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There is such a thing as theoretical RTP and
actual RTP,,, you will see this in most casino slots and live games which publish the RTP (a fixed number) and the actual RTP (which they will show for 24 hours, 7 days, and 30 days).
HE is directly linked to the theoretical RTP, but I know I am not wrong here. I always use House Edge to not avoid confusion. The term RTP itself is a theoretical value.
We can argue all we want but the facts are casinos display actual RTP, as well as the theoretical RTP. We can acknowledge these and help people understand better what is HE and RTP.
Well, when @Free Market Capitalist refers to the RTP term and says sample size doesn't matter, I guess he is talking about total potential profit/loss (from casino or player perspective), which, despite n --> infinity, actually still follows a random walk. True is that the average profit per round converges to the RTP. Total profit/loss in a 100% RTP setup still has its own randomness although intuitively you might think it has to be a zero sum game in the long run, but in fact it isn't. However, random walk swings in true 100% RTP setups could make the casino money, but it could as well drain the casino to bankruptcy. If this is what @Free Market Capitalist refers to, then it's correct.
I have done tons of random walk simulations in academic papers about VaR calculations for precious metal and raw material positions held by banks, and then related that to their overall risk profile. It's crazy how random walks can play out. The law of big numbers is not that trivial for someone who is not familiar with the matter, because at first it is not as intuitive as one might think.
@leea-1334 let's assume that the casino really displays what is going on, then it is correct that they can only present numbers for limited time intervals, but here is the thing:
If the "theoretical RTP" (as you call it) is 100% and the casino then provides the "actual RTP" for various time intervals, the actual RTP should fluctuate around 100%. Fluctuate more in smaller time intervals, fluctuate less in larger time intervals. But what is more important for the players, is that the RTP should at least every now and then exceed 100%. If it is truly a
symmetrical game and it is claimed to come with 100% RTP, there should be time intervals when the casino says "this week the
actual RTP was 105%".
Fact of the matter is that no casino would offer 100% RTP across the board with fully asymmetric games because profit/loss would be random, and businesses rather don't bet on randomness while seeking profitability.