How to win more money on Winning Streak guide

MasterSun

Ever wonder why Winning Streak contestants have different outcomes?
It's not all about luck; there is maths behind every game, i'll show u how to possibly win more money in one of games.

If you are lucky to be in that show in the coming weeks and you want to max your winning, here is what you need to know:

Each contestant has different chance of winning (that’s right, different), because the games are flawed, the 1st player of has better chance than the latter ones, take the " the coloured ball game" for example (think this is the 2nd game on the show), where each contestant is allowed to pick a colour, each colour has 3 balls, one of the 3 balls is random selected to be the winning price.



the trick is to pick the right colour, but which one?


After doing a basic descriptive statistics on these figures, we see that "red" has the highest Average Return of 16.67K
1/3*(50+0+0)=16.67
But this does not mean "red" is the optimal choice because we have not considered the element of risk.
We use Standard Deviation to represent risk in this case.

Immediately, we see that between the choices of “orange” and “White”, “White” is the optimal because even through they have the same return, “White” has lower risk.
So on, when “Pink” vs “blue”, Blue is optimal.


Since “black” has the lowest risk, we can use “black” as our base point to judge the others, thus we can calculate the risk premium for each colour. ie. For one K increase in return, how much extra risk we face.

We get:

(hope i have done this right)

So, Black is the safest option, but if you like a bit of risk, White is the most optimal choice, followed by green, yellow, red, blue, orange, and pink.

Colmo52

Cool story bro!

Skid

Can't wait to hear you explain that one to Marty when you are on the show.


(And you would probably have to factor in the contestant's attitude to risk.

Your figures show that the highest average returns (in general) come from the riskier strategies, which is not unusual in GameShows. The Orange and Yellow selections are the only ones out of sync)

Mr E

I think the people in the maths forum will appreciate this more (and would be in a better position to critique).

Moved from Television.

ray giraffe

I think the nicest way to show optimal choices is with a diagram of risk vs return.



It's clear that pink, orange and blue are worse than white by any definition, since they have more risk with no extra return.

Since you are choosing a group of 5 colours, I would say choose Red, Yellow, Green, White and then either Blue or Orange. Pink should never be chosen.

A true determination of the best choice for a particular contestant depends on the person's utility function for money
(e.g. How much more valuable is €50k over €10k, probably not quite 5 times as useful for some contestants!).

Also a parallel analysis of other rounds would be required to examine expected overall return, and overall risk.

MasterSun

Good graph, Ray.
but Red can't be the most optimal choice

erm, interesting, if we connect black and white by a straight line, we can get an inverese captial market line (think each point as a portfolio). Anything above the line would be crappy. Since no other point is below this line, Black and White are the most optimal options.



so on, we can set the optimal preference order in this way.


note: Red can't be the first preference.

ray giraffe

MasterSun wrote: »

Good graph, Ray.
but Red can't be the most optimal choice

Can you define "optimal choice"?

im invisible

Shur isnt all the money in that round pooled, and divided evenly at the end of the round?

ray giraffe

im invisible wrote: »

Shur isnt all the money in that round pooled, and divided evenly at the end of the round?

Do we have any winning streakers :pac: in the house that can shed some light on this?

MasterSun

ray giraffe wrote: »

Can you define "optimal choice"?

Under the rational expectation theory, the option with the lowest risk premium is the optimal one.

In other words, the optimal choice is the one which displays the lowest possible level of risk for its level of return.

For more info, please see
http://en.wikipedia.org/wiki/Capital_asset_pricing_model

MathsManiac

Yes, the money is pooled, so applying the most rational strategy will also depend on convincing the other contestants to go along with you.

I can't recall how many contestants play.

I would not agree that the capital asset pricing model is the best way to look at it. I would be inclined, with n players, to select the n colours with the highest expected returns, unless there are huge risk differences in things with very similar expected returns.

Edit: I think it's five players. Red, Yellow, Green and White are the best four, in my view, although I can see why one might not be enamoured with Orange as the final choice, and plump for Blue instead. This actually gives the same "portfolio" as yours, albeit for different reasons.

ray giraffe

MasterSun wrote: »

Under the rational expectation theory, the option with the lowest risk premium is the optimal one.

In other words, the optimal choice is the one which displays the lowest possible level of risk for its level of return.

For more info, please see
http://en.wikipedia.org/wiki/Capital_asset_pricing_model

I don't know anything about CAPM.

However, either it doesn't apply to this situation or you're not doing it right.

Using your logic, choose between the following options:
(A) Mean Prize €1,000, Standard Deviation €1
(B) Mean Prize €2,000, Standard Deviation €10
(C) Mean Prize €10,000, Standard Deviation €1000

As far as I can see you would choose (A) and (B) as optimal, however you obviously get more money from (C)

RoundTower

last time I saw it it was absolutely luck-based and there was nothing you could do to improve your expectation.

Is there anything that says that each of the balls of a given colour is equally likely?