a little card math help please
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?
How do you calculate a 2 card draw in which both cards must be dealt, such as 3 to a royal?
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?
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?
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.
Quote: djatcI'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?
How do you calculate a 2 card draw in which both cards must be dealt, such as 3 to a royal?
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?
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?
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.
1) 1/47+(46/47)*(1/46)
Means you can hit the card on the first card drawn plus if you miss you can hit it on the 2nd card drawn.
2) 2/47*1/46
Means you have to hit 1 of 2 cards on the first draw and the card you didn't hit on the first draw you have to hit on the 2nd card drawn
3) 20/52*4/51*3/50*2/49*1/48
Means you have to hit 1 of the 20 cards that can make a royal on the 1st card dealt (AKQJT in all 4 suits) and then get dealt the rest of the cards that make a royal of the suit your first card to a royal that was dealt to you.
Quote: djatcI'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?
How do you calculate a 2 card draw in which both cards must be dealt, such as 3 to a royal?
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?
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?
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.
Dealt royal: 52X51X50X49X48/5X4X3X2X1 = 649740
Another way to do it:
52/5 X 51/4 X 50/3 X 49/2 X 48/1 = 649740
When holding 3 to a royal:
47x46/2x1 = 1081
When holding a 2 card royal:
47X46X45/3X2X1 = 16215
When holding a 1 card royal
47X46X45X44/4X3X2X1= 178365
Draw Five:
47X46X45X44X43/5X4X3X2X1 = 1533939
2/47
2) 3 to a royal:
2/47 * 1/46
3) 5 card draw:
20/52 * 4/51 * 3/50 * 2/49 * 1/48
card of day promo: Depends on game and the card. I think Mission posted the chances of 4oak (JOB), and they are different frequency. You are more likely to hit 4oak on Jacks than you are for 4's...because you are more likely to hold a lone Jack than a lone 4 (actually, you would never hold a lone 4)...at least in JOB. Although, I think the difference is rather minimal. If you want to do the work, which wouldn't be hard, find the table Mission posted (I think it was Mission?)....and re-create a JOB chart or whichever game you're playing, to have 13 4OAK payoffs for each rank. Not to mention, if you were savvy enough and wanted to play "perfectly", you could find the value of the 4oak card of day...and add that to the return for that one 4oak. For example, card of day is 8 and the promo is a +$1,000 for 4oak 8's. You would create a table like....
Royal: $4000
Straigh Flush: $250
4oak A's: $125
4oak K's: $125
....
4oak 8's: $1,125
...
full house: 9
etc.
and from there, create a new strategy. for example, you might want to go for 4oak if you are dealt 88855 (FH) instead of holding the FH, when the 3 of a kind is the card of the day. You can use the strategy generator for this. PS: Strategy would be different (theoretically) based on the rank of card. If the JACK is the card of the day, you are in good hands because that card (other than queen I think?) has the highest frequency of hitting 4oak. If it's something like a 2 or 3 (excluding DW), you are in bad hands, because you rarely hold low cards. SO: If you calculate it for 8's one day and learn that strategy, go to the casino and figure out the card of day is 3's....strategy will be diferent! So be careful!
extra credit: Whenever it's +EV. :)
Quote: djatcHow 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?
First, you figure the total combinations on the draw with 47 cards remaining in the deck:
47X46/2X1 = 1081
Then you figure how many combinations will have the 4th deuce. With 47 cards remaining you subtract one card representing the 4th deuce. The 5th card will be one of 46 sidecards. So your chances of catching the 4th deuce is:
1081/46 = 23.5
Quote: djatcIf 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?
Wolf Video Poker has a function where you can set the payout to any particular 4K to whatever you want. Say you are getting a 100 coin bonus for 4 Jacks in 9/6 Jacks or Better. One-hundred coins is 20 bets. You change the 4 Jacks to 45 for 1 while leaving all the other quads at 25 for 1. Then you hit the analyze tab. The resulting stats will show that you make 4 Jacks every 5128.2 games and the overall payback is 99.9329%.
If you do the same thing with a low quad like fives then the stats would show you make 4 fives every 5687.3 games and the overall payback would be 99.8946%.
The difference between making a high quad and a low quad is you are never making holds like 4-5, 7-6, etc., but you are making holds like Q-J, K-J, A-J, or one Jack.
Quote: djatcExtra 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.
How to find a breakpoint. This is based on a FPDW progressive that I used to play in the old days. You are dealt this hand:
AH-KH-QH-JH-2C
The dealt wild royal has a value of 25 bets. The 4 card royal has a value of 19 bets. So at reset ($1000 on a quarter game) you would keep the wild royal. As the royal progressive goes up the royal cards gain in value. Where would the progressive have to be to play the 4 card royal over the dealt wild royal. At reset the difference between the hands is 6 bets. When you make the break you would be drawing one card:
47 X 6 = 282. Multiply 282 by $1.25 to get $352.50.
The breakpoint for playing the 4 card royal over the dealt wild royal would be $1352.50....that is, if you are playing max E.V strategy. If you are playing Minimum Risk strategy you wouldn't make the break.
pic or it didn't happen ;)Quote: IbeatyouracesHeld a single ace the other day and drew all four deuces! Of course it was on 9/6 JoB when they have NSUD :-\
Quote: djatcI'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.
Quote: mickeycrimmDealt 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)
Quote: AxiomOfChoiceYour 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
Quote: IbeatyouracesHeld 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.
