Roulette Odds Comparison Analysis

I need a clear, well-structured breakdown of the true probabilities for every standard wager on both the European (single zero) and American (double zero) roulette wheels. My goal is to see, side-by-side, how the house edge shifts for each game and bet type so I can make more informed choices at the table.

What I expect from you
• One concise odds table that lists single-number, split, street, corner, dozen, column, red/black, odd/even, and high/low bets, displaying:
– payout ratio,
– exact probability of winning, and
– resulting house edge for each wheel version.
• A short commentary highlighting the key differences between European and American layouts and pointing out which wagers carry the smallest and largest disadvantage.
• Calculations shown or cited so I can follow your method (simple Excel sheet or clear step-by-step notes are fine).

Accuracy is crucial, so please base every figure on the standard 37-number European wheel and 38-number American wheel. If you normally work in R, Python, Excel, or similar tools, just let me know which one you’ll use; I’m flexible as long as the final numbers are correct and easy to read.

Once delivered, I’ll give quick feedback and we can make any tiny tweaks that pop up.