Return On Dealt Royal Flush Progressives

[Kshman]

Does anyone know how to calculate the return on dealt royal flush progressive machines?For example:I play a 5 play 9/6 Jacks or Better machine at 50 cents ($2.50/hand = $12.50 per spin).Normally a dealt royal on this machine would be $10,000 (5 hands at $2000/each). But the progressive often goes as high as $18,000-$20,000 for a dealt royal flush. The calculation is different than a single hand progressive because the royal must be dealt to receive the progressive jackpot.Any ideas: 99.54% + ?Thanks.

[Jstark]

https://wizardofodds.com/games/video-po ... alculator/

Just change the royal or any other progressive numbers. It'll give you the return and optimal strategy.

[Kshman]

https://wizardofodds.com/games/video-po ... alculator/

Just change the royal or any other progressive numbers. It'll give you the return and optimal strategy. I appreciate your willingness to help jstark. Unfortunately, I do not think the wizard's strategy calculator will work for my question. I know how to calculate Jacks or Better with a progressive royal.For example: an estimated 100% return for quarters would be a royal at $1,220 rather than $1000 (99.54%).  But the progressive royal for my situation has to be dealt and I believe the math is different.I don't think it is as easy as figuring $12.50 a hand would equal a $10,000 royal and the 100% EV point would be a $12,200 royal. That would work for a single hand game where it does not matter if the royal is dealt. If that was the case, my play would have an EV of somewhere around 102.5% (which is not the case).It is a complicated question and I appreciate your post.

[Jstark]

Ok. I missed the part about a dealt royal.

[dw44]

Per google the odds of a dealt royal are 649,740:1.

9/6 JoB returns .9954 per unit wagered, holding .0046.

The break-even progressive size would be:

(1/649,741)*x = .0046

which comes out to 2988.8 units.


Since you're wagering $2.50 per hand you need a progressive jackpot of $7.472 to be break-even.

For each additional $2,500 you gain an EV of .00154 units.


I'm not a math person, does that look right?

[Kshman]

A break even point (100% EV) on a 50 cent game (2.50/hand) would be $2,440 on a single line game. $12,200 on a 5 play.But this is 5 play 9/6 Jacks or Better that only gives the progressive on a dealt royal. It is another kind of calculation. We probably need Bob Dancer to answer this one. I am a fairly experienced player that has come out ahead most years. But this is a calculation beyond my knowledge. I appreciate the post dw44. I rarely post here because there seems to be a lot of weird posts with people arguing about nonsense (math, machines being rigged). I am just trying to help and ask for help. I am grateful for your effort. The machines aren't rigged and if you have the brain power, patience, and rigor you can at least break even. If you lose, you are playing negative machines badly. Why would anyone play TDB and expect to have an edge? Have fun but also respect that this game is an art. Or it can be if you want to participate on another level.

[billryan]

It is on a five play so one dealt Royal becomes five.
Are you giving the total payout for all five or just one royal?
Does it matter in the math? Shouldn't the math be

(5/649,741) instead of (1/649,741)

You are only hitting one royal but get paid for five. Yes?

[Kshman]

It is on a three play so one dealt Royal becomes three.
Are you giving the total payout for all three or just one royal?
Does it matter in the math? Shouldn't the math be

(3/649,741) instead of (1/649,741)

You are only hitting one royal but get paid for three. Yes?
The game is a 5 play. The same 1/649,741 applies but you are paid for 5. I am trying to figure out what the +EV is in this situation. So the dealt royal would normally yield $10,000 on a 5 play (2.50/hand). But what happens when that dealt royal pays $18,000? 

[dw44]

I missed a couple of points. One was the 5-line versus single-line, the other was that the jackpot does not stack on top of the normal royal payoff but rather replaces it.

I think the first point just means that any per hand EV calculations require us to chop the jackpot five ways. The second point requires us to look at the surplus value of the jackpot over the standard return.

So the relevant figure here is ((progressive jackpot - $10,000) / 5).

This gives us the $ per hand surplus over the standard paytable when we hit a royal.

We then divide that surplus by 649,741 to get the extra expected value per hand.

We then divide that figure by $2.50 to get the extra unit value per hand.


So working in reverse to find the break-even point at 9/6 we need an extra .0046 units per hand.

At $2.50 per hand that equals an extra $.0115 per hand.

Since we only get dealt royals 1/649,741th of the time that means $7,472.0215 extra per royal.

Since the jackpot will be split across all five of our identical royals, that means an aggregate surplus of $37,360.1075 per 10-line $25 pull.

Since the normal royal payoff here is $10,000, that means a total jackpot of $47,360.10 gets us break-even.

Does that seem right?

[Kshman]

[QUOTE] Since the normal royal payoff here is $10,000, that means a total jackpot of $47,360.10 gets us break-even.

Does that seem right?[/QUOTE] The game returns 99.54% if the progressive was not in place. $47,360.10 seems really high for a +.46% EV on the dealt royal. I'm considering that $2,440 would be a break even point on a single line .50 game. It is a hard question. I appreciate your effort.