## Saturday, April 13, 2013

Q. I was recently playing a 25-cent Bonus Poker machine. I bet the maximum number of coins and up came the 7, 10, Jack, Queen and King of clubs. Without thinking, I held all five clubs for a flush and a payout of 25 coins. As soon as I did this, I was kicking myself for not going for the straight flush or royal flush for a payout of 250 coins or 4,000 coins.
I also had six other cards to make my flush and six to make a straight.
I believe I should have thrown the 7 of clubs away and drawn one card. What is the correct play and what are the percentages?
A. The correct play in that situation is to discard the 7 of clubs and give yourself a chance at a royal.
Once you have seen your initial five cards, there are 47 possible one-card draws. One, the Ace of clubs, would give you a royal flush worth 4,000 coins, and another, the 9 of clubs, would give you a straight flush for 250 coins. Any of six cards - the 2, 3, 4, 5, 6 or 8 of clubs - gives you a flush worth 25 coins. Any of six others - the 9s and Aces of hearts, spades and diamonds - gives you a straight worth 20 coins.

In addition, any of nine cards - the Jacks, Queens and Kings of hearts, spades or diamonds - gives you a high pair worth a five-coin return.

That's 23 cards that complete a winning hand; any of the other 24 would leave you with a loser. Per 47 times you make this play, your expected return is one royal flush for 4,000 coins, one straight flush for 250, six flushes for 150, six straights for 120 and nine high pairs for 45. That's a total of 4,565 coins per 47 plays, an average of 97 per hand.

If you stand pat on the flush, per 47 plays your return is 1,175 coins, or 25 per play. You're nearly four times better off taking the chance with a one-card draw.

The only time to stand pat on a hand that includes four cards to a royal flush is when it includes a pat straight flush.