VIDEO POKER

Evaluating A 4-Cards-To-The-Royal Promotion

Using parentheses to represented suited cards, normal 10/7 Double Bonus makes these plays:

a. (KQJ5)K hold (KQJ5)
b. (AQT)A4 hold AA
c. (AQT)AT hold ATAT
d. (KQ4)93 hold (KQ4)

The question becomes, do you make a strategy change for any or all of these hands to take the promotion into consideration? More importantly, since the promotion is over, how do you make the calculations yourself so next time something like this comes around, you can evaluate it correctly in plenty of time to capitalize on it?

Letıs look at the first hand (KQJ5)K using WinPoker. Playing for dollars, WinPoker tell you that (KQJ5) is worth $7.55 and that (KQJ) is worth $7.39. So if this promotion adds more than 16˘ in value, then we should hold (KQJ). Letıs figure it out.

Drawing two cards while holding three always involves 1,081 combinations of cards, as long as weıre talking about a 52-card deck. To end up with 4 to the royal , we will have to end up with a suited A or a suited T on this hand, with a fifth card that doesnıt yield a high pair, a flush, straight, or straight flush. Letıs see how often that happens.

If we draw the suited A, we need the fifth card to be between 2 and 9 (which is eight separate ranks) so as to not end up with a high pair or a straight, and we need that card to be any of the three suits that isnıt the same suit as the (KQJ) --- which means three separate suits. Multiplying these together, we end up 24 different combinations that will suffice.

If we draw the suited T there will be fewer combinations because any 9 will give us a straight or straight flush. But we still have the seven ranks between 2 and 8 and three possible suits --- which gives us 21 combinations that work.

These 45 combinations add 100 coins apiece. To find out how much this adds to the value of (KQJ) we multiply 100 x 45 / 1081 and come up with $4.16 --- which is WAY MORE than the 16˘ difference between the plays.

In hand (b), AA is worth $8.81 and (AQT) is worth $6.62. But since we can pair up any of the unsuited 2-T cards with either the suited K or J (except for the specific 4 that was dealt and discarded), the 4-to-the-royal will add 49 x 100 / 1081 = $4.53 and the correct play, by a mile, is to hold the 3-card royal.

In hand (c), AATT is worth $8.83 and (AQT) is worth $6.60 --- a difference of $2.23. Since we know the promotion adds more than $4 of equity to a 2-card draw, we still hold the 3-card royal.

On hand (d), however, we are drawing three cards. There are 16,215 of these combinations. How do we figure this? To start with, WinPoker tells us that (KQ4) is worth 1.6˘ more than (KQ). Many players will take a ³the promotion has GOT to be worth more than that² attitude and decide to make the switch without doing the exact calculation. This is not a terrible way to go about it. Obtaining all the information you can and making an ³educated guestimate² if often the way to go. But here in the column, letıs work it all the way through.

Drawing 3 cards to (KQ), we can start with (AJ). The fifth card must be between 2 and 9 and unsuited --- except it cannot be the 9 or 3 we were dealt and discarded. There will be 22 of these. A suited (AT) will yield an equivalent 22 combinations.

When we draw (JT), drawing a 9 as the fifth card gives us a straight or straight flush and so we donıt collect extra, but drawing an unsuited T is something that allows us to collect. But each of the eight ranks between 2-8 (or the T) count, for each of three suits, except we canıt draw the 3 we were dealt and discarded. This adds up to 23 combinations.

We now have (23 + 22 + 22) * $100 / 16,215 = 41˘. Since this is indeed more than the 1.6˘ difference between the plays, we should always hold a (KQ) or (KJ) over a 3-card flush with 2 high cards.

There are many other hands to consider, which Iıll leave for you to do. After all, my purpose is to show you HOW to do it rather than to work out everything for you. These are hands I invite you to consider:

A (KT) 85 you normally hold the A. Remember that the numbers will change depending on whether there are one or two low cards, or a card suited with the A, or both.

[A83] (KT) you normally hold [A83]. What about during the promotion?

[456] (QJ) you normally hold [456]. What about during the promotion?