Quote:
Originally Posted by Superman707
If your 99.99 % machine gave out a royal right before you got there, while the odds remain the same, the probability of you hitting one decreases.
Odds and probability are 2 different things.
Quote:
Originally Posted by MuckPls
Also RTP doesn’t take things like getting a royal back to back to back into consideration, chances of it happening is exactly the same, otherwise it wouldn’t be truly random, but that’s another story.
Quote:
Originally Posted by leon
I think there are two things being conflated here- % payback based on a paytable, AND chance of hand occuring.
As others have stated, past events make zero difference in future outcomes. One could get dealt 10 royals in a row and your odds of being dealt a royal the 11th time are still the same.
Disclaimer: I have an economics degree and a minor in math which included a lot of statistics courses. However, that was some 35 years ago and I've forgotten most of it, so the "probability" of me butchering some of the math here is greater than 0 and less than or equal to 1.
What I think is being conflated here are independent outcomes (odds) and probability (future outcomes) which are based on the odds.
For example. When rolling a single die one time, the odds of rolling a six are 1/6 or 16.67%. As an independent outcome this will never change.
But, the probability of rolling a six and then rolling a six on your next roll is 1/6*1/6=1/36 or or just a 2.78% "chance" of that happening.
Let's look at roulette and assume ther are no green slots, just red and black. So on each "independent" spin there is a 50% chance of landing on black or red. As many have stated before, if you are walking thru the casino and notice its landed on red eight times in a row, putting your money on black, because it's "due", is irrelevant. You are basing you wager on a single independent outcome, which is 50/50.
If however, the table offers you a bet of wagering $1 and paying you $4 if FOUR reds in a row occur. Would you take that bet? Let's see.
The probability of spinning FOUR reds in a row are 1/2*1/2*1/2*1/2=1/16 or 6.25%. So what "odds" do we need on our bet to break even? We need to win 1 out of every 5 wagers, 1:5, or 20%. So for 100 spins we win 20*$4=$80. But lose 80*$1=$80. So this would be a horrible wager to make when we need 20% to break even and the house is only offering 6.25%.
So as it pertains here, I'll just use the odds of making (not dealt) a royal flush in most basic variants of VP at roughly 1 in 40,000. So while the odds on each hand remain the same, the probability of making a royal flush on consecutive hands are 1/40,000*1/40,000=1/1,600,000,000.
So the question is, if we see someone make a royal flush and cash out, should we play that machine? The answer is it doesn't matter. In the next 40,000 hands, on average, someone will make a royal flush. It's just that doing it back to back the probability is 1 in 1,600,000,000. But it's the same probability (before any future hands are dealt) if we say you'll hit a royal flush on exactly hand number 29,236.
So in any given independent hand, your odds are 1 in 40,000. But then pick a specific hand in the next 40,000 and your probability of making a royal on that exact hand are 1 in 1,600,000,000. Doesn't matter if you pick hand #1 (the next hand) or hand #40,000 (the last hand) or any hand in between.
So I agree with Superman707. Odds and probabilities are 2 very different things.
Disclaimer: Disclaimer: I've been day drinking and I might be stoned, so YMMV. (Your Math May Vary)