Advertisment as a game of chance

Let there be no doubt: Ads are a gamble. Their purpose is to increase the chance someone buys your product. I realized this only when i red Seth Godin's thought: "If your ads work throw all the money on them." I think he failed to understand that there can be no determinism between ads and turnover, since an ad is never (1) forcing someone to buy or (2) informing that there is a product fulfilling a desperate need. In both cases: p(ads)=1

What we see is: there is a correlation between ads and turnover. Especially you don't know if the campaign works until you try it, a.k.a. subjective probability. Therefore we should model advertisement as a probabilistic game. Therefore the Kelly Criterion is highly relevant.

Thank you for listening

How should I call it?

Did you know that german is the only language that preferrs notebook over laptop?

Monty Hall Problem

The Monthy Hall Problem shows how little intuition humans bear to solve probabilistic enigmas.

Tree doors, one hides a price. The candidate chooses one and then the show master opens another one bearing no price. Would the candidate increase his probability in choosing the leftover door, giving up his first choose?

The astonishing answer: the two doors left (the first-chosen and the remaining-closed) are not of the same probability the price-doors. But the remaining-closed now has a probability of 2/3 in comparison with the first-chosen 1/3.

The trick: the show-master opened a door, given the candidates first choice. in 2/3 of the cases he had to avoid the price-hiding door, indicating that the other bears the price. only if the candidates original try was right, the show-master could open any other door.

I modeled this as BN with GeNie:

The candidate chose State0, the quiz-master showed State1 and the price probability resulted in p(Door0)= 1/3 and p(Door3)= 2/3.

Download the original Genie Ziege.xdsl.

Belief Nets

Based on the Bayesian Theorem we are able to model a network of evidences and influences to conduce a prediction: a Bayesian Network or Belief Net (BN). Somebody found out, such BNs beat other techniques in predicting certain sportsbets.

BNs allow an expert to map his expertise as causal dependencies leading to a certain prediction.

While Humans have shown skills in doing so, there is evidence that they fail in computing the overall estimate well.

While the domain expert and data available to us build up the nodes and their node probability table (NPT), the reasoning is left to Bayesian Theorem. Machine Prediction with a human designer.

A second benefit is the documentation of the evidences and influences leading to prediction and decisions. The state of the art is in combining Decision Analysis and Belief Nets in the model.

With University of Pittsburgs GeNie modeling tool, the world of Belief Nets opens for experimenting also to the interested layman.

Lets share some experiments!

Belief

The Bayesian Theorem is one of the most powerful black magic tools of mathematical occultism. I want to formulate in plain text the purpose and properties of Bayesian Theorem.

Given an evidence, to what degree can we assume a hypothesis is true?

Lets assume

Evidence e: a bettor places a for him unusual high amount on a horse

Hypothesis h: a bettor has inside information

Problem p(e|h): When we know e, to what degree can we assume h?

Hypothesis h is a little hard to prove. We would need a court to judge that there was a inside information or even manipulation of the game. Lets relax h to a more broader term and reformulate the problem. When a bettor places a unusual high amount what is the chance that he wins? We relax h to:

Hypothesis h1: a bettor wins
Where h is part of h1, i.e. a insider needs to win to be an insider.

We could look at what we know about our bettors:

1. Certainly we know when a bettor places an unusual high amount, lets say more that 5 times the average in a similar bet. We know how many bettors do that, p(e).
   
2. We know how many bettors are winning in our horse races, p(h1).
3. We know how many past times winners betted high, p(e|h1) means literally: given that a person wins what is the likelihood he betted high? We know that from the past.

Now Bayes says we can predict from this data if a person will win if he is staking high.

p(h1|e)= p(e|h1) p(h1)/p(e)

Lets say p(e|h1)>0.5, then we know winners are usually staking high. This gives us evidence that they are confident to win. Why could that be? Reflect on this :-)

p(h1) in a game like horse race should not exceed 0,5 since all the money is in the pot, i.e. there are no more winners than losers and winners are just a few. p(e) will be also under 50%, just because otherwise the amount would be "usual". Whats important here: the smaller p(e) in comparison to p(e|h1) p(h1), the greater p(h1|e).

The chance a highstaker is winning rises when fewer people are betting high amounts, while the ratio of winners that betted high stays the same. That is certainly true.

What is when p(h1|e)>0.5? Then its likely that high stakes lead to big wins.

In the case of p(h1|e)<0.5 I would certainly bet with the bettor without spending a doubt on his reputation.

The Guy said it all

Forecast from the bottom up. Most entrepreneurs do a top-down forecast: There are 150 million cars in America. It sure seems reasonable that we can get a mere 1 percent of car owners to install our satellite radio systems. That’s 1.5 million systems in the first year. The bottom-up forecast goes like this: We can open up ten installation facilities in the first year. On an average day, each can install ten systems. So our first year sales will be 10 facilities x 10 systems x 240 days = 24,000 satellite radio systems. That’s a long way from the conservative 1.5 million systems in the top-down approach. Guess which number is more likely to happen.

http://blogs.openforum.com/2008/11/25/the-art-of-bootstrapping/

Ads and Kelly

Seth Godin is asking a good question: "do ads work?", and if, why you dont buy all of them.

I want to make a game of it to look at everything through my Kelly Glasses.

What Ads do is improving the edge or advantage you have on a coin where head means buy, and tail means not. The odds are turnover minus costs, lets simplifiy and account only for the marketing costs.

Kelly knows that in a game of chance it's no good idea betting you entire bankroll. You could go bankrupt within one throw. The same is valid for everey amount of investment greater than a certain amount f>f'. 

If you could guesstimate your edge right, then G=edge/odds denotes your optimal investment rate

Guessing the Future of IT

Finaly I found an interesting new years profecy 

No more PCs.  I think that all Internet communications and work will be done on a handheld wireless device. The device will continue to function as a cell phone, but when you sit down at your desk you will "plug" it into a keyboard and monitor. This wireless device will have 4-8 GB of ram and a sizeable hard drive but all your content and most applications will be stored on the Web.

Howard Reingold used to say: "Think of your cellphone as the remote-control of your life"