Oodds of Getting a Full House and Four of a Kind in Pick 'Em Poker
Here is a question about pickem poker:
What are the odds of getting a full house and also four of a kind in Pick 'Em Poker? I play mostly at the Soaring Eagle casino in Mt. Pleasant, Mich., and Pick 'Em Poker is their only full pay machine.
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I played 16,016 hands of Pick 'Em Poker using the Bob Dancer Presents WinPoker software.
Here are my results keeping track of four of a kinds, which I feel is the main hand you would need to get in order to have a winning session. According to your Video Poker Answer Book, the odds on getting a royal flush are extremely high. I presume the odds on a straight flush must be pretty high also. (Maybe you could give me those odds also.)
I used the correct strategy on every hand because I used the "warn" signal if I was making a mistake. I played max coins. I received seven four of a kinds in the first 5,530 hands, which I think must be above average because I didn't get my eighth four of a kind until the 16,016th hand, which means it took 10,486 hands to get the last one. I would have been 1,625 coins ahead after my seventh four of a kind but 1,170 coins down after my eighth.
Well, here is one answer to the above:
Let's start with a little explanation of Pick 'Em, which is not as common on casino floors as are five-card draw poker games. In Pick 'Em, the player sees four cards on the initial deal. On two, there is no decision -- they remain part of the player's final five-card hand. The others are the top cards in two three-card stacks. The player chooses one stack to round out the hand.
There is no draw once you have your five cards. Since you're really only eliminating one possible card from a 52-card deck, odds are much closer to those on five-card stud poker than on five-card draw. Royal flushes occur an average of once per 315,818 hands, instead of the once per 40,000 or so on five-card draw games.
Straight flushes come up an average of once per 38,451 hands in Pick 'Em, making them nearly as rare as royals in draw poker.
As for four-of-a-kind hands, Bill is correct -- hitting seven within 5,530 hands is far above normal frequency. On the average, Pick 'Em players hit four of a kind once per 2,361 hands. In Bill's 5,530 hands, normal expectation would be for two to three sets of quads.
Frequency of other winning hands in Pick 'Em comes to once per 424 hands for full houses; once per 314 hands for flushes; once per 197 for straights; once per 33 for three of a kind; once per 16 for two pair, and once per 4.4 for a pair of 9s or better.
Overall, Pick 'Em players win about 33 percent of all hands, compared with about 40 percent in most five-card draw games. However, payoffs on winning hands are higher in Pick 'Em than in other games. Given a five-coin wager, full-pay Pick 'Em pays 6,000 coins for a royal, 1,199 for a straight flush, 600 for four of a kind, 90 for a full house, 75 for a flush, 55 for a straight, 25 for three of a kind, 15 for two pair and 10 for a pair of 9s or better. The expected return in the long run with expert play is 99.95 percent.
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