You’re playing Texas Hold’Em. ~ Which of the following has the best chance of winning?
Jack-10 suited (e.g., a Jack of diamonds and a 10 of diamonds)
Ace-7 unsuited (e.g., an Ace of spades and a 7 of clubs)
Pair of sixes
The answer, to nobody’s suprise, is: it depends! ~ The absolute probability that you will win obviously goes down if you are playing against more opponents with randomly-chosen cards, just because there are more ways they could beat you. But, much more interestingly, the ordering of which hand is best also changes.
What happens if, instead of putting one of these three hands against some other random cards, we put them up against each other, two at a time?
Sixes are likely to beat A7, and A7 is likely to beat JTs, but JTs is likely to beat a pair of sixes. It’s a kind of combinatorial rock-paper-scissors situation.