Another QUICK QUADS Question

[COLTON]

I was impressed with New2VP's analysis of the recent quick quads conundrum. I have another one that's been bugging me. There are two strategy charts I have used for DOUBLE DOUBLE BONUS 9/6 QUICK QUADS (one is Bob Dancer's accessible on this website; the other is from Wizard of Odds). There is one area where they are not consistent.

In Bob Dancer's Strategy Chart, it says that you hold three Aces, 3's and 4's over a full house (excluding, of course a Quick Quad 4 of a kind--i.e. 44422). Wizard of Odds says you only hold three Aces and 4's over a full house, which would mean that you keep a full house with three 3's. I would love an answer to the question, because it has popped up from time to time and I don't know what the best play is.

[Vman96]

Well, let's do an instructional lesson shall we?

Let's use 33388 as example:

If you hold the full house you win 45 credits. On a per credit basis, this is an expected value of 45/6 = 7.5

Now for the more difficult part. Only holding the three 3's. There are 1081 possible combinations of cards to draw (47*46/2) = 1081.

Four 3's with an Ace, 2, or 4: 12 ways (4 each rank) x 1000 credits = 12,000
Four 3's: 34 ways (46 kickers-12) x 400 credits = 13,600
Quick Quads: 16 ways (need A2: 4 Aces times 4 Deuces) x 400 credits = 6400
Full House: 67 ways (11 ranks of 6 combos each plus last 2 8's in deck) x 45 credits = 3015
No improvement: (1081-12-34-16-67) 952 ways x 15 credits = 14,280

Total wins possible: 49,295
Divide by 1081 combinations: 49,295/1081 = 45.601295

On a per credit basis this equals 45.601295/6 = 7.600216.

The Dancer strategy chart is correct. The Wizard's strategy as written is in error. However, the site's strategy calculator and hand analyzer that JB worked on both say to only hold 333, which is correct. The hand analyzer gives the exact same value: 7.600216.

http://wizardofodds.com/games/video-pok ... alculator/

http://wizardofodds.com/games/video-pok ... -analyzer/

[New2vp]

Thanks Colton, for the kind words.Well, there is a tricky play here, another example showing that Quick Quads strategy is a bit more difficult than regular strategy.There is a "treys-full" boat that calls for holding all 5 cards:  33344; so neither "always holding trips" nor "always holding the full house" is totally correct.If you look at Vman's calculations above, the difference is that if you hold just the 3's, the quads without and with kickers goes from a 34-12 split to 36 without and 10 with (since the pair of 4s would no longer be available in the stock), reducing the value of the trip 3's to 44.49, just below the 45-coin value of a full house.Vman and others are correct in that you usually hold only the trips regardless.  If you were really risk averse and were concerned with variance as well as expected value, you might be tempted to hold all 5 cards all the time.  There is considerable risk in going for the extra 0.60 coins; you will get more than 45 coins after drawing to trips less than 6% of the time.  Since I generally "worship at the altar of expected value," I admit to always taking the chance and holding only the trips unless there is a pair of 4s.  (Of course, with 33322 and 333AA, you hold 3332 and 333A, respectively, holding neither trips only nor the full house.)Don't feel too bad if you missed 33344.  I think one of Mr. Dancer's columns indicated that he just noticed this exception sometime last year.  Here at videopoker.com, we got an advanced look at Quick Quads (I think in 2007).  Shadowman and others took turns analyzing this game. At that time, some of the members worked out their own strategies before there were aids like what is at the Wizard of Odds and even the book that came out posted here by Glen Richards and Bob Dancer (which focused on basic strategy, generally ignoring penalty cards).  Because of the many different kinds of holds that you have to learn to play these games correctly, Quick Quads became my favorite game six years ago (sort of like the even more complicated One Eyed Jacks seems to be shadowman's favorite).  Quick Quads with the Wheel has even more strange combinations.  And I’m sure I spent more time playing around trying to determine the correct plays than it’s worth to get the occasional 0.51 or 0.60 coins in expected value.  But that’s part of the fun of video poker for some of us who look at it as a hobby or diversion rather than an income generator.

[COLTON]

Thanks to both of you, Vman96 and New2vp, for your prompt and thoughtful responses. I should have asked for assistance on this issue some time ago! We're fortunate to have such members in this forum.

[Vman96]

Whoops, I did forget about 33344. And as new2vp says, from a variance/risk of ruin standpoint, holding 3s full may actually be a desirable play for certain types of players like me who have terrible bankrolls.