The same hands on two tables at once! What are the odds?

I have been reading the forums lately. One thing I have seen a lot is people debating about on-line sites being rigged because they frequently see the same hands on separate tables. Some even assume the RNG must be shared because they see it happen at different sites.



This actually isn't a question but instead a response to many other posts. I wanted to take a few minutes to explain WHY the odds of this happening are not ridiculously high and maybe put a few player's minds at ease about “on-line rigging”.


To understand this let me explain how to calculate the odds of being dealt aces. Then we can use the same method to calculate the odds of being dealt the same hand at two tables (yes, regardless of what site those tables are on!). One can calculate this using conditional probabilities. For example...


There are 52 cards in the deck and 4 aces. The odds of being dealt a single ace is 52:4 or 4/52 which is reduced to 1/13.


After the first ace is dealt there are 51 cards and 3 aces left. This means the odds are 51:3 or 3/51, reduced to 1/17, to be dealt a second ace.


KEEP READING! There is a point to this mathematical junk.


You may be wondering why the odds are so low; “roughly 52 to one?”. Well thats the conditional part. We must take those two reduced fractions in bold above and multiply them. 1/13 * 1/17 = 1/221. So the odds of being dealt aces is exactly 221 to one!


One last thing we will need. How many possible hands are there in holdem? The first card can be any one of 52 cards in the deck and the second card can be any one of the 51 remaining cards. This gives 52 × 51 ÷ 2 = 1,326 possible starting hand combinations. We divide by two because the order of the cards is not significant, unless the player suffers from obsessive compulsive disorder lol. So the 2,652 permutations are divided by the 2 ways of ordering two cards. Yes that was pretty straight forward, third grade math .


NOW FINALLY!!


What are the odds of being dealt the same two cards on two tables at once.


DEEP BREATHE ALMOST THERE!


For simplicity, lets use the same method of computing the odds; see I told you there was a point to all that math!


Two tables are like the two cards in the first equation. The only number we need to change are the number of cards. Since we are not looking for cards, instead combinations, we have to use the 1,326 possible combinations from above.


So using the same math 2 (tables) /1,326 (combinations or “cards”) which is reduced to 1/663. So the odds are 663:1 of being dealt the same hand on two tables at once. Play a few thousand hand a weeks and you will certainly hit those odds frequently. Are on-line rooms rigged? Maybe. Can we say they are rigged because we constantly see the same hands at two tables over and over? No!


I hope that clears up the question of "What are the odds? It has to be huge!" I haven't seen any responses that explain it easily without any funky math symbols or asking an "Einstein" for help. Just simple math for normal people like myself to understand.

Thats all good, but what about being dealt the same hand twice in a row, LOL, now thats also happened to me. ok I'm just kidding, I've come to the conclusion it happens lol!!

The correct answer is 1/1326. Picture this:

You've been dealt Ad Js on one table. The next table is a second away from dealing. You want to know what the odds of Ad Js being dealt on that table.

The math is 1 in (2/52)*(1/51) which is 1 in 1326.

The generic form of this question might be:

"What are the odds of a particular two cards being dealt on the next hand?"

7h 2d? 1/1326

Ah As? 1/1326

Ah As is better