Video Poker Initial Draw Probability Math
December 21st, 2010 at 2:21:42 PM
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From the book:
Draw Poker Odds: The Mathematics of Classical Poker By Cătălin Bărboianu
starting on page 31
Google Book review: HERE
This is on the Deal only.
Calculate the probability of:
(not on the draw)
1) any 2pair
0.047539016 = COMBIN(13,2)*1584/2598960 easy
2)4 to a flush (4 suited cards)
0.042917167 = 4*39*COMBIN(13,4)/2598960 easy
3) 4 to an outside straight (4 consecutive cards) not so easy, a lot of math to get:
124928/2598960=0.048068458
4) 4 to an inside straight
I'm lost here
I'm looking for help with #4, 4 cards to an inside straight.
Why?
I need the probability for any 2 pair, 4 to a flush, 4 to an outside straight or 4 to an inside straight, on the deal only.
Answer should be above 0.138524641
Thank you.
Combinatorics makes my head spin in circles.
Draw Poker Odds: The Mathematics of Classical Poker By Cătălin Bărboianu
starting on page 31
Google Book review: HERE
This is on the Deal only.
Calculate the probability of:
(not on the draw)
1) any 2pair
0.047539016 = COMBIN(13,2)*1584/2598960 easy
2)4 to a flush (4 suited cards)
0.042917167 = 4*39*COMBIN(13,4)/2598960 easy
3) 4 to an outside straight (4 consecutive cards) not so easy, a lot of math to get:
124928/2598960=0.048068458
4) 4 to an inside straight
I'm lost here
I'm looking for help with #4, 4 cards to an inside straight.
Why?
I need the probability for any 2 pair, 4 to a flush, 4 to an outside straight or 4 to an inside straight, on the deal only.
Answer should be above 0.138524641
Thank you.
Combinatorics makes my head spin in circles.
December 21st, 2010 at 3:39:57 PM
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Here are some hints:
1) How many 4-inside straights are there where the highest card is 7?
2) How many 4-inside straights are there where the highest card is 8?
3) How many 4-inside straights are there where the highest card is 9?
See a pattern?
1) How many 4-inside straights are there where the highest card is 7?
2) How many 4-inside straights are there where the highest card is 8?
3) How many 4-inside straights are there where the highest card is 9?
See a pattern?
"In my own case, when it seemed to me after a long illness that death was close at hand, I found no little solace in playing constantly at dice."
-- Girolamo Cardano, 1563
December 21st, 2010 at 8:47:01 PM
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Thank you.
I was making it too hard on myself.
And I also did not need to know the information.
Instead I do need to know how to subtract out the probabilities of having a pair of Jacks, Queens, Kings and Aces from a four card flush deal and a 4 card outside straight. In other words, the probability that a four card flush deal would also contain a pair of Jacks and higher.
And a four card outside straight deal would also contain a pair of Jacks and higher.
2)4 to a flush (4 suited cards)
0.042917167 = 4*39*COMBIN(13,4)/2598960
this probability includes pairs of jacks and better pairs.
example: 3h, 6h, 10h, Qh, Qd
Because playing VP, one would keep the high pair and not go for the flush or straight in most cases.
3) 4 to an outside straight (4 consecutive cards) not so easy, a lot of math to get:
124928/2598960=0.048068458
again, some are better than others at Combinatorics.
I have a text book in front of me and its talkin' but I ain't understanding!
I was making it too hard on myself.
And I also did not need to know the information.
Instead I do need to know how to subtract out the probabilities of having a pair of Jacks, Queens, Kings and Aces from a four card flush deal and a 4 card outside straight. In other words, the probability that a four card flush deal would also contain a pair of Jacks and higher.
And a four card outside straight deal would also contain a pair of Jacks and higher.
2)4 to a flush (4 suited cards)
0.042917167 = 4*39*COMBIN(13,4)/2598960
this probability includes pairs of jacks and better pairs.
example: 3h, 6h, 10h, Qh, Qd
Because playing VP, one would keep the high pair and not go for the flush or straight in most cases.
3) 4 to an outside straight (4 consecutive cards) not so easy, a lot of math to get:
124928/2598960=0.048068458
again, some are better than others at Combinatorics.
I have a text book in front of me and its talkin' but I ain't understanding!
