Texas Hold'em Bonus

Hi wizard/s,

I'm a complete dunce when it comes to working with odds and probabilities so was hoping to pick the brains of those with more insight.
I have an idea to introduce a "bad luck" bonus bet to Texas Hold'em Bonus where a player achieves a Royal Flush on the turn or the river, whereby missing the 100% jackpot payout, and only earning the same pay out as any winning hand of a flush or higher. The payout would still require an eligible jackpot wager and would come from the jackpot pool but would be minimal and a fixed amount. e.g. $500.
My questions to you are, would this be a viable payout, odds wise? And would the suggested amount change/be impacted by the probability?
I currently work in the industry, and the Jackpot payout on our Texas Bonus game has reach $1,000,000 (with a $5 jackpot bet) this has made the game a popular talking point, but also quite formidable, and our patronage has stagnated somewhat.

All advice or feedback would be greatly appreciated!
Cheers

Quote: SpennyJ

My questions to you are, would this be a viable payout, odds wise? And would the suggested amount change/be impacted by the probability?
I currently work in the industry, and the Jackpot payout on our Texas Bonus game has reach $1,000,000 (with a $5 jackpot bet) this has made the game a popular talking point, but also quite formidable, and our patronage has stagnated somewhat.

All advice or feedback would be greatly appreciated!
Cheers

Okay, so essentially, this would be a Royal Flush in seven cards, but not the first five.

That seems simple enough to me, the first thing you want to do is look at the probability of a Royal Flush in seven cards:

0.0032% (per Wikipedia)

Subtract from that the probability of getting it in five cards:

(20/52 * 4/51 * 3/50 * 2/49 * 1/48) = 0.00000153907 or .000153907%

.0032 - .000153907 = 0.003046093

Okay, so you want to pay $500 when this happens:

.003046093 * 500 = 1.5230465

That means the actual cash value of that addition is $1.5230465 per hand played.

The percentage that you are subtracting from the cumulative house edge just depends upon how much is being bet, but I'm guessing that is way too big of a payout to be offering on this thing. On a $20 total bet, the value of the seven-card Royal proposition is over 7.5% of the total amount bet by itself.

If you only need to bet $5 to unlock that $500 potential, then the return just on that $500 payout is right around 30.5%.

ADDED: Am I hired? At $100/hour, that would have only cost you about twenty bucks. (Kidding)

Thanks heaps Mission146,

Hiring is above my pay grade sadly, but considering I can't crunch numbers very successfully its probably for the best.
Are you ok if i quote your response directly in a proposal to my managers?

Quote: SpennyJ

Thanks heaps Mission146,

Hiring is above my pay grade sadly, but considering I can't crunch numbers very successfully its probably for the best.
Are you ok if i quote your response directly in a proposal to my managers?

No need to thank me, my work is its own reward. Just kidding, you're quite welcome!

You may quote my response directly in a proposal to your managers.

Mission, in the analysis, you went from 0.0032% to 0.0032, essentially introducing an error by a factor of 100. You need to divide your calculated return by a factor of 100.

Hi Gordon,
Can you explain how they are different?
Please forgive my ignorance I have never had an affinity for this type of maths hence why I posted originally.
Thanks

Quote: gordonm888

Mission, in the analysis, you went from 0.0032% to 0.0032, essentially introducing an error by a factor of 100. You need to divide your calculated return by a factor of 100.

Great catch! Maybe I should have taken a few more minutes.

Just divide all results by 100 and it’s fine. I forgot to convert from percentage to proper decimal on the seven card probability is the problem.

In short, it doesn’t add 30.5% (roughly) to a $5 bet, it adds about 0.305%.

Quote: SpennyJ

Hi Gordon,
Can you explain how they are different?
Please forgive my ignorance I have never had an affinity for this type of maths hence why I posted originally.
Thanks

When you convert a percentage to a decimal, the decimal place slides two to the left.

So, 1% becomes .01.

When converting from a decimal to a percentage, the decimal place moves to the right.

.01 becomes 1%.

Anyway, my procedure and math were otherwise right, I just forgot to move the decimal place when I converted the percentage on a seven card Royal to a decimal. Just an oversight. That’s what you get when I’m working free...JK

I knew that didn’t look right for a Royal...lol