Odd Video poker question. Please help.
August 8th, 2016 at 10:41:38 PM
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Hello I am a bit of a math geek but I am drawing a blank on how to answer this question. I want to be able to show how I came to the answer since people at my casino I work at are all getting many different, and wildly incorrect answers to this question. Thanks much and here goes.
At the poker room I work at we have a promotion. We pay you $100 if you get 4 of a kind, $200 for a straight flush, and $500 for a royal flush. But we have an extra bonus that goes with this. We then let you play one hand of draw video poker and if you get the same high hand that sent you to play your one hand of video poker you win $12,500. For instance if you get 4 nines at the poker table you need to get 4 nines on your one hand of video poker, 10 high straight flush you have to get a 10 high straight flush, etc. One person hit it a few years ago. What are the odds for getting the specific four of a kind you need and what are the odds of getting the specific straight flush or royal flush you need. I should mention that the kicker (fifth card not used in the four of a kind) doesn't have to be that same as the one you got at the poker table. And the suit of the straight flush or royal flush doesn't have to be the same for the straight flush or the royal flush. The machine deals you 5 cards, you hold the ones you want and then hit draw getting your remaining cards. So say you get 4 fives at the poker table, 5-5-5-5-9, you would go play the hand of video poker. If it deals you 5-5-6-7-8 you would hold the 5 and the 5 and if you get two more fives you will win the $12,500.
I am also curious how long until this machine will be in the casino most likely since once this silly promotion hits we will be removing the video poker machine and getting a much better promotion. But I know you guys can't answer that without knowing how many hands are dealt per day on average and I don't feel I should give away that information. Also I simply don't know that answer either haha. But I will make a rough estimate once I can get an answer to this question. Thanks much and if you could show how you came up with either of these answers it would be very helpful. I look forward to once and for all not having to hear all these wrong answers at my work lol. And being able to show people why the correct answer is in fact correct.
So what are the odds of getting a specific four of a kind in one hand of draw video poker where the fifth card doesn't have to be the same. And what are the odds of getting the same straight flush or royal flush in one hand of video poker where the suit doesn't have to be the same. A royal flush just has to be a royal flush, and a 9 high straight flush just has to be a 9 high straight flush. It doesn't matter it is clubs or diamonds or whatever. Thanks guys and I look forward to seeing why I was stuck on this and seeing hw exactly how you came up with the correct answer. Much appreciated in advance everyone. :)
At the poker room I work at we have a promotion. We pay you $100 if you get 4 of a kind, $200 for a straight flush, and $500 for a royal flush. But we have an extra bonus that goes with this. We then let you play one hand of draw video poker and if you get the same high hand that sent you to play your one hand of video poker you win $12,500. For instance if you get 4 nines at the poker table you need to get 4 nines on your one hand of video poker, 10 high straight flush you have to get a 10 high straight flush, etc. One person hit it a few years ago. What are the odds for getting the specific four of a kind you need and what are the odds of getting the specific straight flush or royal flush you need. I should mention that the kicker (fifth card not used in the four of a kind) doesn't have to be that same as the one you got at the poker table. And the suit of the straight flush or royal flush doesn't have to be the same for the straight flush or the royal flush. The machine deals you 5 cards, you hold the ones you want and then hit draw getting your remaining cards. So say you get 4 fives at the poker table, 5-5-5-5-9, you would go play the hand of video poker. If it deals you 5-5-6-7-8 you would hold the 5 and the 5 and if you get two more fives you will win the $12,500.
I am also curious how long until this machine will be in the casino most likely since once this silly promotion hits we will be removing the video poker machine and getting a much better promotion. But I know you guys can't answer that without knowing how many hands are dealt per day on average and I don't feel I should give away that information. Also I simply don't know that answer either haha. But I will make a rough estimate once I can get an answer to this question. Thanks much and if you could show how you came up with either of these answers it would be very helpful. I look forward to once and for all not having to hear all these wrong answers at my work lol. And being able to show people why the correct answer is in fact correct.
So what are the odds of getting a specific four of a kind in one hand of draw video poker where the fifth card doesn't have to be the same. And what are the odds of getting the same straight flush or royal flush in one hand of video poker where the suit doesn't have to be the same. A royal flush just has to be a royal flush, and a 9 high straight flush just has to be a 9 high straight flush. It doesn't matter it is clubs or diamonds or whatever. Thanks guys and I look forward to seeing why I was stuck on this and seeing hw exactly how you came up with the correct answer. Much appreciated in advance everyone. :)
August 8th, 2016 at 11:54:07 PM
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Here are my results for four-of-a-kind:
An example: Suppose the player was trying for four aces and was dealt two aces. The probability of this would be combin(4,2) * combin(48,3) / combin(52,5) = 0.0399298. The probability of the player getting two more aces on the draw would be combin(2,2) * combin(45,1) / combin(47,3) = 0.0027752. So, the probability of the player getting two aces on the deal and two on the draw would be 0.0399298 x 0.0027752 = 0.0001108.
I get an overall probability of success of 0.0002955 or 1 in 3,384.0625.
| Good cards dealt | A (=Prob. Deal) | B (=Prob. Success on Draw) | A x B |
|---|---|---|---|
| 0 | 0.6588420 | 0.0000280 | 0.0000185 |
| 1 | 0.2994736 | 0.0002467 | 0.0000739 |
| 2 | 0.0399298 | 0.0027752 | 0.0001108 |
| 3 | 0.0017361 | 0.0425532 | 0.0000739 |
| 4 | 0.0000185 | 1.0000000 | 0.0000185 |
| Total | 1.0000000 | 0.0002955 |
An example: Suppose the player was trying for four aces and was dealt two aces. The probability of this would be combin(4,2) * combin(48,3) / combin(52,5) = 0.0399298. The probability of the player getting two more aces on the draw would be combin(2,2) * combin(45,1) / combin(47,3) = 0.0027752. So, the probability of the player getting two aces on the deal and two on the draw would be 0.0399298 x 0.0027752 = 0.0001108.
I get an overall probability of success of 0.0002955 or 1 in 3,384.0625.
August 9th, 2016 at 1:38:05 AM
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Below are my results for straight flushes:
My overall probability of success for getting a straight flush of the same rank is 0.000043 or about 1 in 23,080.75.
| Good cards dealt | A (=Prob. Deal) | B (=Prob. Success on Draw) | A x B |
|---|---|---|---|
| 0 | 0.0774833 | 0.0000026 | 0.0000002 |
| 1 | 0.6661126 | 0.0000056 | 0.0000037 |
| 2 | 0.2394035 | 0.0000617 | 0.0000148 |
| 3 | 0.0166374 | 0.0009251 | 0.0000154 |
| 4 | 0.0003617 | 0.0212766 | 0.0000077 |
| 5 | 0.0000015 | 1.0000000 | 0.0000015 |
| Total | 1.0000000 | 0.0000433 |
My overall probability of success for getting a straight flush of the same rank is 0.000043 or about 1 in 23,080.75.
August 9th, 2016 at 8:46:12 AM
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I did an intensive and exhaustive mathematical analysis on this question while enjoying my morning yogurt and came up with: really f***ing unlikely.
For instance, let's say you needed four 9s, and let's also say you were fabulously lucky in that you actually got dealt a pair of 9s. Getting dealt any pair at all is about 11-9 against, and it's 12-1 that said pair would be the one you want, so you'll only get that pair in the initial deal about once every 26 hands. You're still only 1 in 1024 to hit it. Getting dealt a singleton 9 would make it something like 50,000 to 1. Straight flushes would be about 48 times worse, in that you'd need all five cards. (The above numbers are approximations, of course.) So I estimate the EV of the promo to be about 40 cents if you have a four of a kind, and less than 10 cents if you have a straight flush. You'd be better off if they gave you a bonus bag of peanuts.
So this promo is pretty much a waste of time. They should instead give everyone a drawing ticket and at the end of the month, give away that video poker machine to the winner.
For instance, let's say you needed four 9s, and let's also say you were fabulously lucky in that you actually got dealt a pair of 9s. Getting dealt any pair at all is about 11-9 against, and it's 12-1 that said pair would be the one you want, so you'll only get that pair in the initial deal about once every 26 hands. You're still only 1 in 1024 to hit it. Getting dealt a singleton 9 would make it something like 50,000 to 1. Straight flushes would be about 48 times worse, in that you'd need all five cards. (The above numbers are approximations, of course.) So I estimate the EV of the promo to be about 40 cents if you have a four of a kind, and less than 10 cents if you have a straight flush. You'd be better off if they gave you a bonus bag of peanuts.
So this promo is pretty much a waste of time. They should instead give everyone a drawing ticket and at the end of the month, give away that video poker machine to the winner.
August 9th, 2016 at 9:53:28 AM
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I think the promo would be much better if they set up the machine to say bonus poker and you got 1 free hand. If you win the hand you received that payout but if you matched your hand you got a 10k bonus.
Expect the worst and you will never be disappointed.
I AM NOT PART OF GWAE RADIO SHOW
August 9th, 2016 at 2:24:24 PM
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Quote: JoeshlabotnikThey should instead give everyone a drawing ticket and at the end of the month, give away that video poker machine to the winner.
Unless they're using a 25-year-old VP machine, everybody living in California would be ineligible for the prize.
August 9th, 2016 at 3:01:36 PM
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ChesterDog -
Unless I'm mistaken, the numbers you provided are the odds of getting the match on the video poker machine. But this is AFTER you've already gotten the qualifying hand at live poker. Am I right?
Unless I'm mistaken, the numbers you provided are the odds of getting the match on the video poker machine. But this is AFTER you've already gotten the qualifying hand at live poker. Am I right?
I agree, and will go you one better. Give the player one, two or five free hands on a standard Jacks or Better $100 machine, where they keep whatever they win plus the bonus if they get a match.Quote: GWAEI think the promo would be much better if they set up the machine to say bonus poker and you got 1 free hand. If you win the hand you received that payout but if you matched your hand you got a 10k bonus.
I invented a few casino games. Info:
http://www.DaveMillerGaming.com/ —————————————————————————————————————
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August 9th, 2016 at 4:19:15 PM
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Quote: DJTeddyBearChesterDog -
Unless I'm mistaken, the numbers you provided are the odds of getting the match on the video poker machine. But this is AFTER you've already gotten the qualifying hand at live poker. Am I right?
...
Yes. That's the question I was trying to answer. For example, after getting a royal flush in clubs at the live poker table, my result suggests the probability of the player getting any royal flush on one play of the video poker machine is 1 in 23,080.75.
August 9th, 2016 at 7:21:09 PM
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FWIW, I got the same exact numbers as ChesterDog.
4 of a kind: 1 in 3384.0625
Straight Flush: 1 in 23080.74743
4 of a kind: 1 in 3384.0625
Straight Flush: 1 in 23080.74743
August 9th, 2016 at 7:30:32 PM
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Quote: PeeMcGeeFWIW, I got the same exact numbers as ChesterDog.
4 of a kind: 1 in 3384.0625
Straight Flush: 1 in 23080.74743
Hmmm. I was pretty far off with my guesstimates of the EV of the promo. It's actually almost $4 for the quads and about 50 cents for the SF. I think it would be a pretty decent promo if you could get ANY quad or SF for the bonus.
August 9th, 2016 at 8:01:37 PM
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Who thinks this shit up? This is a terrible promotion.
First of all you're giving away a large amount of money to a single poker player. Poker rooms promotions should give small to moderate amounts of money to many players. The latter money just goes back into the rakehole while the former money goes into a bank account.
Secondly this will take way too long to give out and just leave a salty taste in the mouths of your rooms regulars after three weeks of seeing how impossible this one is to win.
First of all you're giving away a large amount of money to a single poker player. Poker rooms promotions should give small to moderate amounts of money to many players. The latter money just goes back into the rakehole while the former money goes into a bank account.
Secondly this will take way too long to give out and just leave a salty taste in the mouths of your rooms regulars after three weeks of seeing how impossible this one is to win.
