Straight Flush/Royal Flush bonus

[Bulldog]

We've got a bonus in my home game for straight flushes and royal flushes. We set it up that everybody puts a quarter in the jar every time they play, and a straight flush takes the jar. (We had only had one in about nine months of once or twice weekly 2-4 hour NL tourneys.) Of course, in the first and second game after starting the jar, we had straight flushes in each.

So we changed it up to the following: straight flush takes $5 from the jar, royal takes the jar. I'm trying to figure how often the bonuses will be hit. Here's my raw (estimated) data:

hands/hr: 20
average tourney hours: 3.5
hands per tourney: 70
average players/hand: 7
average starting hands per tourney: 500

Of any seven cards, odds of a royal: 30940:1
Of any seven cards, odds of a SF (non-royal): 3216:1

Without taking folds into consideration, we should have a non-royal SF once per 6 or 7 tourneys and a royal once every 60 tourneys, correct?

Now how do I factor in the folds?

My next calculation will be what the average royal jackpot will be. If we have 10 players per tourney, the jackpot will grow $2.50 per. If we go 60 tourneys until the royal, there will be $150 in there less the $50 paid to the 10 SFs hit, or $100, yes?

[hotquietday]

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Now how do I factor in the folds?

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Unfortunately there is no way to do this without either running a simulation or having a lot of empirical evidence (which amounts to the same thing). The reason, of course, is that the answer depends on how people are playing. At a table full of maniacs you will see more straight flushes than you would at a table full of extremely tight players.

To get an estimate, you'd need to create a computer lineup of players to approximate the play at your game, and then simulate it. TTH has this capability, but I wasn't able to find the data to answer your question in the output of the simulation (TTH simulations are actually quite limited).

HTH,
John

[magiluke]

Now if I have a royal flush, and everyone folds to me (like they always do when I have one), do I still win the jar?

Actually, that sounds like a good idea, and I might think about trying to implement it somehow...

[Bulldog]

We were looking for something fun to add to the games and everyone likes this so far. We did settle the rules of winning when one guy rabbit-hunted the turn and river and would've had a SF. He asked for his five bucks and got shouted down by everyone else in the game, so that was easy. We agreed that if you have it and everyone folds, you can show it and win, but you can't get it on a rabbit hunt. Also, nobody wins if the SF is on the board unless you have a higher SF.

[Bulldog]

Thanks, I was already assuming this was the response but I thought I'd throw it out there. We have pretty loose games so I'm expecting a SF once every ten games or so.