4 to a royal in jacks or better vp

[SilentBob420BMFJ]

i found this in the wizards faqs..

I started to play $5 single-line Jacks or Better recently. Since I started the number of times I have had four to a royal after the draw is 170, while my number of royals is zero. What are the odds of this? – Steve from Oxnard

In 9/6 Jacks or Better with perfect strategy you will see a royal on the draw once every 40,601 hands, but four to a royal once every 460 hands. For every royal you see, you will be one card away 88.33 times. Of the four to a royal hands, 50.37% will pay nothing, 24.89% will pay as a pair, 7.89% as a straight, 16.16% as a flush, and 0.69% as a straight flush. Here are the exact numbers.

Possible Outcomes in 9/6 Jacks or Better
Hand Combinations Probability
Four to royal + straight flush 299529168 0.000015
Four to royal + flush 7005972000 0.000351
Four to royal + straight 3420857076 0.000172
Four to royal + pair 10793270244 0.000541
Four to royal (non-paying) 21844510692 0.001096
Royal flush 490952388 0.000025
All other 19889375425632 0.9978
Total 19933230517200 1

The expected number of royals for 170 four to a royals is 170/88.33 = 1.92. The probability of seeing zero with a mean of 1.92 is e-1.92 = 14.59%.


im confused because your chance of getting a royal when you draw to a 4 card royal is exactly 1 in 47 (52 cards in a deck, 5 are gone, so 47 left, and you are only drawing 1 card, and only 1 card will make that royal), so why wouldnt you get 1 royal for every 47 draws to a 4 card royal, thus meaning that you should get 3.62 royals for every 170 four to a royal? above he says you would get 1.92 royals for every 170 four to a royals, which doesnt make sense.. i know im the vp guy, but can anybody make sense of this? i think im misunderstanding the question, and i think the wizard misunderstood the guys question..

[miplet]

Originally Posted by SilentBob420BMFJ

i found this in the wizards faqs..
....
Since I started the number of times I have had four to a royal after the draw is 170, while my number of royals is zero...

I bolded the important part of the question. He has 4 to a royal after drawing cards. In some of the times he may have had 3 (or less) to a royal before drawing, and ended up with 4 to the royal, but not all 5.

[SilentBob420BMFJ]

Originally Posted by miplet

I bolded the important part of the question. He has 4 to a royal after drawing cards. In some of the times he may have had 3 (or less) to a royal before drawing, and ended up with 4 to the royal, but not all 5.

ya, i knew i wasnt seeing something.. you should get a royal once every 47 draws with 4 to a royal, and once every 1081 hands with 3 to a royal.. people should be aware of these numbers, because it seems people think they have like a 1 in 10 shot or something when they have 4 to a royal with the way they act