RationalSkeptic
• Posts: 3
Joined: Jun 20, 2021
June 20th, 2021 at 12:25:50 PM permalink
This recently happened to me. Was playing a 100 play 9/5 JoB machine, held three to a Royal, and got 3 royals. Most times I don’t even get 1. Curious what the odds are of this happening. Thanks in advance.

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CrystalMath
• Posts: 1911
Joined: May 10, 2011
June 20th, 2021 at 4:28:07 PM permalink
About 1 in 8355 to get 3 or more.
I heart Crystal Math.
Wizard
• Posts: 26619
Joined: Oct 14, 2009
June 20th, 2021 at 5:06:59 PM permalink
The chances of a royal on any one hand is 1/combin(47,2) = 1/1081.

The chances of getting exactly three in 100 hands is combin(100,3)*(1/1081)^3*(1080/1081)^97 = 1 in 8545.85.
"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)
RationalSkeptic
• Posts: 3
Joined: Jun 20, 2021
June 20th, 2021 at 7:35:43 PM permalink
Thank you! I thought it was pretty unusual. The next day I also hit 2 royals on the same machine with 3 to a Royal dealt. Seems a bit “rigged” but this is in Vegas so it should be random chance rather than the virtual lottery machines in other states.
DRich
• Posts: 11889
Joined: Jul 6, 2012
June 21st, 2021 at 7:21:15 AM permalink
Quote: RationalSkeptic

Thank you! I thought it was pretty unusual. The next day I also hit 2 royals on the same machine with 3 to a Royal dealt. Seems a bit “rigged” but this is in Vegas so it should be random chance rather than the virtual lottery machines in other states.

To put it in perspective, if dealt three to a Royal on a hundred play machine you should hit one Royal every eleven times you are dealt three to the Royal.
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RationalSkeptic