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Video Poker Odds of flush holding 4 cards

Discussion in 'Video Poker' started by oldbrewzer, Jun 6, 2019.

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  1. oldbrewzer

    oldbrewzer Low-Roller

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    For the math experts, I was playing 25 hand DDB and got 4 to a flush dealt to me, discarded the off card and hit deal and did not get a single flush. Wondering what the odds of that happening might be. I know you can go through some extended droughts trying to get that one card to fill a flush, but 25 hands? Ouch!
     
  2. HuskerBB

    HuskerBB High-Roller

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    Odds for one hand should be 9/47 to get the flush - 38/47 not to get it. To get the odds of going 0 for 25 I think you would take that latter number to the 25th power.
     
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  3. subafrk

    subafrk Longing to be sipping a Scotch at the Cromwell...

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    Lol, I feel your frustration. A few years ago at Monte Carlo, I drew 4 cards to a royal on a 50 play machine. I thought for sure that I was going to get a royal somewhere in there but struck out. I'm not a math guy so have no idea what the odds are.
     
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  4. topcard

    topcard Celebrating 40 Years of Vegas Trips in 2020!

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    Each of those 50 hands is an "independent event". Your odds will be 1-in-48, for each of those events.
    For the flush - same thing, only there are more cards that fill the flush.
    9-of-48, for 25 events.
    Don't think about it as one 25-hand, or one 50-hand event.
     
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  5. zignerlv

    zignerlv VIP Whale

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    Which is just under a half of a percent 0.5%
     
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  6. OddsWrkin

    OddsWrkin Low-Roller

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    Minor correction, the odds of filling the Royal holding 4 is 1-in-47.
     
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  7. Norman Chad

    Norman Chad Low-Roller

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    I'm just enough of a math person to be dangerous, but it's the ole roulette argument that a bunch of blacks in a row means a red has to come next. Well, no. So everyone is right in this case. While the draw from hand X has no bearing on any other draw, and each of the 25 hands is an independent event (just like that of a roulette spin), there is still an expectation in play. You would expect to hit more flushes with 25 chances than with 1, and mathematically it is more likely to hit 1 flush with 25 hands than it is with 1 hand. So independent events, yes, but as with any game you expect to realize true odds with a larger sample size. Not to go on a tangent, but I'm reminded of the time Michael Shackleford simulated millions of hands of blackjack in two ways: one which simulated tablemates that played correct basic strategy and one that simulated tablemates that consistently made strategic errors. Over that large of a sample, the constant player in question had the same result under both simulations.
     
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  8. topcard

    topcard Celebrating 40 Years of Vegas Trips in 2020!

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    That's right...I forgot the discarded card! Thanks for catching that.

    To Norman's point - yes - the more events one has upcoming, the greater opportunity that one (or more) will result in the card you want... and that's true regardless of the quantity. Even playing just two identical hands (1-card draw to 4 of a Royal) doubles your chances of getting your card versus just one hand... but only when predicting in advance! Each single hand still holds a 1-in-47 chance of drawing your card.

    This leads right to the gambler's fallacy: That, after failing to hit in 49 events, you (somehow) must have a 50x greater chance of hitting on that 50th event then you did on the first event. After all, that would be 1-in-50...and that's pretty close to the advanced probability! "It's due!"

    It works when computing probability, in advance; i.e. - If I flip a coin 100 times, tails will probably come up close to the quantity of heads coming up - a true statement.
    If, on the other hand, you have already flipped the coin 36 times and tails has not come up yet, that is NOT an indication that, among the remaining 64 coin-flips that the chances of tails coming up should be somewhere near 50/64 (you know - to get things closer to "even" for the entire batch of 100 flips).
    The probability is actually about 32 out of the 64... it will always be a 50% probability each & every time before you flip the coin - whether we're talking about 1 event or a 1000 that haven't happened yet.
     
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  9. subafrk

    subafrk Longing to be sipping a Scotch at the Cromwell...

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    I'm the casino's favorite type of customer.....An emotional gambler, the worst kind.
     
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  10. NJS24

    NJS24 Voice of Reason

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    Although the OP’s scenario is extreme, forget math.

    Get real.
    In that case it’s not math at all, it’s a sketchy machine.

    If you deal the same scenario LIVE with real cards, no tricks... 100/100 times at least ONE flush of 25 will be dealt.
     
  11. tringlomane

    tringlomane STP Addicted Beer Snob

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    Possibly in a sample of 100 times you'll get 100 times with at least one flush. But it's not 100% likely. If VP machines don't behave like real decks, then they are breaking the law.

    1 in 203.17 events happen daily in a casino. Making a quad on your very next hand is harder than that.
     
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  12. NJS24

    NJS24 Voice of Reason

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    That is exactly what I’m suggesting. I think it is more likely the machine is/was set illegally than out of 25 hands, not ONE flush came.

    Tring, I appreciate your logic, but I am a realist. So much in fact, I just dealt the OP’s scenario. Sure enough, out of 25 draws (new shuffle each time) a flush was drawn 5 times (20%).

    I’m guessing that is about the expected outcome 9/47 (19%)? And if you or I dealt the same scenario over and over, I’m expecting 4 or 5 flushes would be the outcome every time. Sure, there would be a couple outcomes of 2, 3, or 6 flushes... but NEVER zero.
     
  13. jack v

    jack v Low-Roller

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    Had the same thing happen to me last year - 4 to the royal(50 play), I thought "I should get 1, maybe I'll get 2 or even 3, ", then i hit draw and watch them fill in...nothing.
     
  14. tringlomane

    tringlomane STP Addicted Beer Snob

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    Do it 999 more times and get back to me with your results. Serously though, don't bother doing that, that would take days.

    Missing 25 in a row is (38/47)^25 = 0.004922 or 1 in 203.17. Whether they are real cards or from a video poker machine.

    Thinking this happening is rigged is being anything but a realist. In random events, sometimes you get the short end of the stick. It sucks, but it has to happen to some people.
     
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  15. zignerlv

    zignerlv VIP Whale

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    "I’m guessing that is about the expected outcome 9/47 (19%)" --- There is no need to guess, yes, that is the exact probability of a single hand.

    "And if you or I dealt the same scenario over and over, I’m expecting 4 or 5 flushes would be the outcome every time" --- Based on what? Why would you "expect" this? We don't need to guess at events that are probability related. They can (and have) been calculated.

    "Sure enough, out of 25 draws (new shuffle each time) a flush was drawn 5 times "

    25 draws is an extremely tiny sample. It's meaningless in terms of assessing the probability. How about this? Hold 3 cards to a royal, and draw 25 times to a 25 play. How many royals did you get? Most likely zero? Then by your logic, royals are impossible if holding 3 cards.

    "Sure, there would be a couple outcomes of 2, 3, or 6 flushes... but NEVER zero"

    On the contrary, it is CERTAIN, that with enough attempts, there will be some draws where there are zero flushes. The math of this calculation has been already posted on this thread. The probability of this happening is about 0.5%. It can and WILL happen to EVERYONE if you play enough hands. So, given that, how can anyone state the probability is zero? Do you have any alternative ways to calculate the probability, that shows the probability is zero? Post it here and we can discusss it.

    There is a thread on another board, where someone stated that they were certain that probabilities presented in a game wouldn't hold. The person was so convinced that the math didn't hold that they put up more than $1,000 and the two of them ran a simulation to settle the disagreement. Needless to say, the math held, and the person is $1,000 poorer.
     
    Last edited: Jun 8, 2019
  16. Guy_

    Guy_ VIP Whale

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    @zignerlv
    I agree with everything you said except "It can and WILL Happen to everyone"
    Just because something can and/or "Should" happen does not mean it "Will" happen.
    Nothing that involves an element of randomness has any certainty.... That is why they call it probability.. not certainty
     
  17. zignerlv

    zignerlv VIP Whale

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    For all intents and purposes, if you play enough hands, this will happen to everyone. The scenario presented was that it will NEVER happen. If you want to contend that if drawing to this 100,000 times, that 1 in 10 million times (something ridiculous like that) someone wouldn't get zero flushes on all those draws, something like this is true. But digressing to such discussion will only confuse those who need to grasp the probability discussion of the original topic.
     
  18. NJS24

    NJS24 Voice of Reason

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    I am willing to bet that the OP has never had the same scenario where he drew 0/25 when 4 to a flush, so for him when this exact hand happens he is 100% not to make a flush.
     
  19. tringlomane

    tringlomane STP Addicted Beer Snob

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    Maybe so, but that's completely different than assuming a game is rigged just because he got unlucky for the first time in this scenario.
     
  20. oghuman

    oghuman VIP Whale

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    The original question was properly answered. You have a 9 in 47 chance that you'll get the card. Other than that all the rest of the math is not required. All the math guys here forget that the game is called GAMBLING. If you you want to just play according to the BEST play to win a minimum amount that's worthy discussing. However, if your sitting down to gamble the idea is to win as much as you can with the hand dealt to you. Otherwise, you are acting like professional and ensuring that you win something, at minimum get your money back for your effort. When you get a pair of Jacks didn't win anything you got your money back. I'm in a Royal drought , I usually play 3-5 play $1. That means a majority of the time I'm drawing to 3 hands. I've gone at minimum 750 hands an hour for 4 hours a day for 26 days without a Royal. All I know is the "numbers" "every 43,000 hands" are not working for me. At minimum I've play 80,000 hands times 3 without a Royal. What that means is the numbers don't work per machine they work at all machines everywhere. That means someone else somewhere else is getting that to average out.
     
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