Figuring It Out

I received an email to be answered on the podcast. Here it is:

I have a strategy question about 8/5 ACE$ bonus. I’ve been told that you play it the same as you would 8/5 bonus with the following exception: when dealt a full house with 2 or 3 aces where ACE$ is possible, you only hold the aces. Is that true? When dealt 2 pair and one of the pair are aces in the right position do you go for the full house or just hold the aces?

First of all, the correct strategy deviation is to break an aces full hand with THREE aces in the appropriate ACE$ position. Two aces in position are not enough. Today’s blog discusses the way to figure how big an error it would be to break either a full house or two pair with only two aces in the appropriate positions.

For those unfamiliar with the game, the four aces each have one of the four letters, A, C, E, and $, superimposed in yellow. The order of the superimposed letters is either contract bridge order or alphabetical order (which are identical in this particular instance), namely clubs, diamonds, hearts, and spades. 

If you get the four aces in the appropriate positions, with the fifth card in either the first or fifth position, you get paid 4,000 coins rather than the normal 400. It increases the return on the game from 99.17% to slightly more than 99.4%.

For simplicity, I’m only going to consider the ace of clubs and ace of diamonds (which I will call A and C, since those are the yellow letters superimposed on those two cards.) So, a two pair hand, with these two cards in order, might be listed as AC553. The suits of the non-ace cards do not matter. We’re going to be holding the aces, at least, so flushes are out of the question.

With AC553, holding two pair is worth $12.55 to the dollar five-coin player. If you have computer video poker software, this is easy to find out. If we hold AC only, how much is that worth? 

Holding AC, we get 45 quads out of the 16,215 drawing opportunities. The two extra aces must be in one of the following positions, where an x represents any card: E$x, Ex$, $Ex, $xE, xE$, and x$E. Each of these possibilities is equally likely. The first one pays us $4,000 while the other five pay $400.

So we let the computer program figure it out. One sixth of the time we get $4,000 for this hand, and five sixths of the time we get $400. This makes the hand worth, as a weighted average, $1,000. I don’t know about you, but I was surprised that it came out to be an even number like this. But the math is ($4,000 + 5 * $400) / 6 which equates to ($4,000 + $2,000) / 6 or $6,000 / 6 or simply $1,000. 

Plugging in $1,000 for four aces into the computer program, we find that with four aces worth $1,000, two pair is still worth $12.55 and holding the aces by themselves is worth $10.08.

This means the error is worth $2.47 every time it comes up, and it arises about every 136.7 hands. For somebody playing 800 hands per hour, this one error is worth an additional $14.45 per hour. Since we’re talking about playing $4,000 per hour ($5 * 800) through the machine, you’re giving up an extra 0.36%. Better off playing correct 8/5 Bonus strategy with no corrections at all!

The math for a full house with a pair of aces, such as AC777, is basically the same. Holding AC and drawing three cards is now worth $10.15 (because of additional chances for getting a full house throwing away 555 rather than 554), but we’re comparing it to the guaranteed $40 you’ve giving away by not keeping the full house, making the error worth $29.85. 

Dealt full houses happen every 694 hands. One in 13 times, aces are the pair (with some other rank as the 3-of-a-kind part of the full house). This multiplies out to a little over 9,000 hands, or a bit more than every 11 hours when you play 800 hands per hour.

Because this error happens so infrequently, it’s not that expensive over all. Each error is worth $10.15 on average, and if it takes eleven hours to make such a mistake, let’s call it 90 cents an hour. 

Adding them together (because you’re not going to make one of the errors without making the others), you’re giving up about 0.4 percent because of this misconception. In round numbers, you’re giving up about $20 per hour compared to playing regular 8/5 Bonus Poker strategy on the same machine. 

Calling it $20 per hour is approximate. Whether it’s actually $18 or $22 doesn’t matter to me. Even if it were a $2 per hour deficit, I would avoid the play. Especially when the “cure” (which is to play regular 8/5 Bonus strategy on these hands), is so easy. 

More than coming up with exact numbers and strategy, today’s blog is about “How do you figure it out?”  Video poker math isn’t difficult, but some players can’t figure it out without some guidance.