# Apparently this is wrong!

A while ago I discussed a probability problem, I suggested that by adding a choice of a set, when the first value is designated to the player(s), changed the probabilities of event/outcome.  Science and elsewhere,  categorically said I was incorrect and talking out of my backside.

In the above illustration, I have expressed  the problem and represented directional vector paths by yellow and orange lines.

Each individual row, represented by the horizontal yellow line, is an individual identical set of three individual different components.

E.g

123

123

123

We shall denote this, the X-axis and we shall also denote a golden constant ratio of 1:3.   If we were to pick a card from any individual  row, we have a 1/3 chance of picking any value.  This remains true for also the first card/top card on the left of each row after any random shuffle of the rows denoted by the directional arrows.

We can observe , that P1 , P2 and P3 are all equal and have a 1/3 chance of the first card after the shuffle being any one of the three individual values. We can also observe that the golden constant ratio remains constant.

We can express that-

P1{X}=φ=1:3 or 1/3

P2{X}=φ=1:3 or 1/3

P3{X}=φ=1:3 or 1/3

P1=P2=P3

Where φ is the golden constant ratio and P1-P3 are players and X is axis alignment of player.

We can also express that the probability of any individual variant within X is –

P(A)/{X}=1/3   and each set independently has these odds has independent sets.

To offer a choice of set can be expressed has this -X ∆ Y which translates to X change to Y.

The Y-axis is represented by the orange vertical line.  We have realigned the players and now named them , P4, P5 and P6 to save any confusion.

You are now the player P4, who was P1, you now have a choice of three sets and will receive the first card/top card of your chosen set.  However your odds are no longer dependent to the rows of X, they are now dependent to the columns of Y and your alignment with the first cards of each row, the derivative of Y is made by the shuffle of X, so how could we possibly know what  values that was aligned of a column by the random shuffle of each X row.

We can express that Y=var(X) which means that Y is made of a variance of the values of X and not a golden constant of 1:3.

We can also express a density function change  f{X]∆f{Y}=σ2{A} /Y