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Coin Toss - Variance Perentage and Variance Number
Coin tossing.... people often say that in the long run it will return to equal ... that is simply not correct ... it might, but it is increasingly unlikely as the number of coin tosses increases
what is correct is that the variance percentage of all coin tosses from a half chance set of results will most likely reduce in the long term, nevertheless the variance number will most likely be greater.
if you are relying on this falsehood to restore your bank roll, it won't. however what will almost inevitably happen is that with more events the variance number will be disguised by a lowering variance percentage. so you will feel better even though you're probably no better off.
regards
aussie09
Comments
it wouldn't and can be disproved in one simple way... with infite spins, what happens on the next spin?
regards
aussie09
you'd go blind
Probability works the same way. The % of times the coin lands on heads approaches 50 as the number of times the coin is tossed approaches infinity. When the number of times the coin is tossed equals infinity then the % of times the coin landed on heads equals 50 (similiar to being the limit of a converging quadratic sequence).
exactly, as you increase the number of events the proportions will almost certainly get closer in percentage terms of the total and almost certainly the difference between the two numbers will be greater. what this means is that bad luck does not automatically recover it just gets disguised. it would be greater than a million to one chance that the number of heads and tails were the same. infinite in fact.
all that aside, the original point is that variance percentage is disguising variance number. you can't be consoled that luck will even everything out. skill will prevail. low skill players will over time increase their variance numbers negatively whilst good plyers will increase their variance numbers positively. interestingly at the same time both skill levels will have a reducing variance percentage.
regards
aussie09
In terms of luck evening everything out, it will even out the chance element of poker, such as when you are all in etc. This will also mean that everyone will get the same chances and situations etc in the infinite long term. So the skill comes in maximising every opportunity, or minimising losses.
I dont really understand what you mean about variance numbers and variance percentage. can you clear this up for me pweez.
You're confusing two totally un-related issues.
convergent series approach a specific limit or number ok.
in the same way the greater the number of coins you toss the closer and closer it will get to a 50 50 split.
so you have convergent series getting closer and closer to a limit, and you have coins being tossed getting closer and closer to a 50 50 split...
common factor being that the greater the number of times the closer it gets to something (not sure if that makes sense lol) but hmmm absolutely nothing like each other, two totally un-related issues... not so sure about that.
you proposed that at infinity the number of heads and tails would be the same... that is not correct.
if you are confused over number and percentage you might feel that luck will turn your way correcting any previous spell of bad luck. it won't.
example
Coin tossed HHHTTTTHHH.
That is 6 heads 4 tails
Variance number is +1 for heads
Variance percentage is +20% for heads
if we then spin the coin for another ten events with the results going with probaility
That is 11 heads and 9 tails
Variance number is +1 for heads
Variance percentage is +10% for heads
As we increase the number of events some might conclude that things even themselves out because the percentage has "halved"
However the original run of "bad luck" remainds the same
Variance number is still +1 for heads
One final example, if it helps further, consider 1,000 events of coin tossing. I will bet you that the result will not be 500 heads and 500 tails. I will give you odds too. Bigger odds for more spins. Send your stake to my Sky Poker account
regards
aussie09
blackfish....i think you're bluffing.
It is not true that "the greater the number of coins you toss the closer and closer it will get to a 50 50 split". The expectation is that it will tend towards 50/50 but this is a completely different concept.
In terms of luck turning your way correcting any previous spell of bad luck... chance is not dictated by the past, so if a coin was heads 5 times in a row, the next spin will still be a 50 50.
In terms of your variance number and variance percentage thing, are you showing that the variance % decreases, but the variance number does not necessarily? Because surely 6/10 heads is worse than 11/20 heads? Or are you just illustrating how it gets closer and closer to a 50 50 split but that does not mean that just because of a bad run things will improve in the future? Because surely they will in order for the mean to even out at 50 50. Sorry im getting a bit confused by this variance number, variance percentage thing so this part of the post probably is full of contradictions etc lol.
In terms of us gambling on whether 1000 coin tosses will have the exact same outcome of heads and tails then i would be happy to oblige. IF you gave me better odds than the statistical probability of it being exactly even. In terms of the number of possibilities. This is a calculation for mere novice lol. In terms of me sending you my stake on sky... point me to the transfer funds... oh there isnt 1
i refer the honourable gentleman to the responses given earlier.
I really dont care if im right or wrong here, i just want to understand it.
Obviously each spin is independant but thats just when you look at single spins.
So i cant understand why the more flips you do why it wont approach a 50 50 split. How does the real world outcome differ from the expectation?
help me mere novice!!
This is all difficult to comprehend
i guess the probability of something happening does not mean that it definately will... i think this is where i am getting confused.
Just dont understand how expectation can differ from real world outcome :S
ok i give up now lol... im doing my head in, and probably everyone else who reads this.