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Dealt winning hands that you should toss

By Henry Tamburin

 

You might think that’s a strange topic for an article. I mean, come on, why would anyone want to throw away a dealt winning hand in video poker? Stay with me and I’ll explain.

It’s true that the majority of times you should hold all the cards in a dealt winning hand, hit the deal button, and happily watch your credit meter increase by the amount of the payoff. But always holding a dealt winning hand isn’t necessarily the right play to make in some cases. Take for example the following hand (Jacks or Better).

hand1

Well congratulations, you were just dealt a paying flush in hearts. For a five-coin wager, the payback is 30 coins on a 9/6 Jacks or Better machine (or 25 coins if you happen to be playing a short-pay 9/5 or 8/5 game). But wait a minute! If you take another look at this hand, you’ll notice it also contains four cards to the royal flush (10-J-Q-A of hearts). It’s tempting to take that certain 30-coin profit right then and there rather take the risk of going for the royal flush and possibly ending up with a zero payoff. (As the saying goes, “a bird in the hand is worth two in the bush.” Really?)

If you hold a four-card royal flush, here are the possible results when you draw one card.

  1. You could draw another heart, which will give you a paying flush. There are 13 hearts per deck. You hold five of them in your hand; therefore, there are 7 hearts left in the remaining 47 undealt cards that would give you a paying flush. (This excludes the K of hearts, the card you need for the royal flush. The seven cards that would give you a flush are the 2-3-4-5-7-8-9 of hearts). If you drew one of those seven cards, you’d get paid 30 coins.
  2. Another possibility is you could get a straight when you draw to the four-card royal flush. In the above hand, if you drew a king in spades, clubs, or diamonds you would end up with a straight that pays 20 coins.
  3. A third possibility is to draw another jack, queen, or ace that would give you a high pair for a five-coin payout. There is four of each of those cards in a deck. You hold three of them in your hand. Therefore, there are nine of these high cards left in the remaining 47 cards that will give you a high pair and a 20 coin pay out.
  4. The last possible result is the one you are praying for; namely, drawing the king of diamonds, which will give you a royal flush and a big 4000 coin pay out. (There is only 1 king of diamond in the 47 remaining cards; therefore, the odds of this happening are 1/47.)

There are no other possible winning hands when you hold a J-Q-A-10 in hearts and draw one card (e.g., you can’t get two pair, or four-of-a-kind or even a straight flush).

I’ve tabulated the possible results of drawing one card to the J♥ Q♥A♥ 10♥ in the table below. The first column shows the possible winning results, the second column summarizes the number of times you could get each result, the next column shows the probability of getting each result, and the fourth column is the product of the probability times the payoff. If you sum the last column, you arrive at an expected value (or EV) of 92 coins. The latter is the average payback you can expect when drawing one card to a four-card royal flush, after an infinite number of trials.

chart

Putting this into perspective, let’s assume you are a dollar player playing $5 per hand (max coins). If you decided to hold the paying flush, your return will be a certain $30. If instead, you decide to hold the four-card royal flush, your average payback will be about $92. Yes, some of the times you will win nothing when you draw one card and don’t get a royal flush, flush, straight, or high pair (that will happen 27 times out of 47); other times, you’ll get a flush and win $30 (probability 7/47), or get a $20 payoff for a straight (3/47), a $5 payout for a high pair (9/47), and, if you are lucky, a whopping $4000 payout for a royal flush (1/47).

When you average all the possible payouts for this hand times the probability that each winning hand will occur, your average payback will be $92, which is slightly more than three times the certain $30 payback for holding the paying flush. Unless you plan to play one video poker hand in your lifetime, a $92 average payback in the long run is a whole lot better than a certain $30 payback.

Are there any other dealt winning hands that you should toss? Yes, and that’s a dealt straight containing a four-card royal flush. For example, glance at the following hand.

hand2

The hand contains a paying straight (9-10-J-Q-K) along with a four-card royal flush (10◆J◆ Q◆K◆). If you do a similar analyses (as I’ve done above for a paying flush), you’ll arrive at the mathematical fact that tossing the paying straight and drawing one card to the four-card royal flush has a higher EV (98 vs. 20)

There are a few more dealt paying hands that shouldn’t be held and a future column I’ll discuss them. For now, just remember to always break up a paying flush and straight if your hand also contains four-cards to the royal flush. In the long run, you will win more money compared to taking the immediate pay out.

Henry Tamburin is a blackjack and video poker expert. He is the host of the smartgaming.com website and the editor of the Blackjack Insider newsletter (for a free three-month subscription, visit www.bjinsider.com/freetrial).For a free copy of his Casino Gambling Catalog, which contains books, strategy cards, and software for casino players, call toll free 1-888-353-3234, or visit the web store at smartgaming.com.

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