Is there a term used to show that mathematical odds will reveal themselves through increased repetitions?
For instance a coin flip always has 50:50 odds. However if tossed 10 times you may end up with a heads to tail ratio of 70:30 or 60:40.
But if you toss that coin 100 times the ratio may end up being 55:45.
1000 times and it gets even closer to something like 52:48
Is there a name for this? Do casinos call it something? Where their house edge comes to fruition the more someone plays?
The Law of Large Numbers, perhaps?
I feel sure this is the answer that OP is looking for.
There’s also the closely-related Central Limit Theorem, which states that, no matter what a probability distribution looks like, if you repeat an experiment numerous times and examine distribution of the averages of those outcomes, it approaches becoming a standard bell curve.
NM. Too slow.
That sounds like what I’m looking for. I wanted to use it in the thread about Vegas and why casinos comp winners. For the very reason:
“Any winning streak by a player will eventually be overcome by the parameters of the game.”
The casinos comp rooms so hopefully the guest gambles his winnings (increased repetions) and can get their money back.
Also the reason why I can believe someone when they tell me they never go to casinos but the one time they did they came out ahead,
over someone who says they are a casino regular and they typically come out ahead.
Just one point. Suppose you throw a fair coin. Then the H/T ratio will certainly approach 1/2 (that defines a fair coin, actually) but the difference H - T will not tend to 0. It will fluctuate a lot, being positive some times, negative others. Most likely it will stay in the range of plus or minus the square root of H + T (the total number of tosses).
A related term is regression toward (or reversion to) the mean.
Not “no matter what a probability distribution looks like”. There are a few conditions on the distribution for the Central Limit Theorem to apply, and though most distributions one will ever encounter do meet those conditions, some don’t. For instance, if your starting distribution is Lorentzian, then your distribution of averages will also be Lorentzian.