while we have a greater than 99% chance of winning, there is that 1% chance of losing
Nobody could say you're not giving this at least 101% effort.
Thanks? hehhehe. It's been fun so far ... (it's all fun until you lose, as the saying goes.)
To answer your last question, "loss runs" are series of losses in a row before a win, for 0, 1, 2, 3 ... For example, if you're tossing a coin, a head run of HHHT is 3, and a head run of T is zero. A "loss run" is just the same as a martingale sequence, and an analysis based on loss runs was how I intuitively understood martingale sequences, and how I thought everyone else would.
However I'm not a gambler, and the first quote shows me that you're interested in probabilities based on rolls, not loss runs. So the spreadsheet you made and the functions I posted are of no use to you.
However I'm not a gambler, and the first quote shows me that you're interested in probabilities based on rolls, not loss runs. So the spreadsheet you made and the functions I posted are of no use to you.
I'm also not a gambler until recently. I am interested in both the probabilities and the loss runs, now that you have defined it. So you mean to say, that at 87.7779% chance to win, I need to get (on average) 300,000 loss runs? Meaning, 300,000 martingale sequences before I hit a 6 loss streak?
If my inputs are as follows:
p = 0.877779
n = 5
Then,
The average number of loss runs until the next expected number of losses in a row: 1.5266
The average number of loss runs until the next 5 losses in a row: 41,772.0366
The average number of loss runs until the next greater than 5 run of losses in a row: 300,002.5896
So, a loss run is any martingale sequence? Not including just 1 loss. That means at least 2 losses in a row? Or does loss run mean any sequence of losses, including a single loss?
I read all three posts of your blog multiple times, and I'm still trying to get exactly what you mean. (I also read a lot of your other posts.)
In case you are not aware, I did a "live" experiment on the site, where I lost 6 times in a row twice, the first time after about 800,000 rolls, and the second time after another 492,000 rolls.
According to the same formulas (and even other formulas from other websites) the probabilities of a 7 loss streak or run at this chance to win is extremely low, which I took and interpreted as, the 6th roll in these two sequences are most probably the last to lose, the next one (the 7th) will most likely win.
That was true with the first time. On this second time, I still don't know yet if it will win since I have not yet made the 7th roll. However, since the average number of loss runs until the next greater than 6 run of losses in a row is about 2.4 million, and I've only rolled 1.3 million times, I think I'm not going to lose the next roll.
I also understand that, they keep saying all rolls are independent and dice have no memory, and assuming that, I still have an 87.7779% chance the next roll will win.