Someone asked me about a promotion at a Rounder’s bar that paid you an extra $20 for a max-coin 45678 straight or straight flush when played for quarters. The best game there is 6-5 Bonus.
My gut feeling is this can’t be a smart play for serious players. Rounder’s is an “everybody knows your name” kind of place for people more interested in socializing and drinking than they are at playing profitable video poker. Still, it’s a good exercise to find out just how good this promotion really is.
An extra $20 for a particular straight is an 80-coin bonus for max-coin quarter players. Looking at Video Poker for Winners we find that regular 6-5 Bonus returns a dreadful 96.87% and if we got the 80-coin bonus on all straights, the game would return 131.95% — for a difference of 35.08%. The key question is what percentage of all possible straights is 45678?
There are 10 possible different straights from A2345 to TJQKA. It’s tempting to say that one in ten of them would be specifically 45678. But that’s an overestimate. You hold cards such as QJ, suited or not, in this game, which could lead to any of three different straights: 89TJQ, 9TJQK, or TJQKA. But holding a 45 (which could lead to a 45678 straight) isn’t a smart play. So you’re going to end up with more straights with at least one high card in it than you will straights with no high cards in it.
I’m guessing about 1-in-11 straights will be 45678, which makes the bonus on the 45678 straight equal to 3.19% (35.08% / 11 = 3.19%). This actually pushes 6-5 Bonus Poker to slightly greater than 100% by a few pennies an hour!
This actually becomes a positive play — although considerably less than 25¢ an hour. But if you want to drink for free while playing a breakeven game, it’s not bad. If you tip the bartender a buck whenever he/she brings you the $20 bonus every couple of hours, you’ve taken the game into negative territory again. If you don’t tip the bartender, you look strange because there are only 15 machines there and players tip more in these types of places than they do in not-at-the-bar games in regular casinos.
A knowledgeable-player friend tried to figure this promotion and came up with about half the gain that I did. He took the 80-coin bonus, and figured it happened one straight in 10, so he divided by 10 and came up with 8, and added that number to the 20 coins you normally get for the straight.
This is incorrect. There are a lot of strategy changes you get when you have a straight of 100 (which you only make if the 45678 straight or straight flush is feasible) and there are only a few strategy changes to make when straights pay 28. While it makes some difference whether you divide by 10 — or 11, as I prefer, to get the correct answer, you need to use the methodology outlined here.
This promotion is far stronger for the player than I originally thought. Which is why I check out the math each time. And once I figured that it is slightly positive, I now need to look at what changes you need to make to the strategy.
Figuring out the strategy is a bit tricky — but not all that hard once you understand the technique involved. I’m not going to hand-feed you the strategy, but I will give you enough clues so you can figure it out yourself if you are so inclined.
Let’s look at the hand 7’458K’, where the quote marks means the cards are suited with each other (i.e. all hearts, or all spades, etc.) In regular 6-5 Bonus you NEVER hold inside straights with no high cards, so the 7458 draw is not even on your radar. How do we use VPW to find out with this promotion whether we go for the 4-card inside straight or the 4-card flush?
This is actually pretty easy. We simply set the value of straights to 100 (i.e. the normal 20 you get plus the 80-coin bonus), and enter in the five cards. When we do, we find out that the 4-card inside straight (worth 8.51 coins) is worth a lot more than the 4-card flush (5.11 coins). I strongly suggest you make the relevant changes to the pay schedule using VPW or other computer software and verify that you can duplicate these numbers. You’re going to need to get the technique down to continue with the exercise.
Now let’s consider ‘456K’7. Off the top of our heads, it’s easy to deduce that if the right 4-card inside straight is better than a 4-card flush, surely the right 4-card open-ended straight would be worth more, and hence also preferable to the flush draw. This is absolutely correct. But there’s a reason why I want to go through the exercise. What value of straight do you enter in VPW to do the calculation?
Entering in 100 again would be incorrect. To be sure, you’ll collect 100 coins if you draw an 8 and get the 45678 straight. But what if you draw a 3 and get the 34567 straight? Now you only get paid 20. How do you do this calculation?
The answer is to use the average of 100 and 20 [(100+20)/2 = 60)]. The value of the 4-card flush doesn’t change, but the value of the 4-card straight increases to 10.21.
Let’s look at 3-card straight flush draws. From the two-gappers (‘458’, ‘468’, and ‘478’), we use a value of 100 for the straight and 330 for the straight flush. After all, every time we collect one of these hands from this starting position, we will get the bonus.
From the one-gappers (‘457’, ‘467’, ‘568’, ‘578’) we use values of 60 for the straight and 290 for the straight flush. As we showed a few paragraphs back, half of the straights and straight flushes we’d get from this start will be the right one and half will be “un-bonused.”
From the no-gappers (‘456’, ‘567’, and ‘678’), now only one third of the straights and straight flushes will receive the bonus. One-third of (20+20+100) = 46.67. VPW needs to have the values for the hands divisible by 5, so I’d use 45 for the straight and 275 for the straight flush.
One more step in the learning curve. Let’s assume we’re looking at a hand such as 4h 5h 8h Qc Jc. We’ve already discussed that we use a values of 100 and 330 for the straight and straight flush to figure out the value of the hearts. But for the clubs, values of 20 and 250 are appropriate. How do we do this? We can’t enter both 20 and 100 in the same field at the same time. It’s not hard, but can you figure out how to do it?
The answer is we do it twice. We use 100 and 330 and enter in the hand and record the value of ‘458’. Then we go back and use values of 20 and 250, enter in the same five cards, and record the value of “QJ”. Whichever value is higher, that’s the one we use.
Which play is correct? I don’t know. I haven’t done the exercise. My goal here was to open your eyes as to how to use VPW to figure out this kind of problem rather than to do it all for you.
You might want to think about the hand 56789 of mixed suits. You need to at least consider the value of just holding 5678, hoping to hit a 4. Hopefully you now have enough tools to figure out the value you should enter into VPW for the straight to take into account the number of times you’ll draw a 4 and the number of times you’ll draw another 9. If you can figure out that a value of either 65 or 70 for the straight is correct (depending on how you round), then you’ve learned the lesson of this column
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