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Bob Dancer writes a video poker column for beginners to experts. He also writes a column with Jeffrey Compton, "Player's Edge", featuring information on promotions at various Las Vegas casinos. Player's Edge is published each Friday in the Neon section of the Las Vegas Review-Journal. Click here to send Bob Dancer an e-mail.

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Feb 26, 2008

Jack-High Double Inside Straight Flushes with an off-suit Queen in Bonus Poker

There are three Jack-high 3-card straight flushes (SF3) with two insides --- namely 'JT7', 'J97', and 'J87'. This is true in all video poker games. Also in all video poker games, these three combinations have equal values --- everything else equal. The most interesting hands, to me at least, are those where everything is NOT equal.

In 8/5 Bonus Poker, let's add an off-suit queen to each of these 3-card straight flushes. The interesting questions are: when do you hold QJ, when do you hold the SF3, and (the rest of the time) when do you hold something else? First let's look at the answers and then let's look at the "why".

	2	3	4	5	6	8	9	T	K	A
Q 'JT7'	SF3	SF3	SF3	SF3	SF3	QJ	QJT9	TT	KQJT	AQJT
Q 'J97'	QJ	QJ	QJ	QJ	QJ	QJ	99	QJT9	KQJ9	SF3
Q 'J87'	QJ	QJ	QJ	QJ	QJ	88	QJ	QJ	KQJ	SF3

Along the left-hand column we see the four starting combinations. Across the top we have the unsuited fifth cards. Whether this card is suited with the queen or not is irrelevant. I didn't include a 7, J, or Q along the top because in every case the correct play would simply be to hold the pair.

The bottom line is we usually hold the SF3 with 'JT7' (we only hold the QJ once). When we start with 'J97' or 'J87', we usually hold the QJ (we only hold the SF3 once in each case). Since these combinations have the same values "everything else being equal," why is there such a big discrepancy in the actual holds?

First let's look at the value of the unsuited QJ. This combination gets its value from the chance of becoming a high pair, two pair, three of a kind, straight, full house, or four of a kind. All of these categories have the same frequencies in the three cases EXCEPT for the straight.

There are three possible straights starting from QJ, namely AKQJT, KQJT9, and QJT98. In addition to the queen and jack, all three combinations we have one additional card that is found in one or more of these straights.

In the first case, with 'JT7', we have the ten which is found in all three possible straights. In the second case, with 'J97', we have the nine, which is found in two of the three straights (KQJT9 and QJT98 but not AKQJT). In the third case, with 'J87', we have an eight which is only found in one of the straights (QJT98 but not AKQJT or KQJT9).

Whenever we draw three cards to a combination (in a 52-card deck game), there are 16,215 different combinations of cards we can draw. If we compare cases where the fifth card is neutral, say a deuce, then drawing to QJ in the first case gives us a straight 144 times. In the second case, we get a straight 160 times, and in the third case we get a straight 176 times.

How much is this worth in real money? For the 5-coin dollar player, QJ is worth $2.48 in the first case, $2.50 in the second, and $2.52 in the third. Since QJ is worth the least in the first case, the fact that it is almost never held makes sense. Since sometimes we play it one way and sometimes we play it the other, obviously it's a close play --- and a 2¢ difference in value can shift which play is preferred.

The only time in the first case (Q 'JT7') where we hold QJ is when the fifth card is an eight. Let's look at why this is such a special case.

The eight is a straight penalty to the 'JT7', meaning that it's harder to get the JT987 straight when there's an eight missing from the deck than when there's all four of them left. To be sure the eight is also a straight penalty to the QJ, but it hurts the value of the QJ by about 1.5¢ and the value of the 'JT7' by about 2.8¢, so the net effect is that it hurts 'JT7' by more. Hence the change in plays.

The nine is also a straight penalty to the 'JT7', which also makes QJ preferable to 'JT7', but there is now a QJT9 4-card straight in the hand which is worth quite a bit more.

Now let's look at Q 'J97' and Q 'J87'. We've already seen that the QJ in these cases are worth either 2¢ or 4¢ higher than in the Q 'JT7' situation, so it isn't a surprise that QJ is usually the preferred play. The only time we prefer the SF3 in these cases is when the fifth card is an ace. Why does the ace act differently than other cards?

The answer, like we've seen before, is that the ace hurts the value of QJ because of the straight possibilities. It is also a high card, so the removal of an ace from the deck hurts the chances of ending up with a pair of aces. Overall, if you compare Q 'J87' A with Q 'J87' 2, you'll see that the QJ in the latter case is worth 5.3¢ more than in the former case.

A king is also a straight penalty to the QJ, but here the resulting hand contains KQJ and/or KQJ9 which are more valuable than either the SF3 or the QJ.

In the Dancer / Daily strategy card for this game, and in the Dancer / Daily Winner's Guide for Jacks or Better, which discusses this game, in the advanced strategy we have the following rule for this case:

QJ É. (< 'JT7' with no 8p; < 'J97' or 'J87' only when Ap)

Once you understand that "8p" means "8 penalty" or "there's an extra eight in the hand", this rule should make sense to you after reading this article.