Non-transitive Dice

Typically, when playing a game of poker, one considers a pocket pair (22, 33, 44, etc.) in a game of Texas Hold'em, vs. two "overcards" (2 hole cards bigger than the pocket pair) to be considered, for quick calculation purposes, a coin toss. However, the pocket pair in a given situation vs. two overcards of a different suit, is a slight favourite overall.

So this problem typically presented - I believe it was originally stipulated by Daniel Negreanu, a professional player, but I could be wrong - is, a knowledgeable poker player challenges a poker player with less knowledge to a speculative bet.

The knowledgeable poker player offers the opponent to choose a hand from the following: AKo, JTs, or 22. Then the player on the up-and-up chooses second - and given their knowledge of the slight advantage in a given situation, chooses the hand with the higher odds.

However slight they may be, of course, the expected value always allows the player choosing second to edge out the person who chose first.

Because they are so similar in odds, an average or below average player may not realize the slight advantage 22 has over AKo, while JTs has the slight advantage over 22. AKo over JTs is of course a larger advantage than the other two situations - almost a 60/40 advantage.