What are the odds of getting three Full Houses in a row at a table of 10 playing Texas Hold'em?

Answer 1

If all ten players were to see showdown then the chance of one of those ten players having a full house is about 15.5%. Thus to see three full houses in a row has a chance of 15.5%^3 = 0.37%.

This may not seem like much, but with a 15.5% chance of occurring it means there is a 27% chance that 3 will happen in a row if 100 hands are played.

However, you rarely, if ever, will have all ten people play to showdown. In face you'll probably only ever have 2 or 3 players at showdown. Here we need to approximate, but let's assume for each hand played the players are playing any reasonable hand, they are particularly aggressive. This results in about an 8% chance of one of the two players getting a full house. So in 100 hands there is a 4.5% chance that a full house wins three times in a row.