VP Odds

I am new here, but play a lot of VP. I have some VP odds questions that I can't find the answers to here. If they have been answered, please point me to them. Thanks.

First, what are the odds of catching quads holding one card that is NOT part of the quads?
Second, what are the odds of catching quad aces with a 2-3-4 kicker holding one ace?

Thanks in advance for your help.

Quote: kadad

I am new here, but play a lot of VP. I have some VP odds questions that I can't find the answers to here. If they have been answered, please point me to them. Thanks.

First, what are the odds of catching quads holding one card that is NOT part of the quads?
Second, what are the odds of catching quad aces with a 2-3-4 kicker holding one ace?

Thanks in advance for your help.

1.) Assuming a 52 card deck, (not a Jokers game) you need:

(4/47) * (3/46) * (2/45) * (1/44) = (0.00000560648) * 8 = 0.00004485184 = 1/0.00004485184 = 1 in 22295.6293432


Or, if you want:

nCr(4,4)*nCr(43,0)/nCr(47,4) = (0.0000056064810921) * 8 = 1/0.00004485184 = 1 in 22295.6293432


2.) This one is a little tougher, but not much, since the kicker can be anywhere. The first thing you want to do is look at the probability of hitting the other three Aces:

nCr(3,3)*nCr(44,1)/nCr(47,4) = 0.0002466851680543 = 1/0.0002466851680543 = 1 in 4053.75

Okay, another thing you didn't tell me is if you threw away any 2's, 3's or 4's, and that is totally relevant. There are 12 such cards within those ranks, and there are 44 cards remaining assuming you caught three Aces (regardless of position) (52 -5 (Deal) - 3 (Drawn Aces) = 44 Remaining)

Therefore, the probability that you are going to do that if you did not throw away any Kickers is:

0.0002466851680543 * 12/44 = 0.00006727777 or 1/0.00006727777 = 1 in 14863.7506861

The probability that you are going to do that if you throw away one Kicker is:

0.0002466851680543 * 11/44 = 0.00006167129 or 1/0.00006167129 = 1 in 16215.0005294

The probability that you are going to do that if you throw away two Kickers is:

0.0002466851680543 * 10/44 = 0.00005606481 or 1/0.00005606481 = 1 in 17836.5002931

The probability that you are going to do that if you throw away three Kickers is:

0.0002466851680543 * 9/44 = 0.00005045832 = 1/0.00005045832 = 19818.3371939

NOTE: I'm not going to do it for throwing away Four Kickers, because you'd have a pair of Kickers, so you wouldn't do that.

Thanks very much. Was very helpful!

Mission is a pretty smart guy... when he stays away from Chicken McNuggets ;-).

The odds of anything in VP, if you didn't notice how he did it, is the number of chances left in the deck to draw the specified cards.

So, what are the odds of getting four Kings and a nine assuming you held the 9?

Well, there are 52 cards in the "deck" 4 of which are kings. ON THE DRAW means 5 cards were dealt out, you held the 9 and discarded the rest (assuming no kings). That means there are 4 kings left in 47 cards. Each spot has a chance of drawing the kings. In order to get kings you must first get 1 king, then 2 kings, then 3, etc.

SPOT 1 = held 9
SPOT 2 = need a king... still 4/47 left, so that's the odds.
SPOT 3 = assuming spot 2 got a king, there's 3/46 left.
SPOT 4 = assuming spots 1 & 2 got king, there's 2/45 left.
SPOT 5 = assuming spots 1, 2, & 3 got king, there's 1/44 left.

You'd multiply need all of these to occur and in mathematics when they're dependent on one another you multiply the individual odds.

odds of redrawing 4 kings holding a single 9 = SPOT2*SPOT3*SPOT4*SPOT5 = (4/47)*(3/46)*(2/45)*(1/44) = .0851*.0652*.0444.0227 = .00000559, or about 1 in 180,000.

I try to teach people to fish around here. Though Mission did show his work, so maybe I'm just re-iterating to try to drive the point home =).

#1, I don't think Mission did it properlys.

First off I'm assuming you didn't throw away a pair and held 1 (high) card, and you want the odds of getting ANY 4oak, not a specific 4oak, as long as it's not a 4oak of the single card you held.

Ok, so you're dealt 5 cards, throw away 4 of them, and hold one. Out of 13 ranks, there are only 8 ranks remaining which can fulfill a 4oak under the conditions posed. With 4 cards per rank, there exist 32 cards that are "good" to fill the first spot. After that, there are only 3 of that rank remaining....then two then one...

32/47 * 3/46 * 2/45 * 1/44 = 1 in 22,802.

Wow, three different guys answered the question, showing their math, but came up with different results. I'm not a math aficionado and don't want to check your work, but I'm gonna go out on a limb and say I think at least two of the answers are incorrect.

There is quite a gap between Mission's 1 in 22,296 and Romes' 1 in 180,000. Then RS implies that Mission gave the odds for a specific 4OAK and that the odds should be lower (my impression anyway) for any 4OAK. However, RS' odds of 1 in 22,802 are higher than what Mission posted.

Quote: kadad

First, what are the odds of catching quads holding one card that is NOT part of the quads?

Quote: Mission146

1 in 22295.6293432

Quote: Romes

odds of redrawing 4 kings holding a single 9 = about 1 in 180,000.

Quote: RS

1 in 22,802

Actually I may have ducked up. And I think Mission's is right. Forgot he had the * 8 in there.

Mission is correct. 47x46x45x44/4/3/2 then/8 = 22295.625

Do they have a promotion for this situation? IE. Hold any card ,get a 4oak in a different rank and receive xxx.

If not...

I say, who cares?

Quote: RS

Actually I may have ducked up. And I think Mission's is right. Forgot he had the * 8 in there.

Looks like Romes merely forgot to multiply by 8 for the remaining ranks in the deck. Looks like the odds of one particular rank is 1 in 178,365.

Quote: AxelWolf

Do they have a promotion for this situation? IE. Hold any card ,get a 4oak in a different rank and receive xxx.
If not...
I say, who cares?

My guess is a disagreement between the OP and an acquaintance.

I remember playing DDB one time, held a King (or Jack?) only, next 4 cards were Aces.

Quote: RS

I remember playing DDB one time, held a King (or Jack?) only, next 4 cards were Aces.

I had it happen Saturday. Held a Q and drew the four J's on JoB.

Quote: Ibeatyouraces

I had it happen Saturday. Held a Q and drew the four J's on JoB.

Why weren't you playing Super Double Double or DDBAF? n00b

Quote: RS

Why weren't you playing Super Double Double or DDBAF? n00b

I wasn't in Toledo, that's why :-) (they have 8/5 SDDB, 99.69%)