The Odds strategy is a mathematical procedure from the decision theory to select it made possible with large probability an optimal "„opportunity "“from a consequence of events. The procedure developed of the Belgian mathematician F. Thomas Bruss.

The strategy can be used then, if a temporal succession of events is present, by which some as "„opportunities "“applies, and before occurring an opportunity it does not admit is whether still another better opportunity follows later. A popular example is the situation of a used-car dealer, who does not know when being present a bid whether a further prospective buyer makes a better offer later.

Definitions

In order to be able to use the Odds strategy, the reality must be mathematically modelled. In addition a consequence of n events is accepted, e.g. each event could be a bid. The events are durchnummeriert with the index k from 1 to n: E1, E2,"… Ek,"… EN

Each event Ek is with a certain probability pk one "„opportunity "“.

If pk the probability for it is that Ek is the looked for opportunity, then is q_k = 1-p_k the probability for the fact that it is not it.

The strategy of the quotient has their name r_k = \ frac {p_k} {q_k}, which is called English Odds.

Algorithm

The strategy functions simply by the fact that starting from a certain index s, which "„stop index "“the first opportunity is noticed. In the example of the used-car dealer that that the offers of the first s-1 does not accept customers and notices starting from the event it the first opportunity, is called thus that customer sold, who s-ten as the first after that a better offer than all its predecessors makes.

The stop index s is determined, by odds are backwards noted: rn, rn-1, rn-2 etc. thereby are summed them, until the sum 1 is reached. That k, with which this sum is reached, forms the stop index.

Probability of success

This strategy is mathematically provably the best under all the strategies, which must select an optimal opportunity on the same assumption.

The probability for the fact that the best opportunity is used computes itself from the sum R-S rk and the probability of the QA for the fact that under the which are applicable events no opportunity is.

R_s = \ sum_ {k=n} ^s r_k

Q_s = \ prod_ {k=n} ^s q_k

Then the probability of success W = R_s is \ cdot Q_s.

Example

Assumed, the used car salesman knows that in one month average 16 customers are interested in a car, and it would like to naturally sell to that customer, who offers the highest price. An event is for the used-car dealer thus one "„opportunity "“if it is better than all previous. To the first offer applies with security, therefore is p_1 = 1. For the second offer p_2 = \ is frac {1} {2} etc. general applies p_k = \ frac {for 1} {k}.

From this q_k = \ frac {k-1 follows} {k} and r_k = \ frac {p_k} {q_k} = \ frac {1} {k-1}.

Since the used-car dealer has on the average 16 customers per month, is n = 16. The accompanying table shows that the stop index is 7, because with k=7 the sum 1 is reached.

The used-car dealer must wait thus up to the sieved offer, and then first to assume, that is better than all previous.

The probability of success is W=R_s \ times Q_s = 1.0349 \ times 0.3750 = 0.3881, thus approx. 39 %. In other words: The used-car dealer sells the car in 39 % of all cases at the best price.

Literature

• F. Thomas Bruss: The art of the correct decision. In: Spektrum der Wissenschaft. June 2005. Spektrum der Wissenschaft publishing house company ltd., pages 78-84.

Articles in category "Odds strategy"

We found here 1 articles.

Related Websites

We found here 6 related websites.

• Blackjack Odds Strategy
  blackjack odds strategy.blackjack odds strategy. A success delay for the anonymity single 9.3 <b>blackjack odds strategy</b> offer people.


• Fixed Odds Strategy - Why Hedge when you can Gain an 'Edge'
  Fixed Odds Strategy - Why Hedge when you can Gain an 'Edge'


• Online Blackjack casinos with special bonuses for internet black ...
  An Online Blackjack strategy is basically a set of recommendations how to ... when played without a general knowledge of your winning odds and game rules, ...


• Part 1 Odds-strategy, Odds algorithm, and Applications Part 2 On a ...
  Abstract: The odds-strategy solves a certain class of sequential decision. problems. Although, as we will show, the result needs only elementary to- ...


• Poker Hand Odds - Mike Caro University Poker Strategy
  Strengthen your poker strategy by learning what the odds are for different poker hands.


• Pot odds strategy question
  Pot odds strategy question, Expand / Collapse ... to win 100 on the next card) for the correct pot odds