What makes DDB is how much you get for 4-of-a-kinds.
The picture above illustrates the “9/5” version of the game (where you are paid 9-for-1 for the full house and 5-for-1 for the flush) where good play yields 97.87% on average. There are better pay schedules and worse. The plays we talk about today will be accurate for all common pay schedules.
How much the errors are worth is calculated assuming you are playing for dollars, betting five coins at a time.
K♦ Q♦ J♦ 10♦ 9♦
Are you a coward or are you a gambler? The cowards hold all five cards, while the gamblers toss the nine, say a prayer, and go for the royal flush.
In this case, being a coward is worth $250 and being a gambler is worth $92.34. It would be a huge mistake to gamble it up when you already have a straight flush dealt to you. Compare that hand with K♦ Q♦ J♦ 10♦ 8♦ (where you have a flush worth $25) or K♦ Q♦ J♦ 10♦ 9♠ (where you have a straight worth $20). In these two cases, being a gambler is much the better play.
K♣ K♥ 7♠ 7♦ 5♠
A lot of players hold the kings (worth $7.24) instead of KK77 (worth $8.40). That’s a big error and it happens frequently.
Since you get your money back if you don’t improve the kings and you get the same amount if you don’t improve two pair, it seems like these two combinations are worth the same. And since that seems to be true, why not try for four kings worth $250?
The fact is that these two combinations are only equal if you end up with them as a final hand. As a hand you draw to, they are not worth the same at all. You are nine times more likely to get a full house (worth $45) if you hold two pair than if you just hold the kings.
Compare that with A♣ A♥ 7♠ 7♦ 5♠. Here the correct play is the aces, which are worth $9.65 on average. What’s the difference? You still have approximately a 1-in-360 shot of converting the pair of aces to a 4-of-a-kind as you would for converting a pair of kings, but four aces (worth $800 or maybe $2,000) are worth a lot more than four kings ($250).
A♠ A♥ A♣ 6♥ 6♠
Holding all five cards is a full house worth a guaranteed $45, but just keeping the aces is worth $63.58. When you start with 3-of-a-kind and you draw two cards, you have a 4.25% chance of getting the quad. This time, go for it!
Compare that with 3♠ 3♥ 3♣ 6♥ 6♠. Holding the threes by themselves is “only” worth $37.68, since four threes aren’t worth nearly as much as four aces. So in this case, keep the $45 full house.
A♣ A♥ 3♥ 4♥ 5♥
Double Double Bonus players love getting four aces, but you’re a long way from getting four aces drawing three cards to a pair. Holding the pair of aces here is worth $9.50.
Going for the hearts, where drawing a 2♥ is worth $250 and several other cards give you a regular flush or straight, is worth $11.64 on average. This is by far the better play.
Q♣ J♣ 10♣ 9♣ 8♥
Keeping all five cards for a $20 straight is sort of a “kiss your sister” hand. It’s not terrible, but not too exciting either.
Still, dropping the eight and trying for the $250 straight flush is only worth $17.13. You only end up with the straight flush 4.25% of the time, and you end up with nothing at all more than 57% of the time. Better to keep the guaranteed straight.
Notice this is a different answer than we gave in the first problem, where we said to toss the nine from K♦ Q♦ J♦ 10♦ 9♠ and gamble it up. What’s the difference? In the first problem, we were going for a $4,000 royal flush. In the current problem we’re going for a $250 straight flush. Not the same at all!
So, how’d you do?
Playing correctly is trickier than many people realize. Fortunately there are a number of software products that allow you to practice and correct you when you make a mistake. I use Video Poker for Winners, but there are other good ones as well.
I only showed a few hands today. There are many other hands where players also make mistakes. A little bit of practice will improve your results immensely!