Quick Quads Strategy

[Webman]

After Bigboy's report, I found the following interesting tidbit for those of you discussing strategy for this new game. I posted it in that topic but figured it belongs here as well:

If you bet 5 per hand, the payout would be as you expect.

But betting that 6th coin not only opens up quick quad chances but it bumps up the payout for a few things as follows:

4 5s-Ks: 250 -> 260
4 Aces: 800 -> 1000
4 2s 3s 4s w/ A,2,3,4: 800 -> 1000I don't think that has been noted thus far in this topic.

[MikeA]

After Bigboy's report, I found the following interesting tidbit for those of you discussing strategy for this new game. I posted it in that topic but figured it belongs here as well:

If you bet 5 per hand, the payout would be as you expect.

But betting that 6th coin not only opens up quick quad chances but it bumps up the payout for a few things as follows:

4 5s-Ks: 250 -> 260
4 Aces: 800 -> 1000
4 2s 3s 4s w/ A,2,3,4: 800 -> 1000I don't think that has been noted thus far in this topic.


I noticed that right off.  However, with the strategy in holding for QQ's you will definitely not get as many "naturals" as when you were always just holding Trips.  For instance, if you have 333A5 you would be holding the 333A instead of the 333 which would reduce your chances of hitting the natural quad 3's with the kicker in favor of having 5 cards to hit for the QQ and 400 credits.  Does that make sense?  The bonus of 1000 would come in when dealt trip 3's with no potential kicker where you would discard the two extra cards and go for the natural or in the example, you got really lucky and hit that fourth 3 for the natural with a kicker!  Same sort of thing with 33327.  Basically, the same thing in holding the 3332 and hoping for either a three or an Ace!If you played this game a lot, I think you would see a large reduction in the number of natural quads you hit.  And, it would be foolish to discard a potential QQ card if favor of the natural in the case of trips.  Playing 5 hands, you hit QQ's almost as often as NOT hitting them when you make that hold.  It is a big bonus when you can hold an Ace with 2-4 when drawing to trips because of the outside chance of drawing the natural!It is a very interesting game when you start analyzing the strategy for it.

[Webman]

Good points.  However for the larger gain (+200) hands, I would think you are actually more likely to get 2s, 3s, 4s with a kicker in this one since you will be holding more kickers to have a shot at both the kicker hand or the natural payout (via quick quad). In other words, are your odds of hitting 4's with a kicker really better holding 444 instead of 444A?For the 4 Aces, I'm not sure the quick quad strategy harms that much so it is more of a straight up bonus.Getting fewer natural quads doesn't hurt much if the quick quad payout has higher odds and the same return. Right?Of course, there are a lot of variables involved here so I will defer to further experience before making any claims. Please correct me as necessary.

[MikeA]

Without having the capability of simulating this game (Shadowman is working on it) I can do nothing other than speculate also.When you are going for natural quads you first have to hit the 1 card in the deck you need to make the quad.  The kicker is a lucky bonus.  At least using DDB strategy.  When you are dealt low trips and don't have a kicker, then you have two chances of hitting the natural with the potential of hitting the big bonus if you do get the kicker.  That is the way I usually catch my 800 credit low-balls.  Observation...I think that is correct:Your best low-ball chance of getting a QQ draw is with trip 4's.  You can hit them with either Ace/3 or with 2/2.  So you are more likely to have a draw for QQ than with 3's or 2's.  If you have and Ace or 3, then you have a 4/47 chance of drawing what you need.  If you are holding a 2, then you have only 3/47 chance of getting what you need.  And that's interesting because the draw with the least liklihood of
hitting is the 4442? and with it, you still have the chance of getting
the fourth 4 with the kicker as well as one of the other three deuces
for 400.Next would be 3's.  With 3's, you have to have an Ace/Deuce.  If you have one of these then you have 4/47 chance of getting the other one that you need.  But you won't have as many draws to 3's as you do 4's because there is only one instead of 2 ways to draw to 3's.  And that's interesting because the draw with the least liklihood of hitting is the 4442? and with it, you still have the chance of getting the fourth 4 with the kicker as well as one of the other three deuces for 400.With 2's you have to have Ace/Ace and one of the aces would be in your hand so at best, you have only 3 cards to hit to make the QQ and 1/47 of getting the other deuce for 1000.None of that comes into question though.  If dealt a 222A? you are going to hold all 4 cards simply because you have 3/47 odds on getting one of those 4 cards that would pay 400 and 1/47 of getting the killer 4th deuce for 1000.How all that factors into the overall ER, I don't know.  It really is a facinating game concept.  I'd like to see it offered as a single line game.

Good points.  However for the larger gain (+200) hands, I would think you are actually more likely to get 2s, 3s, 4s with a kicker in this one since you will be holding more kickers to have a shot at both the kicker hand or the natural payout (via quick quad). In other words, are your odds of hitting 4's with a kicker really better holding 444 instead of 444A?For the 4 Aces, I'm not sure the quick quad strategy harms that much so it is more of a straight up bonus.Getting fewer natural quads doesn't hurt much if the quick quad payout has higher odds and the same return. Right?Of course, there are a lot of variables involved here so I will defer to further experience before making any claims. Please correct me as necessary.

[shadowman]

Drum roll please ..........
 
I FINALLY got my program to work correctly (I think) and here are the final results: The perfect play expected return of DDB quick quads is 99.16%. Here are the various cycle times.
 
Result  Frequency      Cycle Time                 % of Payback
 

rf    0.002347  42605.901639      1.877674   
sf    0.010735   9315.268817      0.536753
acesK 0.006002  16660.000000      2.400960 
aces  0.017084   5853.513514      3.416751 
2-4K  0.015968   6262.554217      3.193585  
2-4   0.093691   1067.334702      7.495306  
5-K   0.482924    207.071946     25.112045   
fh    0.991166    100.891304      8.920491   
fl    1.148998     87.032349      6.893988   
st    1.155732     86.525285      4.622926   
k3    7.021924     14.241111     21.065772   
p2   12.182950      8.208193     12.182950  
hp1  21.099478      4.739454     21.099478  
zip  55.769500      1.793095      0.000000    
 
I will start working on the strategy next.

[shadowman]

OK, started working on the strategy and I noticed a previous post of mine was incorrect. There are more situations where one breaks up a full house than just aces.
 
3 3 3 1 1 ... keep 3 3 3 1 (or 2)
4 4 4 3 3 ... keep 4 4 4 3  (or 1)

[shadowman]

Post unable to migrate

[Webman]

Sure, but can you do it left handed? Great work, shadowman.

[shadowman]

I did a quick analysis of the JOB version of QQs and came up with an ER of 99.41%.
 
I did this one left handed.

[MikeA]

Printer Friendly? But it lost the color coding.



9/6 QQ DOUBLE DOUBLE BONUS 99.16%
 


 
 


800.0000
Royal Flush
1.0365 Pair 8


400.0000 Four Aces w Kicker 
1.0047 Pair 7


251.0638 Four Aces 
0.9679 Pair 2,3


200.0000 Four 2-4 w Kicker 
0.9398 Pair 6


110.6383 Four
2-4
0.9186 Pair 5


100.0000 Trip
2-4 w/QQ duo
0.8723 TJQK


52.0000 Four
5-K
0.7979 9TJQ


52.0000 Trip
5-10 w/QQ duo
0.7447 89TJ


50.0000
Straight Flush
0.7317
123 


18.4255 4
Royal
0.7086 QJ9


14.1277 Trip
3,4 w/lower card (not half value)
0.7021 JT9


13.7846 3
Aces
0.6809 4 St,
2345-789T


9.0000 Full
House
0.6540
145 


8.5957 Trip
5-10 w/lower card (not half value)
0.6475
235 


8.5911 Trip
10
0.6098
QJ8 


8.3691 Trip
2-4
0.6050 3 StFl, 345-89T 


8.3525 Trip
9,8,7
0.6004 KQ9, KJ9 


7.1702 Trip
6, w/3 kicker
0.5939 QT9, JT8, J98 


7.1406 Trip 6
0.5938 AKQJ


6.9019 Trip 5
0.5840 QJ


6.0000 Flush
0.5658 KQ, KJ


5.4514 Trip
J-K
0.5566 AK, AQ, AJ


4.0000
Straight
0.5514 3 Flush, QQ pair, w/Ace 


3.5106 Pair
5-10 w/QQ pair
0.5514 347, 246 


3.4282 4 STFL, Open,
2345s-9TJQs 
0.5319 4 Inside St, 3
Hi Cards


2.3404 Pair
5-10 w/QQ duo
0.5180 3 StFl, 2
Gaps, 1 Hi


2.2307 4
STFL, Inside
0.5143 StFl, 1 Gap, 0
Hi, +234s


2.0279 Pair
Aces
0.5150 Ace


1.6809 Two
Pair
0.4903 KQJ


1.4478 Pair J-K 
0.4681 4 Inside St, 2
Hi Cards


1.4542 3RF,
QJT,KQJ
0.4630 QJ


1.3733 3RF,
KQT,KJT
0.4709 JT


1.3617 3RF,
AKQ,AKJ,AQJ
0.4535 KQ, KJ


1.2766 4
Flush
0.4566 QT


1.2498 3RF,
AKT,AQT,AJT
0.4580 3 Flush, QQ pair w/o Ace 


1.2350 Pair 3
w/ Ace,2 kicker
0.4383 KT


1.2350 Pair 4
w/ Ace,3 kicker
0.4461 Jack


1.1415 Pair T
0.4416 Queen


1.1204 Pair 4
0.4371 King


1.1014 Pair 9
0.4181 3 StFl, 2
Gaps, 0 Hi


1.0592 Pair 2
w/ Ace kicker
0.3488
Redraw