# What are the odds someone has a three of a kind at the same time as me?

I looked at the poker probability wiki and had a question, if I have a 4.83% chance of getting a three of a kind, how could i calculate the odds someone else would get one too, of any rank.

If anyone could help i'd appreciate it, This is one of those times I wish I knew any math wizards.

• Are you only concerned with your opponent also having a "three of a kind" (of any rank), or do you care about them having "three of a kind or better"? Commented Mar 15, 2021 at 3:27
• Im trying to keep it simple and not ask hard math out of anyone, so i meant "of any rank" as thats the 4.83% I was referencing. I assumed it being a solid percentage would make it as easy as a coinflip calculation. When you say "or better", I also think you might be referencing the "cumulative probabilties" in the chart that cover i.e "3 of a kind or better hand" not including ranks or kickers. in this case it would be 15.3% for a "3 of a kind or better". I'd imagine if the 4.83% is multiplied per simultanius person, then the cumulative 15.3% would use the same logic. Commented Mar 16, 2021 at 7:02
• To be clear im unsure if you can multiply say.. 4.83% x 4.83% = 2.3% for the odds that a second player also has a three of a kind. Or for the cumulative.. 15.3% x 15.3% x 15.3% = 0.35% for 3 players having a three of a kind "or better" at the same time for example. Thanks for your time. (Appologies if you got pinged a bunch, i made a lot of comments that i condensed into these two for simplicity) Commented Mar 16, 2021 at 7:17
• You can't just multiply because the two hands are not independent (due to the shared board cards). I don't have a pure formula for an answer right now. Commented Mar 16, 2021 at 15:56
• thanks, i removed that from the question Commented Mar 16, 2021 at 17:54