In poker, the probability of many events can be determined by direct calculation. This article .. Barring a straight or flush, a pocket pair needs to make three of a kind to beat a higher pocket pair. See the section "After the flop" for the odds of a.
In hold em, the probability you hit a royal flush by the flop is the same as in draw poker. However, we can compute an upper bound for the Odds of a Royal Flush in Omaha - Poker Theory.
High Hand Probabilities in Texas Hold 'Em Royal Flush.