View Full Version : Fear Factor: Kh vs. 7h4h

04-20-2005, 03:27 AM
So fear factor the other night had a 'poker' game.

The contestants were in three teams of two, and each contestant had some disgusting thing to eat. they would each recieve one (faceup) hole card for completing their stunt (therefore max. 2 holecards per team, but receiving 1 or 0 is possible)

Then 5 community cards were revealed one at a time and whoever had the best 5card hand (using any of the 7 - gee just like holdem) won 25,000 USD.

Team 1 completed one dish and got one card: 4s
Team 2 completed two and got: 7h 4h
Team 3 completed one and got: Kh

What would you rather have in this situation?
Imagining that team 1 wasn't there, and that you are all in for a $25000 pot: would you pick 7h4h or Kh ?

My thoughts in white:
<font color="white">
my instinct was I'd rather have the King then 74s, even if that other 4 wasn't dead.
My subsequent 'research' showed a close coinflip with K2 slightly ahead. I ran K2 vs (74 or similar 85) with the other 2s as dead cards </font>

04-20-2005, 02:49 PM
Your experiment, comparing 74s with K2 with the other 2s removed, is biased in favor of 74s. In general, you should expect removing cards to favor the drawing hand when the removed cards don't help the drawing hand.

Taking out the 2s:
pokenum -h kh 2c - 7h 4h / 2h 2s 2d
2c Kh 0.522
7h 4h 0.478

Taking out 2s and aces:
pokenum -h kh 2c - 7h 4h / 2h 2s 2d ah ad ac as
2c Kh 0.491
7h 4h 0.509

Taking out 2s, aces, and queens:
pokenum -h kh 2c - 7h 4h / 2h 2s 2d ah ad ac as qh qs qc qd
2c Kh 0.454
7h 4h 0.546

If you extrapolate backwards, Kh should be more than a 52:48 favorite, perhaps 54:46.

04-20-2005, 10:07 PM
P(Kh wins) = 0.526991154
P(7h4h wins) = 0.464297776
P(tie) = 0.00871107


04-21-2005, 11:42 AM
well, knowing that one team had a 4 and that another team had the king of hearts which is one of the 7-4's flush drawing cards I'd have to go with the king high. 3-7's plus 2-4's gives them 5 out's in the entire deck to beat the king high. All the king high has to do is dodge 5 cards and a shot in the dark at a flush to win the hand while the 7-4 has to hit atleast one of 5 cards to win. (assuming a King doesnt pop, which in the real example 2 kings did pop giving them trips and the winning hand). I'd take the King high any day of the week against the other hands.