Looking at a 50-coin Penalty for the Straight Flush in 10-6 Double Double Bonus

There is a version of 10-6 DDB that pays 200 for the straight flush rather than 250 and that change drops the return from 100.06% to 99.96%. Casinos which have a firm policy of never offering a game returning more than 100% sometimes have this game. I refer to the games as 10-6-50 and 10-6-40, where the 50 and 40 represent the one-coin return for the straight flush.

The strategy for the two games is very similar, of course, but not identical. If I had places where I could play both games, I’d likely use one strategy for both. But I don’t know of any casino with the 10-6-50 game where I want to and am welcome to play, so I concentrate on the 10-6-40 strategy. The Dancer/Daily Winner’s Guide for Double Double Bonus covers the 10-6-50 game completely. Today I’ll just discuss the differences between the two games. All money amounts assume you are playing for dollars, betting five coins at a time.

1. A♠ K♥ Q♥ J♣ 9♥ — When you get 250 for the straight flush, KQ9 is superior by 0.9¢. When you get 200, AKQJ is better by 3.8¢. In this example, I showed the A and the J unsuited with each other. The result would have been the same if they were both the same suit. And the relationship between KJ9 and AKQJ is exactly the same as presented here.

In this example, the value of the straight flush only affects one of the possibilities, namely KQ9 or KJ9. The value of the straight flush has no affect on AKQJ because there are two or three suits involved. In the rest of the hands we’re going to discuss today, both of the top two possibilities are affected by the value of the straight flush.

2. Q♥ J♥ 3♠ 4♠ 5♠ — In 10-6-50, holding the 345 is superior by 10¢. In 10-6-40, holding the QJ is better by 3.2¢. The other 2-card royal flush draws (KQ, KJ, AK, AQ, AJ) remain lower in value to 345. The play, and the amounts, will be the same for 456 and 567 as they are for 345.  For 678 and 789, the same rule applies but the amounts are different.

3. K♦ Q♦ J♣ 9♣ 5♦ — Here the J and 9 may or may not be suited with each other, and the 5 may be any card in the range of 2-8. In 10-6-50, the correct play by 0.3¢ is KQ. In 10-6-40, the correct play by 0.03¢ is KQJ9. Yes, I know that it’s tough to get excited with a distinction worth only 0.03¢. If it helps you get over that a bit, the play and numbers are the same in K♦ J♦ Q♣ 9♣ 5♦. See! Isn’t that better now?

4. There is a group of 3-card straight flush draws with no high cards and one inside, including one outside straight penalty, compared to an A by itself. In each of these cases, the straight penalty to the straight flush sometimes must be unsuited with the A in order for the play to change, and sometimes not. In 10-6-50, we always hold these 3-card straight flushes. In 10-6-40, we hold the

These plays are affected by low straight penalties to the A, namely 2, 3, 4, and 5, and sometimes also affected by a kicker penalty, namely a 2, 3, or 4, since it reduces the chances for the hand AAAA2, AAAA3, or AAAA4. Saying this slightly differently, the 5 is a low straight penalty without being a kicker penalty. The 2, 3, and 4 are both.

a. 2♠ 3♠ 4♠ 6♦ A♣; 2♠ 3♠ 5♠ 6♦ A♣; 2♠ 4♠ 5♠ 6♦ A♣ — In all three of these cases, the value of the 3-card straight flush is identical.   With the 6 unsuited with the A, and the straight flush 234, in 10-6-40 hold the A by 4.8¢. In 10-6-50, hold the straight flush by 4.5¢. When we have 235 or 245, the value of the A is increased by about a penny because there is now one additional kicker available than when the straight flush combination was 234. Why? Because 234 has three kickers, and 235 and 245 have only two. After a card is discarded before the draw, it cannot come back after the draw.

b. 2♠ 3♠ 4♠ 6♦ A♦; 2♠ 3♠ 5♠ 6♦ A♦; 2♠ 4♠ 5♠ 6♦ A♦— In these three cases, the A is suited with the 6. This has no effect on the value of the straight flush combination, but lowers the value of the A by about 3.7¢. This is not enough to change the play, namely, hold the A in 10-6-40 and the straight flush combination in 10-6-50.

c. The following nine hands are all similar to each other. In each case, the outside straight penalty is unsuited with the A. In each case, you hold the A in 10-6-40 and the straight flush draw in 10-6-50. In five of the cases there are similar hands which do not follow the same rule. In this latter group of hands, we go for the straight flush draw in both games.

Before I announce my rule for keeping these hands (and their exceptions) straight, see if you can come up with a rule that covers each of these cases. 

4♠ 6♠ 7♠ 8♥ A♣  (but not 4♠ 5♠ 7♠ 8♥ A♣ or 4♠ 6♠ 7♠ 3♥ A♣)

5♠ 6♠ 8♠ 9♥ A♣  (but not 5♠ 6♠ 8♠ 4♥ A♣)

5♠ 7♠ 8♠ 9♥ A♣  (but not 5♠ 7♠ 8♠ 4♥ A♣)

6♠ 7♠ 9♠ 5♥ A♣ 

6♠ 7♠ 9♠ T♥ A♣ 

6♠ 8♠ 9♠ 5♥ A♣ 

6♠ 8♠ 9♠ T♥ A♣ 

7♠ 8♠ T♠ 6♥ A♣  (but not 7♠ 8♠ T♠ J♥ A♣)

7♠ 9♠ T♠ 6♥ A♣  (but not 7♠ 9♠ T♠ J♥ A♣)

These are all 3-card straight flush combinations with no high cards and one inside. They all have an outside straight penalty card unsuited with the A. There can neither be two low straight penalties nor an additional high card in the hand. I think this rule correctly accounts for all of the cases.

d. The next group of hands contain an A and a suited JT. You always hold the A by itself if there’s a flush penalty to the JT or a 9 penalty. Once you eliminate these two conditions, there are special rules depending on whether there’s a 7 penalty or 8 penalty (or neither), and also depending on whatever kind of penalties the A has. This is covered thoroughly in the Winner’s Guide to Double Double Bonus and there’s no need to repeat those conditions here.

There are several hands where the additional two cards are unsuited with the A and have exactly one kicker penalty and one card in the range of 5-8. It doesn’t matter if these two cards are suited with each other or not. If these conditions are met, you hold the JT in 10-6-50 and the A in 10-6-40. The entire list is:

2♥ 5♥ J♣ T♣ A♦ 2♥ 7♥ J♣ T♣ A♦
2♠ 5♥ J♣ T♣ A♦ 2♠ 7♥ J♣ T♣ A♦
3♥ 5♥ J♣ T♣ A♦ 3♥ 7♥ J♣ T♣ A♦
3♠ 5♥ J♣ T♣ A♦ 3♠ 7♥ J♣ T♣ A♦
4♥ 5♥ J♣ T♣ A♦ 4♥ 7♥ J♣ T♣ A♦
4♠ 5♥ J♣ T♣ A♦ 4♠ 7♥ J♣ T♣ A♦
2♥ 6♥ J♣ T♣ A♦ 2♥ 8♥ J♣ T♣ A♦
2♠ 6♥ J♣ T♣ A♦ 2♠ 8♥ J♣ T♣ A♦
3♥ 6♥ J♣ T♣ A♦ 3♥ 8♥ J♣ T♣ A♦
3♠ 6♥ J♣ T♣ A♦ 3♠ 8♥ J♣ T♣ A♦
4♥ 6♥ J♣ T♣ A♦ 4♥ 8♥ J♣ T♣ A♦
4♠ 6♥ J♣ T♣ A♦ 4♠ 8♥ J♣ T♣ A♦

I suspect that I’m one of the few players to attempt to learn and apply these differences between the two games. I’ll leave it to the reader to decide whether this is a sign of professionalism on my part, or a symptom of some disease.

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