I play an online free poker game from time to time. I usually play the Omaha variant. en.wikipedia.org/wiki/Omaha_hold_'em
The probabilities are here. en.wikipedia.org/wiki/Poker_probability_(Omaha)
Some weeks back I had 4 of a kind in three consecutive hands. Today I saw three consecutive hands of 4 of a kind but with different players.
So if the probability of getting that once is 20,824 : 1 what's the odds of getting it three times in a row? I realise each time it is 20824 : 1 but there must be a much bigger figure of consecutive ones.
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For each new game the cards don't remember what was drawn previously so the odds remain the same - I think?
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Assuming the cards have been shuffled (or more exactly, randomised) between deals then I suppose the odds that one will be 4 of a kind are the same each time.
But the odds given are for the first four cards taken off the pack. They must be different for the other hands in the game, and the odds that one of say four hands dealt in one game will contain 4 of a kind must be lower than if only one hand is dealt. It's seems likely that the odds against a single hand in a game being 4 of a kind reduce as the number of players increases.
But I have never been much good at probability. At least I am aware of that, which has probably limited my gambling losses.
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If it's online then you could have any old odds, depending on whether it's decided you're going to get a good hand or not this time.
Like fruit machines. Long since decided whether you're going to hit the jackpot irrespective of how long you fiddle about with the pretty buttons.
Or is that too cynical?
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I'm no mathematician but I'm not sure Zippy is right. The odds of 4 of a kind in any one game don't change but the odds of it happening multiple times in succession is a different probability isn't it?
I wasn't really expecting a definitive answer. Crankcase probably has it right though. Reminds me that many years ago I had on my PC what was said to be the exact ROM for a fruit machine (Club Cops 'n' Robbers) which should have behaved identically to the "real thing".
However with the ability to slug performance, you could slow the blinking lights on the feature so that it stayed on each light for a second or more, thus in theory enabling you to select the top prize. However it often would not stop when you pressed the button on the top prize, but would flip on one spot to a lower prize.
(Oh, and on a similar vein, when I was in my early 20s I had something of an addiction to fruities. There was one machine which, if waited for a specific sequence of lights then dropped your coin in, would always come up with the jackpot on the next spin. Until they reprogrammed it anyways...)
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The odds of an event happening multiple times is calculated by multiplying the odds together. For example throwing a five on a dice is a one in six chance. The odds of throwing two consecutive sixes are one in 36. Three in a row would be 216:1
So if the odds of getting a particular hand in poker are one in 20,834 then the odds of being dealt the same hand three time in a row are 9,030,098,036,224 :1
Long enough for your opponent to be reaching for his six gun I would think .
Last edited by: CGNorwich on Tue 22 Nov 16 at 23:46
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>> Like fruit machines. Long since decided whether you're going to hit the jackpot irrespective of
>> how long you fiddle about with the pretty buttons.
>>
>> Or is that too cynical?
>>
Not at all. Having had those things destroy my first marriage (ex-wife was addicted) I've long believed that the only winner is the owner.
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What's the odds of that...? - zippy
