Probability Formula

At https://wizardofodds.com/videopoker/tables/deuceswild.html it shows the probability of getting a natural royal is 0.000022. I assume this means playing perfect strategy. For a blog post, I am trying to make sure the correct formula for ascertaining the chances of never hitting the natural royal is then 1 minus 0.000022 to the power of the number of trials. For 38,000 trials I get 0.43343683785456. This using the calculator at http://web2.0calc.com/.  Am I on the right track?

Quote: odiousgambit

At https://wizardofodds.com/videopoker/tables/deuceswild.html it shows the probability of getting a natural royal is 0.000022. I assume this means playing perfect strategy. For a blog post, I am trying to make sure the correct formula for ascertaining the chances of never hitting the natural royal is then 1 minus 0.000022 to the power of the number of trials. For 38,000 trials I get 0.43343683785456. This using the calculator at http://web2.0calc.com/.  Am I on the right track?

Yes, you're on the right track. I agree with you calculation.

To increase the accuracy of your final answer, instead of using 0.000022 you may use 440202756/19933230517200, which is the ratio of the number of ways of getting a natural royal to the total combinations.

Quote: ChesterDog

you may use 440202756/19933230517200, which is the ratio of the number of ways of getting a natural royal to the total combinations.

thanks!

how is that such a known set of numbers? the WoO seems to have had to calculate something different for each game.

Quote: odiousgambit

...how is that such a known set of numbers? the WoO seems to have had to calculate something different for each game.

For each different poker game, the Wizard's computer program would count the number of ways of getting each payout. See the Wizard's "Methodology" section of the deuces wild page you cited. If I understand it correctly, the program cycles through all 2,598,960 possible Deuces Wild hands, calculates the EV of each of the 32 ways to play, and chooses the best play for that hand. After each hand, the program updates the sums of the ways of getting each payout and then goes to the next hand.

It is important to note that this is not the same as, "Do whatever it takes to get a royal", which could involve dropping pat hands to pursue suited pictures. This strategy would produce the most royals, but will lose more money if you don't hit it early, as you drop smaller paying hands.