4 Aces with a Kicker odds = 1/16,236?

[spxChrome]

So, I'm looking over the stats and I see Special Aces (4 aces, w/234) odds are 1 / 16K+ and 4 Aces are 1 / 5k+. 
 
Could you statistically argue these numbers?  Given that any 4 of a kind is 1 / 423.  It appears they just multiply this number by 12 or 13 (the number of cards in a suit).  So saying that then any 4 of a kind is 1 in 423 and also any particluar 4 of a kind is 1 in 5k just like 4 Aces are 1 in 9K so would say quad 9's be 1 in 5K.
 
I'd like to see a more accurate statistic on getting Quad Aces because I don't think those numbers are correct.  Reason being for this example I don't always hold a 9.  But I always hold an Ace.  Think about this scenario on DDB or TDB you would never hold 99XAA here you would even throw away the 9's.
 
So given that you would hold and Ace or Pair of Aces over the other 12 cards in the deck it seems getting Quad Aces are alot more frequent than on 1 in 5K??
 
Same goes for getting Quad Deuces, noway are the odds 1 in 5K because you always hold the Deuces.  Mathmatically yes but in reality maybe a math genious can give a more accurate stat on getting quads if you favor that quad set.
 
(edit: any particular 4 of kind is 1 in 5K+ not 9k+ which is roughly 13 x 423) 
 

[Webman]

Where are you getting those numbers from? On this site we list the odds as:Four Aces
1 / 5,761


Four Aces with a kicker
1 / 16,236


Four Deuces
1 / 4,909I'm not arguing that these are more accurate, and clearly the odds will vary based on strategy. I'm just curious where your number of more than 9K came for quad Aces and Deuces.http://www.videopoker.com/insideScoop/statistics/

[shadowman]

I think he is looking at the cycle times for DDB and is confusing a straight flush cycle with four aces. SF is close to 9K hands.
 
The cycle time numbers are generated by cycling through all possible dealt hands and all possible draws while counting each result. They are accurate.

[New2vp]

Spx, As you indicated, you will get more quads in a rank that is favored, most of the time anyway.  There are some exceptions.  In Triple Double Bonus, you actually get fewer quad 2s-4s than quad 5s-Ts.  Plus you get fewer quad aces than you would get in Double Double Bonus.  This is because the strategy in Triple Double Bonus has you sacrificing the number of regular quads to go harder after quads with kickers.  Specifically in TDB, you hold AAA2 rather than AAA and 2223 rather than 222.  The numbers below for Deuces Deluxe do not include situations when there are natural quads plus a deuce because those count as 5 of a kind in that game.What is the least common quad in DDB?  Four Tens, go figure.  But four Deuces are the least common in TDB.  And four Aces are least common in Deuces Deluxe.Following are some numbers similar to what you asked for.  Enjoy!



Double Double Bonus 9/6






Frequency
out of 2,598,960 final hands






No kicker
Kicker
Total
% of total
Cycle


FOUR Aces
451.1
160.1
611.2
9.8%
4252


FOUR 2s
332.9
124.0
456.9
7.3%
5688


FOUR 3s
333.0
124.1
457.1
7.3%
5686


FOUR 4s
333.1
124.1
457.2
7.4%
5684


FOUR 5s
457.4

457.4
7.4%
5682


FOUR 6s
457.5

457.5
7.4%
5680


FOUR 7s
457.3

457.3
7.4%
5683


FOUR 8s
456.2

456.2
7.3%
5697


FOUR 9s
455.1

455.1
7.3%
5711


FOUR 10s
450.4

450.4
7.2%
5771


FOUR Jacks
499.9

499.9
8.0%
5199


FOUR Queens
501.2

501.2
8.1%
5186


FOUR Kings
501.8

501.8
8.1%
5179










Total


6219.2

418










Triple
Double Bonus 9/7






Frequency
out of 2,598,960 final hands






No kicker
Kicker
Total
% of total
Cycle


FOUR Aces
384.9
182.8
567.8
9.1%
4577


FOUR 2s
277.0
149.4
426.5
6.9%
6094


FOUR 3s
277.1
149.5
426.7
6.9%
6091


FOUR 4s
277.2
149.6
426.8
6.9%
6090


FOUR 5s
450.7

450.7
7.2%
5767


FOUR 6s
450.9

450.9
7.2%
5765


FOUR 7s
450.8

450.8
7.2%
5766


FOUR 8s
448.0

448.0
7.2%
5802


FOUR 9s
445.8

445.8
7.2%
5829


FOUR 10s
445.2

445.2
7.2%
5838


FOUR Jacks
478.9

478.9
7.7%
5427


FOUR Queens
479.5

479.5
7.7%
5420


FOUR Kings
480.0

480.0
7.7%
5415










Total


5977.4

435










Deuces
Deluxe  EV = 100.32%





Frequency
out of 2,598,960 final hands







% of total
Cycle




4 DEUCES
485.3
10.8%
5355




FOUR 3S
336.6
7.5%
7721




FOUR 4S
335.1
7.5%
7755




FOUR 5S
334.2
7.4%
7777




FOUR 6S
333.9
7.4%
7784




FOUR 7S
333.4
7.4%
7795




FOUR 8S
333.2
7.4%
7799




FOUR 9S
333.1
7.4%
7803




FOUR 10S
333.6
7.4%
7790




FOUR JACKS
334.3
7.4%
7775




FOUR QUEENS
335.4
7.5%
7748




FOUR KINGS
336.0
7.5%
7734




FOUR ACES
332.1
7.4%
7825












Total
4496.3

578

[spxChrome]

Yes that was an error on my part I have edited.
 
So New2vp  you are saying in DDB 4 Aces are 1 in 4252 and Special Aces are 1 in roughly 12K when favoring the Aces?

[New2vp]

Yes that was an error on my part I have edited.
 
So New2vp  you are saying in DDB 4 Aces are 1 in 4252 and Special Aces are 1 in roughly 12K when favoring the Aces?For 9/6 DDB, Webman's figures are exactly correct to the nearest integer, but for better understanding the line on this site about Aces might be modified by the words "with no kicker," which might have led to your initial question.  Spx, if you got your roughly 12,000 by subtracting 4252 from 16236, that is not how this math works.  What you do is take the frequency and divide it into 2,598,960.  So, we get:Quad Aces + Kicker:  2.598.960 / 160.07 = 16236Quad Aces with no kicker:  2,598,960 / 451.13 = 5761If you just consider all Quad Aces, with or without the kicker, you get a frequency of 611.20 which equates to 1 set of quad aces in 4252 deals, on average.2,598,960 / (160.07 + 451.13) = 2,598,960 / 611.20 = 4252By the way, what is "spxChrome" derived from?

[New2vp]

To clear up the remaining point in Spx's original question about the discrepancy between quad deuces and any quads:The odds listed on this site for quads in general are from 9/6 Jacks or Better, 1 in 423.  Individual quad odds in this game range from 1 in 5742 for Four Tens to 1 in 5105 for Four Kings.  That may seem like a contradiction to the odds listed for quad deuces, listed as 1 in 4909, because one would go for deuces much more often since they are more valuable at 1000 coins, but there is no contradiction since these odds come from a different game where in general there are not as many quads in final hands.The 1 in 4909 figure is from Full Pay Deuces Wild.  In that game, there is not as big a payoff in having quads 3s through Aces (worth 25 coins, same as a Wild 4oak, instead of 125 coins in Jacks or Better), so the odds for all quads in FPDW is 1 in 534 (not including the few 5 of a kind hands that consist of natural quads plus a deuce).  For the non-deuce quads, the range is from 1 in 6784 for Four Threes to 1 in 7709 for Four Aces.It is sort of nice that the worst odds for quads in Deuces Wild comes from Quad Aces, since many players do not really like seeing them when playing deuces wild, instead wishing they could "save" the aces for bonus natural games, preferably with a valuable kicker attached. 

[shadowman]

I think New2vp's numbers demonstrate the effect of strategy very clearly and not just for the aces. If you notice the number of 8s, 9s and 10s go down there is reason. When dealt 4 to a straight with a pair you go for the straight. This does not effect 7s and below.

[New2vp]

When dealt 4 to a straight with a pair you go for the straight. This does not effect 7s and below.Very good!  I was trying to figure out the reason for the significantly fewer quad 10s and hadn't yet.  Here, you mean 4 to a straight with a pair when at least one high card is present, right?  As in JTT98, JT998, JT988, QJTT9, QJT99, or KQJTT, where you keep JT98, QJT9, or KQJT.  So fewer pairs of Ts held before the draw must result in fewer quad Ts after the draw.  And, as you said this doesn't reduce the number of pairs of 2s thru 7s that are held since with a hand like 66543, you hold the 6s and toss the rest.I did notice a much smaller effect has to do with the very few quads that occur after tossing all 5 cards.   You obviously cannot get quads in the ranks of the cards that are thrown away.  I believe that there is a T among the 5 cards in a garbage deal about 70% of the time, whereas a 6 appears only 1/3 of the time.  Cards on both ends appear more often than cards in the middle since they are less likely to contribute to 4-card straights, both inside and open-ended, that are held in lieu of tossing all 5 cards; thus, deuces appear in about 70% of the garbage hands as well.   So, there will be more quad 6s (and more quads 3-9) than quad Ts from hands where you redraw all 5 cards.  The effect of this is considerably less than the effect that you pointed out, so it didn't account for the discrepancy in the numbers.Sorry guys, I'm sure this is more interesting to me than to others.  I notice that I kill off many of the few threads that I comment on, so I'm glad you responded.  With S-man's insight, the lack of an explanation for the reduction in quad Ts won't continue to bug me.

[cddenver]

Sorry guys, I'm sure this is more interesting to me than to others.  I notice that I kill off many of the few threads that I comment on, so I'm glad you responded.  With S-man's insight, the lack of an explanation for the reduction in quad Ts won't continue to bug me.

 
Not at all, keep it coming!  I hope the issue of fewer quad 10s didn't cause you to lose any sleep. ()   It's one of those things that's "perfectly obvious" - once you see some numbers and think about it for a bit.  Remember, a while back, we had a brief thread going about why more quads are hit in DDB than DB?  And fewer Straights/Flushes?  Same thing - someone posted some numbers (yourself, or maybe SM) and that got everyone's brain cells going.  For a little while, at least.
 
I admire you for originally posting those numbers late-night.  At that time of night it's a challenge for me to remember where the bathroom is when nature calls.  I happened to be awake when you put those numbers up and I thought, "gah, I'll look at them in the morning".