A New Application for a Well-Known Principle

[Mike]

For the past four weeks we've been looking at penalty card situations for 9/7 Triple Double Bonus. For those of you not used to looking at these situations, this was fairly tough going.

Today's column poses a puzzle from the same game --- but you don't need to know penalty cards to understand it. You also don't need to have ever played or studied this particular game to figure out the problem. You do need to have your thinking cap on. While some will find the problem trivially easy, I expect less than half of my readers to figure this one out the first time they read it.

In 9/7 TDB, in general 'KQJ' is more valuable than 'QJT'. That is, from 'KQJ' 44, 'KQJ' is worth $7.70 to the 5-coin dollar player while from 'QJT' 44, 'QJT' is only worth $7.67.(The previous examples presume that the pair of fours are totally unsuited with the 3-card royals.) This is not a major difference in value, but it's true nonetheless that 'KQJ' > 'QJT'.

As we found out a few weeks ago, under the right circumstances 'QJT' is more valuable than a 4-card flush but 'KQJ' NEVER is more valuable than a 4-card flush.

The puzzle is how can the less-valuable 3-card royal sometimes surpass the value of a 4-card flush and the more-valuable 3-card royal is never able to surpass that barrier? At first blush, this appears to be a major inconsistency.

If the answer doesn't come to you immediately, I suggest you think about it for a while. Perhaps entering the hand on Video Poker for Winners and looking at the values will help --- perhaps not. But take as long as you like to solve this one. I don't mind waiting.

The correct answer is hidden in the phrase '4-card flush.' The way the question was posed, it might seem that all 4-card flushes are equal in value. That's not the case. If you compare the values of 'KQJ5' with 'QJT5' you see 'KQJ5' (a 4-card flush with three high cards) is worth 28¢ more than 'QJT5' (a 4-card flush with two high cards). Even though 'KQJ' exceeds the value of 'QJT' by 3¢, it's not difficult to imagine that there 'QJT' can sometimes overcome a barrier 28¢lower than the one 'KQJ' must overcome.

Today's lesson, namely each high card in a 4-card flush adds value, wasn't a tough one, or even one that you didn't already know. But it is a lesson that is easily forgotten. Some players who claim they already knew this lesson were not able to answer the question when posed. I suggest this means they didn't know the lesson as well as they thought they did.

Advanced players should have had no problem with this puzzle, but there is a group of intermediate players who will have had a much easier time with the puzzle than other intermediates. Players who have taken my intermediate classes over the years will have a much better chance at solving this type of puzzle than those who haven't. I've asked very similar questions to this one in my 10/7 Double Bonus classes. Players who've taken the classes, in general, understand video poker better than those who haven't.