All the above is self explanatory when I said "from his perspective", but that's not my question which is "does the overall mathematical condition change if the host guess instead of knowing the same empty door to reveal?"
Wrong.Only applies to the first contestant.2nd player is shown 2 doors only.
Correct, the critical question is does it matter whether the host had opened the SAME empty door knowingly or randomly(independently guess) from the other two doors?
If the host knows everything, it is guarranteed...
So it is the info of which door first player picks rather than knowing which door host reveal that gives the edge from 1/2 to 2/3. The new player may not be aware but from the audience standpoint, is there some kind of a hidden transient change in the probability the moment he happens to pick...
Its already stated that the hidden door is no longer relevant since the host had shown it has no car. As far as the new player who has not observed anything is concerned, he is just presented with a NEW game where there are only 2 doors, one with the car. However, rather than guessing the 2...
For this new player who has not observed anything, there is no longer a 3rd door in the choice equation (it can be hidden behind a curtain).
There are just 2 doors for him to pick from when he arrives.
He can randomly pick one of the two.i.e. Prob=1/2
How can it be 1/3 if it is randomly picked? A new scenario with only 2 doors shown to a new player who has not observed anything should at least be 1/2 chance.
After the host reveal a door, a second contestant joins into pick a door from remaining 2 doors shown.
(1) If he has seen the host revealing the door, is his probability higher than 1/2 if he always pick differently from the first contestant first choice?
(2) If he has not observed what...
That is not what (2) meant or whether the coin has memory or not.
If you win $1 on 9.6 times and lose $3 every 0.4 times out of 10 groups/counts of 6 tosses (applying martingale if necessary only once on 6th toss), it is a positive expectation game conceptually.
However, the assumption was...
Thanks for the reply.Just wondering if we place a bet for consecutive appearance of T or H only after appearance of HTHT or THTH, would there be an advantage since probability is quite high if we count every cluster of 6 tosses as an event instead of every single toss?
I came across a post here which is puzzling:
http://quant.stackexchange.com/questions/4442/coin-toss-system
2 events:
(1) prob(H or T)of a toss = 0.5.
(2) prob(HH or TT) in a cluster of 6 tosses > 0.85.
If you are betting on event(2) .i.e.A group of 6 instead of the very next toss...
Rephrasing the question,
(1) find a way to overlap different sets of 14 numbers to form 2 sets X 3combos =6numbers, without duplicating exactly any of 6numbers.
(2) Expand the link's limited 14numbers fano plane coverage from scretch to N, numbers.
Any ideas how to go about (1) or (2)?
I came across an interesting combinatorics optimisation description for 14numbers.
Maybe someone good in combinatorics can expand this fano plane concept to a full 45 numbers lottery design. Any suggestions?
http://en.wikipedia.org/wiki/Transylvania_lottery
I am trying to analyse a past series of numbers that flucuates between 107&210 with a normal frequency distribution of mean 162.
What is the way to model and project short term future range for trendless but cyclical type of time series?
This is a basic example(1to10) just to try Bayesian analysis.
Let bias be expressed as Pi>Pb, where Pb is user defined, e.g 0.15
The goal is simply to find out if there was user defined level of bias for certain numbers in different historical sample set sizes, e.g last 30draws, last 70draws...