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[Mr J]

 If a coin is tossed 3 times and all three tosses land on heads, the PROBABILTY (odds) of the next toss coming up heads is only 1 in 16.

The "CHANCE", on the other hand, never changes and is 50% on EVERY toss.
 
(Its all in the wording I guess)

Ken

[Dr. Mabuse]

It`s a darn  good   consideration when   betting BLACK or RED ..

Dr. Mabuse

[sqzbox]

Probability and Odds are two different things - you must know that by now surely? And the if the 3 heads have already shown up then the probability AND chance for the next toss is still 50%.

[Rolex-Watch]

If a coin is tossed 3 times and all three tosses land on heads, the PROBABILTY (odds) of the next toss coming up heads is only 1 in 16.

The "CHANCE", on the other hand, never changes and is 50% on EVERY toss.
 
(Its all in the wording I guess)

Ken

The 1 in 16 IMO only applies if you declare the intent before any result.  The Probability and odds over a single out come are 50/50 (omitting the zero), over 4 decisions, sure 15/1 (1 in 16 before the first spin).  You need to state what you are applying them too, a single decision or series of decisions.

[Mr J]

Well......I sometimes post questions if I know I'm right, I post to get a bit of assistance. Meaning? I got into a huge arguement (at another board) so I thought I would post my question to many others so this other moron can read the "results". Thanks !!

Ken

[Albalaha]

If you consider only one toss, it is 50:50 but if u consider the probability of HHHH or TTTT, it is always 1/16.

[BEAT-THE-WHEEL]

WHAT   Albalaha mean, is,..
u should rephrase your question,
Not what the NEXT TOSS probability,
BUT...
"What the probability of SERIES result when a coin,
being 'TOSS FOUR TIME' "

And the answer is 1/16.

I am getting tired of these '50/50' ,
'can't win the edge', and can't win long term ,
and blah, bla,bla.debate...

All because they ask the wrong question
of what they had in mind and get the reply for other intended question!
...and then accuse other as moron...DUH!



List has 16 entries.
{H,H,H,H} {H,H,H,T} {H,H,T,H} {H,H,T,T} {H,T,H,H} {H,T,H,T} {H,T,T,H} {H,T,T,T} {T,H,H,H} {T,H,H,T} {T,H,T,H} {T,H,T,T} {T,T,H,H} {T,T,H,T} {T,T,T,H} {T,T,T,T}

[Leapyfrog]

If a coin is tossed 3 times and all three tosses land on heads, the PROBABILTY (odds) of the next toss coming up heads is only 1 in 16.
The "CHANCE", on the other hand, never changes and is 50% on EVERY toss.
(Its all in the wording I guess)
Ken

Ken - You are right. Don't get lost in the words. If you explain why need an answer to this question, then i will be able to clarify this better. This is the first question i had when i started playing roulette and i have got myself around it.

Let me add a simple addition to your question to explain this better and let me try explaining this with only 3 spins instead of 4 spins.

TTT
TTH
THT
HTT
THH
HTH
HHH
HHT

Out of 8 probabilities (possibilities) there are two probabilities in which HH appears in the first two spin. The next spin appearing H and the sequence becoming HHH is 1 out of 8 probable chances. Also next spin appearing T and the seuqence becoming HHT is also 1 out of 8 probabilities. So there is a equal chance of 1 out 8 possibilities for the next spin to H and next spin to be T.

This is the truth. The issue is whether this 1 out of 8 probability is something whether can be taken to an advantage. To be honest, or to be politically correct - No way that i am aware of - which doesn't mean that it doesn't exist. You expand this any number of spins, lets say 35 spins, and then you will figure out that every single pattern will have equal probability and there is no advantage of some one playing RBRBRBRBRBRBRBRB over someone playing RRRRRRRRRRRRRR or BBBBBBBBBBBB as they all have 1 in multiple chance of occuring.

To me the whole subject of probability and its application to roulette is dented with variances. At one hand you are explaining the expectation and the other hand you are saying there can be variance. So essentially you are saying if you walk down this road you will get to downtown, but it is possible that you might also stray into a jungle. Strange, very strange, it's a drunkards subject to study.

[Mr J]

"WHAT   Albalaha mean, is,..
u should rephrase your question,
Not what the NEXT TOSS probability" >>> They are not my words, per say. I quoted the guy I was debating with, what he said. This way, HE can't say I asked the question wrong. Point being, I was correct (thanks to you guys BTW, thanks!!). 

Ken

[Schoolman]

I always assumed that "chance" and "probability" refer to the same thing. Just goes to show that not defining your terms leads to confusion.

Odds are another way of expressing probabilities, and vice-versa.  Bookies usually use odds, but you can convert from one to the other easily.
   
You can have "odds against" or "odds in favour". The odds against is the ratio of the probability (chance!) of failure to the probability of success. The chance (probability!) of a dozen bet winning, for example, is 12/37, which is the success. The chance of failure is 25/37 because there are 25 "chances" to lose. So the odds against are 25/37 divided by 12/37. The 37's cancel out, and you're left with odds against of 25-12, or as it's sometimes written, 25:12, a bit more than 2-1.

If you want to express it as odds in favour of, just reverse the previous odds, so you get 12-25 in favour.
                           

[sqzbox]

On a single number -
odds = 35 to 1, or 36 for 1.
Probability = 1 in 37.


Totally different things.

It is the difference between the odds and the probability that makes the house money. It is REALLY important to make this difference clear when in discussion - all sorts of misunderstandings will occur if you do not.

[sqzbox]

Oh - and one further difference that comes to mind as I think about it some more - the house can vary the odds but they can't change the probabilities.  I think in certain South American countries the odds for a single number in roulette are 34 to 1, for example. I'm sure somebody told me this recently - but in any case, the odds are a choice whereas probabilities are not.

[Schoolman]

Hi sqzbox,

On a single number -
odds = 35 to 1, or 36 for 1.
Probability = 1 in 37.

Totally different things.

Odds here refer to the payout. Unfortunately the use of the term "odds" isn't consistent, as is observed in the Wikipedia article on Odds. I quote

Odds are a numerical expression, always consisting of a pair of numbers, used in both gambling and statistics. In statistics, Odds for reflect the likelihood that a particular event will take place. Odds against reflect the likelihood that a particular event will not take place. Unfortunately, the usages of the term among statisticians and probabilists on the one hand, versus in the gambling world on the other hand, are not consistent with each other (with the exception of horse racing).^[1][2] Conventionally, gambling odds are expressed in the form "X to Y", where X and Y are numbers, and it is implied that the odds are odds against the event on which the gambler is considering wagering. In both gambling and statistics, the 'odds' are a numerical expression of how likely is some possible future event. In gambling, odds represent the ratio between the amounts staked by parties to a wager or bet.^[3] Thus, odds of 6 to 1 mean the first party (normally a bookmaker) is staking six times the amount that the second party is. Thus, gambling odds of '6 to 1' mean that there are six possible outcomes in which the event will not take place to every one where it will. In other words, the probability that X will not happen is six times the probability that it will.

It remains true, though, that you can express probabilities as odds and vice-versa, without any ambiguity. In fact, it seems advantageous to express probabilities as odds in the world of casino gambling because it's easier to see what the house advantage is (but of course, the casinos probably wouldn't want that). It's not obvious that being paid at 35-1 and a probability of 1/37 shows that the house has an edge, but expressed as odds, it is. In my example of a dozen bet, for example, the odds (probability of a win) are 25-12 against, but you are paid 2-1 or 24-12 on a win. Now it's clear that the bet is not a fair one.

[sqzbox]

Nicely stated.  I would contend, however, that the context we are in is the gambling one and in common parlance when we talk about odds we are really meaning "the odds on offer" which is different to the probability of the outcome. However your point is well made about the logical equivalence. It's just this type of difference in meaning that causes problems in communication.

I confess I always think of odds in terms of what is on offer because I am aware that the game is unfair and the only way to measure the degree of "unfairness" is to compare the odds with the probabilities. The point was made to me quite categorically when I was demonstrating the game "penny ante" to a well experienced gambler friend of mine and once he understood the game his immediate question was "what are the odds"?

Anyway, thanks for your detailed response - very interesting.

[Dr. Mabuse]

A post by Nathan Detroit on the same subject  at another forum:

Quote by palestis *****You walk up to a roulette and decide in advance to bet on black. With a twist. First you wait until you lose 3 times in a row. Meaning RRR. (Of course you don't lose actual money. Only in the virtual loss mode). If the probability of the 4th spin to bring yet another red is 1/16,  then the probability of black should be 15/16. Overwhelmingly  in your favor. The question is this. With 50:50 chances, betting randomly, is it possible to keep on losing spin after spin after spin? How many times? And is there a limit after which, a 50:50 chance finally comes your way? ********

REPLY by Nathan Detroit

Excellent EC   method   based on   longterm   odds . Begin with the  first real bet at spin # 4 and  a  seasoned player familiar with this method  knows  the precise moment when to stop  betting.

This method requires  patience and reduces  the exposure to the  casino`s advantage. To select a table with the le partage rule is a must.********* end of quote