Hopefully it's the door out the front of the Casino and not the one out the back.You can not win at the casino.
If you do find a way to win, they'll call you a cheater and walk you out the door.
With the Casino taking it's margin the house will ultimately win.
It's simple math.
There is no tendency for mean reversion with a coin flip. No amount of previous heads effects the conditional expectation for future outcomes - the 50% expectation only applies to future outcomes from that point forward.
It will revert back to the mean of 50%, therefore a coin-flip is mean reverting. The more times you toss a coin, the closer it's going to get to the mean of 50%, it will never move away from 50% for a sustained period.
You're a little unclear, at least to me. The coinflip itself is not mean-reverting, it's just that the probabilities over an ever-increasing sample will make it appear that way. It certainly can move from 50% over a sustained period.
This is a tiny sample but as you can see it will over time, revert to 50/50 with a larger sample
As in trade 2 has a higher expectancy than trade 1 due to being a different system ? Otherwise why does the next trade have a higher probability of winning?
It won't necessarily revert to 50% due to variance. The sample may actually get further and further from 50%, although this is obviously not likely. I'm sure I know what you mean, I just don't agree with the way of how you are saying it. The distribution as a percentage is very likely to revert to 50% as the sample grows, but the coinflips themselves don't revert to the mean, and I assume that is why you said you don't recommend betting tails just because there have been 9 heads.
I specify that it is the distribution, not the sample, that has a high probability of reverting to the mean.
500flips
3000 flips
The odds of hitting an unlicky streak of 6 losses in a row are low but when you do you lose the lot. With the Casino taking it's margin the house will ultimately win. It's simple math.
A finite number of bets may yield a winning result for the punter (if their lucky) but certainty is mathematically assured for the casino as the number of bets increases to infinity.Likely, but not certain.
Very true.It may be simple to some, but most don't seem to be able to understand probability and expectation.
I once saw the same number come up 6 times in a row in roulette. The odds of that are 37 to the power of 5 or about one in 69 million.Odds of hitting 6 losses in a row isn't that low, 1 in 64... you'll hit that during most sessions at the table.
Runs of 10+ are not uncommon, spend an hour in a casino looking at the roulette displays and I'm sure you'll see at least one.
There is only one game in the casino where you can win money consistently and over sustained period... anyone care to guess?
Odds of x number of wins/losses in a row at 50% probability
1 - 50.00000%
2 - 25.00000%
3 - 12.50000%
4 - 6.25000%
5 - 3.12500%
6 - 1.56250%
7 - 0.78125%
8 - 0.39063%
9 - 0.19531%
10 - 0.09766%
11 - 0.04883%
12 - 0.02441%
13 - 0.01221%
14 - 0.00610%
15 - 0.00305%
16 - 0.00153%
17 - 0.00076%
18 - 0.00038%
19 - 0.00019%
20 - 0.00010%
poker
The most difficult concept for people to grasp is that these odds apply to the string of results.
If I start tossing a coin now, the chance of getting 20 heads in a row is 0.0001%. If I have tossed a coin 19 times and got 19 heads, the chance of getting a 20th head is 50%.
The 20th toss has no memory of what happened in the first 19. Only the tosser does (and hence they become losers).
The thing about martingale system, even without any table limit, is that the payoff isn't actually that good. What you win on say the 20th head is only 1 unit more than what you've bet in the first 19 rounds. And that's only if the odds are truely 50-50 (which they aren't).
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