AxiomOfChoice
Joined: Sep 12, 2012
• Posts: 5761
June 10th, 2014 at 10:57:40 AM permalink
Quote: djatc

I'm not really math saavy so please help me with a few problems:

How do you calculate a one card draw with 2 chances, such as 3 deuces to draw to a fourth one? All I know is you take 1/47 for the first draw, then 1/46 for the second?

It's just 2/47. Think about it this way: You have a shuffled deck with 47 cards, and you win if your card is in one of the top 2 positions, and lose if your card is in one of the other 45.

Quote:

How do you calculate a 2 card draw in which both cards must be dealt, such as 3 to a royal?

The cards can come in any order, so there are 2 good cards for the first dealt card, and, if you hit it, one good card for the 2nd one. It's 2/47 * 1/46.

Quote:

How do you calculate a specific 5 card draw, such as a dealt royal? I know it's 1 in 2.2 million or something like that, but would to see the work. Do you just multiply 1/52, 1/51, 1/50, 1/49, and 1/48?

A dealt royal is actually about 1 in 650k. You are probably thinking of a specific one (ie, a dealt royal in clubs)

Your multiplication is wrong, because, like in the previous question, the cards can come in any order. Also there are 4 different suits. So you would multiply 20/52 * 4/51 * 3/50 * 2/49 * 1/48.

Another way of figuring it out is to say, there are combin(52, 5) = 52! / (47! * 5!) diferent dealt hands, and 4 of them are royals (one per suit), so it's 4 / combin(52,5).

Quote:

If a casino offers a card of the day promotion, can you just add the return to the 4oak and divide by 13 to figure out the return, or are there other factors?

There are other factors. In most games, some 4OAKs are more likely than others, so you can't just divide by 13. For example, in jacks or better, you will hold single king but not a single 5. So quad kings are more likely than quad 5s.

Quote:

Extra credit: When do you break a wild (deuce or joker) for a progressive royal? Certainly it must be quite high, as I've never seen such a strategy deviation.

No clue, but there are a few different tools on the wizard's site that will allow you to figure this out.
AxiomOfChoice
Joined: Sep 12, 2012
• Posts: 5761
June 10th, 2014 at 11:03:27 AM permalink
Quote: mickeycrimm

Dealt royal: 52X51X50X49X48/5X4X3X2X1 = 649740

Your final answer is right but your multiplication is wrong -- that is just combin(52,5). You are forgetting that there are 4 suits. (If you multiply those numbers, you don't get 649740, you get 4x that amount)
rudeboyoi
Joined: Mar 28, 2010
• Posts: 2001
June 10th, 2014 at 11:33:14 AM permalink
For the first question even though 2/47 = 1/47+(46/47)*(1/46) its important to put it in the form of 1/47+(46/47)*(1/46). Not really applicable in video poker but if you had two chances at hitting 1 of 2 cards you may be mistaken thinking its 4/47 instead of 2/47+(45/47)*(2/46) where those two statements are not equivalent.
mickeycrimm
Joined: Jul 13, 2013
• Posts: 2299
June 10th, 2014 at 1:12:27 PM permalink
Quote: AxiomOfChoice

Your final answer is right but your multiplication is wrong -- that is just combin(52,5). You are forgetting that there are 4 suits. (If you multiply those numbers, you don't get 649740, you get 4x that amount)

You're right, I was in too much of a hurry this morning.

52X51X50X49X48/5X4X3X2X1 = 2598960
2598960/4 = 649740
"Quit trying your luck and start trying your skill." Mickey Crimm
DRich
Joined: Jul 6, 2012
• Posts: 8538
June 10th, 2014 at 1:57:02 PM permalink
Quote: Ibeatyouraces

Held a single ace the other day and drew all four deuces! Of course it was on 9/6 JoB when they have NSUD :-\

I had a throwaway hand on Sunday and got back the four deuces on Deuces Bonus. Sadly, i didn't get the Ace or it would have been \$1000 instead of \$500.

Sorry Axel, I don't take pictures unless they are \$5000 or more.
Order from chaos