When Liam W. Daily and I were devising our strategy cards and Winner’s Guides several years ago, we noticed that in many games, the value of certain 3-card straight flushes was similar. In 9/6 Jacks or Better, for example, KQ9 (two high cards and two insides) is worth $3.21, JT8 (one high card and one inside) is worth $3.20, and 345 (no high cards and no insides) is worth $3.18. In all cases, I am assuming a 5-coin dollar player and the last two cards in the hand provide neither flush nor straight interference.
The pattern for all three hands was that there were the same number of high cards (which are good things) as there were insides (which are bad things). We then devised a simplifying naming convention that started with zero, added one for every high card and subtracted one for every inside. Each of the three cases above comes out with a ranking of “0” — we actually refer to it as SF3 +0.
When you use this notational system, the eight different types of 3-card straight flushes get reduced to four, namely SF3 +1 (SF3 2h1i; SF3 1h0i), SF3 +0 (SF3 2h2i; SF3 1h1i; SF3 0h0i), SF3 -1 (SF3 1h2i; SF3 0h1i), and SF3 -1 (SF3 0h2i only). For most games this simplifying system works pretty well, although there is a learning curve involved and when players look at a Dancer / Daily strategy before going through this learning curve, they don’t know what the symbols mean.
But sometimes the simplifying system doesn’t work as well. I decided to look at why. I examined three different games:
A. Jacks or Better where flushes return 6 (could be 9/6 or 8/6)
B. Double Bonus where flushes return 7 (could be 10/7 or 9/7)
C. Super Double Bonus where flushes return 5 (could be 9/5, 8/5, or 7/5) and straight flushes return 80
The reason why it doesn’t matter what the full house returns is because when you draw two cards to a 3-card straight flush, it’s impossible to end up with a full house anyway. Look at the following chart.
| SF | FL | ST | JoB | DB | SDB | ||
| 50-6-4 | 50-7-5 | 80-5-4 | |||||
| KQ9 | SF3 2h2i | 1 | 44 | 15 | 3.2146 | 3.3626 | 3.0250 |
| JT9 | SF3 1h1i | 2 | 43 | 30 | 3.1961 | 3.4089 | 3.1499 |
| 345 | SF3 0h0i | 3 | 42 | 45 | 3.1776 | 3.4413 | 3.2609 |
In the first column we see the combinations we’ve been talking about. In the second column we see the “standard” (loosely defined) 3-card straight flush notation.
The third, fourth, and fifth columns are the number of straight flushes, regular flushes, and straights possible when you draw two cards. There are a few patterns. When you draw two cards to any 3-card flush (assuming the other cards are far away and of a different suit), the number of (flushes + straight flushes + royal flushes) always sums to 45. In our three examples here, royal flushes aren’t possible so this devolves to (flushes + straight flushes) summing to 45.
When you’re drawing two cards to a 3-card straight flush (assuming the other cards are far away and of a different suit), the number of possible straights is always 15 times the number of possible straight flushes. To understand this, consider KQ9. To get a straight, you need one of the four jacks and one of the four tens. Four times four is 16, which means there are 16 different combinations of jacks and tens, of which one is a straight flush and the other 15 are regular straights.
The next column shows the values for Jacks or Better where flushes return 6 for 1. These are the numbers quoted earlier in the article, with slightly more precision. Notice that immediately below the JoB title are the numbers 50-6-4. These are the returns for straight flushes, flushes, and straights respectively. Notice that the values for the three different straight flushes decrease slightly as we go down the chart.
The next column shows the values for Double Bonus, where flushes return 7 for 1 and straights return 5 for 1. The numbers here are a little larger than they are in Jacks or Better. This figures because the values of both the flush and straight increase (from 9 and 4 to 10 and 5) as we go from one game to the other. The numbers are a little more spread out (about 4¢ between numbers rather than 2¢) and now the number increase as we go down the chart rather than decrease as before. Why? Because the one-unit change in the value of 15 straights affects the situation more than a one-unit change in the value of one flush. (I say one flush because as we go from 44 to 43 to 42, these only change by one unit. When we go from 15 to 30 to 45, these change by 15 units each time).
The last column shows the value for Super Double Bonus where the flush returns 5 for 1. For those of you unfamiliar with SDB, this is like DB except that four jacks, queens, and kings receive 120 coins per coin bet rather than 50. Additionally, and this affects things here, the straight flush returns 80 for 1 rather than 50 for 1. Overall, the rankings increase by about 12¢ each as we go down the chart. Compared to the values for 9/6 Jacks or Better, the additional number of straight flushes (increasing by 30 units each) swamps the decrease from the 1-unit lower value for the flush.
I don’t really have a snappy conclusion to this article. Working through this made it clear to me why the simplifying naming convention works better for some games than others. By doing this kind of exercise periodically, I’m better able to understand how a change in the value of straight flush in a progressive affects the way you play certain combinations. Players who never attempt to study this kind of problem will not have the depth to handle slightly-different situations.
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