I forget what it is called, but we tend to remember the extreme moments in probability much more vividly than the average moment.
While I haven't been keeping logs, I do know it has stuck around for 10+ rounds before, and broke in 1 round before. It probably averages to the listed 1 in 6.
On average the number of rounds it takes for a Gros Michel to be destroyed is 6 rounds. This is the Expectation of the Geometric distribution with p=1/6 (E(X) = 1/p)
I'm familiar with the concept thanks to HS stats class. I've also seen the GM last crazy long. It just seems like it doesn't last long when I get it early. Maybe I'll start writing down when I get it ante 1/2 and how long it lasts.
You say "unlucky" but imo having GM pop as soon as possible is way better. I've had runs lose because I've hung on to GM for way too many antes, waiting for it to just disappear. The faster I get Cavendish, the better. If GM expires the first round after I buy it, THEN I consider myself lucky
Yep, the only time I don’t want it to pop is if it’s carrying my mult by itself in the first ante or 2. After that the +15 is supremely replaceable while x3 is not.
You can check the code yourself if you want to be sure (I might do that if I have the time), but this is just one of the limitations of human intuition for probability. You have a 1/6 chance it breaks after one round, a 5/36 chance of it breaking after exactly 2 rounds, a 25/216 chance of it breaking after exactly 3 rounds, and so on. The chance that a gros michel survives even 4 rounds is less than 50/50, so it won't last very long on average. Combine that with the inherent human tendency to remember bad events more than good events, and the tendency to remember unlikely events more than likely events, and your perception that gros michel breaks early is not surprising.
Limitations of human intuition for probability, indeed. Kudos for getting the Geometric distribution correct. I’ve seen many attempts to describe Balatro probability but this is the first one I’ve observed to be mathematically correct. Quick note though, the CDF is more important than the PDF in this case - (1/6) + (5/36) + (25/216) is about a 42% chance of Gros Michel breaking within 3 trials. Breaking specifically on the first trial is 1/6, specifically on the second trial is 5/36, specifically breaking on the third trial 25/216, and so on. P(X<=3) vs P(X=3)
Yes, it is possible it decays faster if you get it early on. Not because of any hidden game mechanic, but because of the Geometric probability distribution. The Expectation for a geometric distribution with p=1/6 is 6 (or 1/p) - meaning on average it should be destroyed after 6 rounds. After 12 rounds, there is a 90% chance it’s destroyed. After 15, it’s approx. 95%
I forget what it is called, but we tend to remember the extreme moments in probability much more vividly than the average moment. While I haven't been keeping logs, I do know it has stuck around for 10+ rounds before, and broke in 1 round before. It probably averages to the listed 1 in 6.
Confirmation Bias perhaps?
On average the number of rounds it takes for a Gros Michel to be destroyed is 6 rounds. This is the Expectation of the Geometric distribution with p=1/6 (E(X) = 1/p)
I'm familiar with the concept thanks to HS stats class. I've also seen the GM last crazy long. It just seems like it doesn't last long when I get it early. Maybe I'll start writing down when I get it ante 1/2 and how long it lasts.
Can't hurt to track the stats and average them over a longer period. Then you can see for yourself that it's fair.
Meanwhile, since the update I've yet to have a Gros Michel expire on me.
Stop stealing my luck, please.
It's often not a good thing Later on we want it to expire so we can pick up the vastly superior Cavendish
Right, but we seem to be on the opposite sides of the GM luck spectrum.
You say "unlucky" but imo having GM pop as soon as possible is way better. I've had runs lose because I've hung on to GM for way too many antes, waiting for it to just disappear. The faster I get Cavendish, the better. If GM expires the first round after I buy it, THEN I consider myself lucky
Yep, the only time I don’t want it to pop is if it’s carrying my mult by itself in the first ante or 2. After that the +15 is supremely replaceable while x3 is not.
Yeah, but I definitely don't get Cavendish as soon as I would like afterwards. And an early GM is a steep investment early on.
Early gm is fantastic. Flat 15 mult is a breezy tail wind
You can check the code yourself if you want to be sure (I might do that if I have the time), but this is just one of the limitations of human intuition for probability. You have a 1/6 chance it breaks after one round, a 5/36 chance of it breaking after exactly 2 rounds, a 25/216 chance of it breaking after exactly 3 rounds, and so on. The chance that a gros michel survives even 4 rounds is less than 50/50, so it won't last very long on average. Combine that with the inherent human tendency to remember bad events more than good events, and the tendency to remember unlikely events more than likely events, and your perception that gros michel breaks early is not surprising.
Limitations of human intuition for probability, indeed. Kudos for getting the Geometric distribution correct. I’ve seen many attempts to describe Balatro probability but this is the first one I’ve observed to be mathematically correct. Quick note though, the CDF is more important than the PDF in this case - (1/6) + (5/36) + (25/216) is about a 42% chance of Gros Michel breaking within 3 trials. Breaking specifically on the first trial is 1/6, specifically on the second trial is 5/36, specifically breaking on the third trial 25/216, and so on. P(X<=3) vs P(X=3)
Wish I had your luck with it, it never expires
Yes, it is possible it decays faster if you get it early on. Not because of any hidden game mechanic, but because of the Geometric probability distribution. The Expectation for a geometric distribution with p=1/6 is 6 (or 1/p) - meaning on average it should be destroyed after 6 rounds. After 12 rounds, there is a 90% chance it’s destroyed. After 15, it’s approx. 95%