In a previous article, we took a look at the MGM poker promo jackpot with a variety of requirements. The MGM jackpot was as follows:
- You had to make at least a full house or higher
- Both of your hold cards had to play
- The river card has to play in your hand and the river card had to be the day’s particular “cash card”. For the sake of my calculations, I used the five-of-clubs (5C) as the cash card, but you can take this to be any particular card that has to come of the river.
In that article, we concluded that 1-in-66,000 poker hands will meet all of these requirements at the same time. That’s a probability of 0.001505%, which is a relatively small number. A long-standing member of the WPDG brought it to my attention that the MGM jackpot was hit approximately 8,000 hands into the promotion. Is it possible to assign a probability to this jackpot being hit in 8,000 hands? Yes, of course there is.
We know this event should happen about once in 66,000 hands. What are the odds it would happen in 8,000 hands?
We are benefitted by the fact that each poker hand is considered an independent event and no hand has any effect on any other hand. So there is a constant probability of 0.000015 of the MGM jackpot being hit on any given hand. This satisfies the rules to utilize the Geometric Distribution and be able to assign a probability to this jackpot being hit in 8,000 hands.
Using the Wolfram Alpha tools, we enter the two inputs that we have and we are provided with the following table:
|Number Of Hands (x)||Probability|
|x < 8000||0.1134|
|x = 8000||0.00001334|
|x > 8000||0.8865|
As you can see, in the x < 8000 entry, we can assign a probability of 11.3% to this jackpot being hit within 8,000 hands. That’s not an event you are going to see every day, but it’s certainly far from rare.
MGM Jackpot: A Caveat
You might be wondering how the 8,000 hand of poker were tracked. As far as I know, there is no formal system to actually track the number of hands that a casino deals over any given period. I tried to do some digging on this at the MGM to find out how they came up with 8,000 and I couldn’t get a firm answer. I’m assuming that the number came from a floorman’s estimate based on their experience in the room. That’s a perfectly valid approach, given the lack of other tools. But, for full transparency in this article, it should be noted that the count of 8,000 is more likely than not just an educated estimate.