principal 100 yuan, expected profit about 10,700 yuan.