The following is a hypothetical problem set at an unidentified casino: Assume the games are single line, for dollars, and I play $20,000 coin-in a month. Assume the slot club pays 0.25% and the mailer gives me $160 a month (i.e. $40 a week times four weeks) as long as I play $20,000 or more coin-in.
One month, however, my mailer includes a coupon that will pay me double for four 4s with a maximum bonus of $500. If I’m playing a deuces wild variation, it has to be four natural 4s, and if I get five 4s with exactly one deuce, I get paid double for that as well. I get to cash the coupon once only and it expires at the end of the month.
Assume the best three games are 9-4-4 Deuces Bonus (99.45%), 9/7 Double Bonus (99.11%), and 9/6 Double Double Bonus (98.98%). I normally play Deuces Bonus at this casino.
This column addresses the question, “How should I attack this coupon?” Some of you may be turned off by this column because it is all hypothetical and I am not aware of any casino where this exact situation is currently happening. If that’s your position, feel free to skip the column this week. No hard feelings. Hopefully some of you believe that learning my methodology might provide insight into how you would solve a somewhat similar problem somewhere down the road.
Please note that the $160 a month doesn’t come into the calculation — at least not directly. I’m going to play at least $20,000 coin-in. If I haven’t collected the bonus by then, I’m going to at least consider whether or not to stop playing.
First of all, which game to play? Using my four 4s coupon in Deuces Bonus gives a bonus of $20 for four natural 4s, or $250 for five 4s with exactly one deuce. In Double Bonus, I would receive a bonus of $400, and in Double Double Bonus, the coupon bonus would be either $400 or $500 — depending on the fifth card. So how much is this worth?
The only software of which I’m aware that will provide estimates of natural 4s-of-a-kind in Deuces Wild games is WinPoker — using the game Deuces Deluxe. On my Windows 7 system, I still use the original disk that I once sold as “Bob Dancer Presents WinPoker.” I don’t know if WinPoker works on Windows 8 or not.
So I go to Deuces Deluxe and use the default pay schedule, but I set the bottom end of the pay schedule to 9-4-4-3-1-1, which is what it is in Deuces Bonus. I set the “natural 4-of-a-kind” category to 4, to give me a baseline. This returns 94.6002%! I know that’s dreadfully low but that doesn’t matter. All I am looking for is the difference between the natural 4s being paid single or double. I then set the “natural 4-of-a-kind” category to 8 and this game returns 95.2249%, for an increase of 0.6247%. This assumes that ALL natural quads get doubled, rather than just 4s, so I divide this number by 12 and learn that the double pay on natural 4s adds 0.052% to the base game.
For the 5-of-a-kind with exactly one deuce, I turn to Video Poker for Winners, which has the game Super Bonus Deuces — where the gimmick to that game is that 5s-of-a-kind with one deuce get paid more. Keeping the lower end of the pay schedule 9-4-4-3-1-1, I set both the regular 5s-of-a-kind and the “includes one deuce” category to a total of 250. This yields a return of 105.722%. When I do the same but make the “includes exactly one deuce” category to 500, it returns 107.393%. This means there is an 1.671% difference, and when I divide by 12, this gives me an added return of 0.14%.
It also says that I will collect one of these 5s-of-a-kind which includes exactly one deuce every 2992 hands. That’s for all quints. Multiplying this by 12 implies I’ll get five 4s with one deuce every 35,904 hands. This is considerably more than the 4,000 hands a month I’m used to playing — and there is no guarantee I’m going to hit it in one cycle. Speaking approximately, I have about 2 chances of 3 to get this hand within 35,904, 19 out of 20 to get it with twice that many hands, and 99 out of a 100 to get it within three times that many hands.
Although I figured it out, these are irrelevant numbers to me. It’s harder to collect four 4s in a deuces variation than it is in a game without wild cards, so if I’m going to play for four 4s, I might as well play for it in a game where it is easier and the game returns $400 rather than $20, or even $250. So for now, anyway, I’m going to reject this game. The bonus pays too little and it’s too hard to get.
Now let’s look at Double Bonus (DB). Video Poker for Winners allows you to set the return of four 4s exactly as you like. If you change the return of four 4s to $800, you’ll find the game returns 100.521%, with four 4s every 5,548 hands. Figuring this out on VPW is not trivial — but if you do the exercise yourself you now have “check figures” to determine whether you’ve done it correctly or not. The features on a computer program are useless if you don’t know how to use them — and now is a good opportunity for you to see if you can figure it out.
On Double Double Bonus (DDB), I’m not going to figure it out exactly. I’m assuming the bonus adds a little more than DB because sometimes I get four 4s with a kicker and in that case my four 4s coupon would pay $500 instead of $400, but since this hand comes about every 18,000 hands or so, I’m not counting on it. If I got four 4s without a kicker I’d turn in the coupon and collect my $400. Since this bonus adds a little more to DDB than it does to DB, but DB starts out being worth 0.13% more, I’m going to assume it’s close enough to be a wash.
If it’s a wash, you take your pick. I personally prefer the lower variance of DB, so that’s the game I would pick.
Strategically I would make two changes to normal DB strategy. First, on a hand like 4s full (e.g. 44433), I would hold the 4s only. And when I got a pair of 4s and a 4-card straight (e.g. 44567), I would hold the 4s instead of the more usual 4567. (I’d make the same plays in DDB, although in that game 44 is normally held over 4567 even without the coupon.)
With a cycle of 5,548 hands, I would play this game until I collected the coupon. Even after I had played the 4,000 hands to qualify me for next month’s premium mailer, the game would still be positive and I would keep going. I wouldn’t consider a stop-limit based on losses. Bankroll issues are very important, but that’s a discussion for another day.
If I was fortunate enough to hit the 4s before I had played $20,000 coin-in, I’d switch back to Deuces Bonus. In this case, the difference between 99.45% and 99.11% would make that decision easy for me.
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