Odds of Royal Flush and Straight Flush Occurring in the Same Game

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Rhoako

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Hello.

I would like to begin by stating that my intent with this post is not to brag about the situation that occurred. I would merely like to know if anyone is able to calculate the odds of this particular situation occurring. I also apologize if this is an inappropriate forum in which to make this post. It seemed like the most appropriate place to me.

Last night, my friend and I played a game of heads-up NL Texas Hold'em. In this game, my friend got a Royal Flush in clubs. A few hands later, I got a Straight Flush 5-9, also in clubs. We played approximately 15 to 20 hands before the game ended.

Does anyone have the statistical knowledge required to be able to calculate the odds of both a Royal Flush and a Straight Flush occurring in the same game, and if so, would you mind providing me with the odds? Not the odds of each hand occurring on its own, but the odds of both hands showing up in the same game of heads up poker involving 15 to 20 hands.

Thank you in advance.
 
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