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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.

For more details and a schedule of Bob's free classes, visit www.bobdancer.com.

Oct. 2, 2007

An Interesting Lesson from Triple Bonus Poker Plus

Triple Bonus Poker Plus (TBPP) is a variation on Double Bonus Poker. You receive more for aces, twos, threes, fours, and straight flushes than you do in Double Bonus, and this is compensated for by receiving less for full houses and straights. The best game is the 9/5 Version, which returns slightly more than 99.80 percent if you get 1,200 for four aces and slightly less than 99.80 percent if you "only" receive 1,199 for the same jackpot. Dollar players are typically very happy to give up this dollar in order to avoid a tax form. This is the same game as White Hot Aces, except that WHA returns 80 for 1 for the straight flush rather than 100 for 1.

Royal Flush	800
Straight Flush	100
Four Aces	240
Four 2s thru 4s	120
Four 5s thru Ks	50
Full House	9
Flush	5
Straight	4
Three of a Kind	3
Two Pair	1
Jacks or Better	1

In some casinos across the country, this is the loosest game available, and with a decent slot club is a money-maker for the knowledgeable player. One player hired me to create a perfect strategy for him. He had the strategy produced by "Video Poker for Winners" but he wanted a perfect one, using the same notation as found on the Dancer/Daily strategy cards, and was willing to pay me for it.

Fair enough. I played with the game for a half hour or so and created a rough draft of every exception I could find. One of the simpler ones was you hold 'KT' if there is no other suited card in the hand, but you hold 'K' from 'KTx'. The quote marks mean the cards are suited with each other. The "x" means a card suited with 'KT' but too low to be in the same 3-card royal flush or straight flush. As a simple example, from Kh Th 9s 5d 3c you hold 'KT' and from Kh Th 9s 5d 3h you hold the K by itself.

When I finished my draft, I looked at the strategy error report from VPW. This report identifies every situation where a hand is misplayed by using the regular strategy. I wanted to make sure that the strategy I was selling covered all of the bases.

Since the basic strategy says to hold 'KT', I definitely expected to see an entry where there was a flush penalty. And I did. Except that there were actually seven different entries --- each with a different value. The different values represent the size of error if you hold the 'KT' rather than the solitary K.

2d 3d 4h Th Kh	0.0052981
2d 3d 5h Th Kh	0.0072604
2d 5d 6h Th Kh	0.0092227
5d 6d 7h Th Kh	0.0111850
2d 3h 9d Th Kh	0.0216130
2d 5h 9d Th Kh	0.0235753
5d 6h 9d Th Kh	0.0255375

The lesson in today's column is to discuss why there are seven different values for these hands. Strategically they can all be lumped together into the rule that you should hold the K over 'KT' when there is a flush penalty. I suggest you try to figure this one out for yourself before continuing. The rest of the column will be here when you're ready to continue.

The sizes of the errors range between a half cent and 2.5 cents for the five-coin dollar player. Today's column isn't about whether you should or not take penalty cards into consideration, but rather why are there seven different values for this one type of hand.

The easiest part of this to understand concerns whether or not there is a nine in the hand. The nine is a straight penalty for both the K and the 'KT'. Straights are percentage-wise a bigger deal when you are "only" drawing three cards rather than four. The presence of a nine tilts the decision to the king by itself by about 1.4 cents.

But what about the other cases? If you look at the hands you'll see that they vary with respect to the number of low cards --- where "low" means 2, 3, or 4. Can you see why low cards affect the decision about whether to hold the K or 'KT'? It certainly won't be obvious to most players.

I'll give you a hint. Whether you throw away a 4 or a 5 makes no difference in the value of the 'KT', but it DOES matter to the value of the holding the king by itself. Can you see how?

Compare the first two hands above. In the first hand, if you hold the king by itself, you can't end up with four twos, threes, or fours. Compare that to the fourth hand where you can't end up with four fives, sixes, or sevens. The difference is that four twos, threes, or fours are worth $600 and the other quads are only worth $250. Every special quad that can't happen means a difference in 0.20¢ in the value of hold the king by itself.

This is a case where the size of the discard doesn't affect whether or not you make the play. It merely affects HOW MUCH the play is worth. A fair question is why would I write about a phenomenon that is interesting, perhaps, but doesn't make a difference in how you play the hands?

The answer is that it DOES make a difference in other games. In 9/5 Super Double Bonus, for example, the number of low cards present affects whether you hold 'QT' or the solitary queen. If you can understand the phenomenon in TDPP, you'll be able to understand the same affect in other games. It's not difficult to see once it's pointed out, but most players can't figure it out without a few hints.