What are the odds there is 2, 3 or 4 on the flop?
Join Date: Feb 2010
Posts: 261
So I was playing cashgame at my local homegame. There was this old dude who wanted to place a sidebet on each flop. He said "If there is on the flop a 2, 3 or 4 I win" the rest of the deck you win.
So alot of players on the table were intrested in this sidebet. They placed 100 euro each time, and funny enough he did win most of the time because on the flop was a 2, 3 or a 4 most of the times :/
Can someone explain? Pure luck or what?
Join Date: Aug 2012
Posts: 282
Pure luck for hitting the "most of the time" but he's a slight favorite
Join Date: Sep 2009
Posts: 4,817
Guy with the 3 cards is like 55%
Join Date: Jan 2009
Posts: 4,987
2, 3, or 4 total to 12 cards. Therefore there are 40 “losers”. The probability the flop does not contain a 2, 3, or 4 is then equal to the probability all flop cards are losers, or
Pr(no 2, 3 or 4) = 40/52 * 39/51 * 38/50 = C(40,3)/C(52,3)= 44.7%.
Thus, the probability of at least one 2,3 or 4 on flop = (100 – 44.7)% = 55.3%
This is a fairly well known "sucker bet".
Join Date: Mar 2009
Posts: 6,733
And, of course, low cards are more likely to appear on a flop since players "tend" to have high cards in their hands on deals that see a flop.
Spadebidder measured this "rank bias" in his fantastic analysis of hundreds of millions of on-line deals.
Join Date: Jan 2009
Posts: 259
Used to offer this bet back in High School for even money, that A23 would flop. An edge is an edge.
