Simulate a script and show me a graph of the following betting strategy:
The model follow a strategy that predict the odds with 79.27 accuracy, following a half kelly criterion, if i start my bankroll with 1000$ how much will i have after 1000 bets?

Here is the graph of the simulated bankroll over time using the half Kelly criterion strategy:

### Results Summary:
- Initial Bankroll: $1000
- Number of Bets: 1000
- Probability of Winning: 79.27%
- Odds: 2 (even money)
- Kelly Fraction: 0.2927 (half Kelly)

The graph shows the evolution of the bankroll over 1000 bets, demonstrating how the bankroll grows over time following the half Kelly strategy with the given parameters.

### Next Steps:
Would you like more details on the simulation or have any questions?

Here are 8 related questions to further explore the topic:

1. How would the bankroll change if the odds were different (e.g., 1.5 or 3)?
2. What would the effect be of using a full Kelly criterion instead of a half Kelly criterion?
3. How would a different probability of winning affect the bankroll growth?
4. What are the risks associated with using the Kelly criterion for betting strategies?
5. How does the half Kelly strategy compare to other betting strategies (e.g., flat betting)?
6. How would the results change with a different initial bankroll?
7. Can we analyze the variance of the bankroll over multiple simulations?
8. How does the bankroll progression look for a longer or shorter betting period (e.g., 500 or 2000 bets)?

### Tip:
Always consider the risk of ruin and potential for bankroll volatility when employing any betting strategy, and remember that past performance does not guarantee future results.

Explore the simulation of a betting strategy using the half Kelly criterion with an initial bankroll of $1000. Analyze the growth of the bankroll over 1000 bets with a 79.27% probability of winning. Includes a graph showing the evolution of the bankroll over time.

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