Bug in the How To Trade script?

[alisalama]

Really like your work. Super interesting stuff and largely aligns with how I see trading. Nice stuff!

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https://github.com/romanmichaelpaolucci/Quant-Guild-Library/blob/6a2ccea4ac4a176ab7a39dff7ae3041ac270ff0d/2025 Video Lectures/22. How to Trade/how_to_trade.ipynb#L256

As per youtube comment on https://www.youtube.com/watch?v=NqOj__PaMec, I think there is an issue in the "One Quant Trader " game.

1. It seems to play for too long after the Probability has dropped below 50% and not lose enough.
2. It also seems to pretty much always win when above 50% - so when Expected Probability = 1 it always wins.

Can see it at 9:35, it continues to play and win all the way up to step 400, whereas clearly the average past about 180 is below 50% and so it should lose for a bit and stop around 210. Can see similar behaviour in a lot of the others too.

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I think this is the error you are returning the wealth_path from dynamic_probability_game, but then re-naming it returns, presumably by accident.

And so I think you are doing "prev_outcomes = (returns[t-window_size:t] > 0).astype(int)" where returns = last 30 cumulative returns, not individual last 30 flips.

def dynamic_probability_game(n_steps):
    ...
    return wealth_path, probabilities;

def adaptive_strategy(n_steps, window_size=30):
    """Simulate game with adaptive probability estimation."""
    returns, true_probs  = dynamic_probability_game(n_steps)

So you just need to change:

return wealth_path, probabilities;

to

return returns, probabilities