Chance of winning

The chance of winning ( English upside risk, odds ) is the mathematically measurable probability whether a specific positive event will occur or not.

General

The positive event can be a win , for example in gambling or the price gain in trading objects (for example, securities , commodities ), the victory in sports or in a political election . If this event does not occur, the complementary event takes place ( failure , price loss , defeat ). The risk teaching is sometimes risk as a winning chance or risk loss ( English downside risk ) defines the future from the entry events can result. Risks in which the risk of loss corresponds to an equally high chance of profit are called speculative risks ; if the chance of winning is completely absent, the risks are pure . Insurance companies therefore only take on pure risks if damage occurs; if there is no damage, this is not a realized chance of winning, because only the state planned in advance has been preserved. The risk of loss can be, on the one hand, unexpected expenditure or higher costs and, on the other hand, lower income or revenues . In terms of risk theory, the risk of loss can be understood as a potential negative deviation of a realized result from the expected one.

The calculation of probability owes its origin to the considerations about the chances of winning in gambling ; its beginning is inextricably linked with Blaise Pascal and Pierre de Fermat .

Measurement

The odds of winning are mathematically understood as the quotient of the expected probability for the event and the expected probability for the corresponding complementary event , where : ${\displaystyle Y=1}$ ${\displaystyle Y=0}$ ${\displaystyle {\text{P(Y=0) = 1 – P(Y=1)}}}$

${\displaystyle {\frac {P_{i}(Y=1)}{1-P_{i}(Y=1)}}}$.

The chance of winning has a value of 1 if the probabilities for both alternatives are the same. If the value of the chance of winning is above 1, then and vice versa. ${\displaystyle P(Y=1)>P(Y=0)}$

example

Throwing a coin: If “heads” falls when tossing a coin, this is the event in the above formula , “number” the complementary event . If someone taps heads or tails as the result of the throw, the probability that you guess correctly is 50%, so you definitely have a chance of winning of 0.5 or 50%. But if the stake is 10 euros , but the promised profit is only 19 euros, because the provider of the game of chance wants to make long-term profit, the expected value is euros. As a player, you can assume an average loss of 50 cents per game, although you have a 50% chance of winning. ${\displaystyle Y=1}$ ${\displaystyle Y=0}$ ${\displaystyle 19\cdot 0{,}5=9{,}50}$

economic aspects

A decision under risk can be systematized as follows with regard to the distribution of opportunities for profit and the risk of loss:

Decision situation	on the capital market	in the company
Safe profit, no risk of loss	Triple A - government bond with positive real interest	arbitrage
Opportunity to win> risk of loss	Corporate bonds with investment grade	Investment decisions
Opportunity to win = risk of loss	Zero sum game	Correction of wrong decisions through restructuring
Chance to win <risk of loss	Junk bonds , junk real estate , subprime bonds	Foreign investment in a non-industry start-up , lotteries
Sure loss, no chance of winning	Investment fraud , total loss of investments	Fraud by customers with bad debts

The arbitrage is completely risk-free, so a chance of winning can be realized with certainty (the probability is 100%). In contrast, certain - and unpredictable - losses occur when affected economic subjects are betrayed by others. If an opportunity to win is realized, the return or profit increases or the expense or loss decreases.

The intention to make a profit is inherent in the profit maximization principle , temporary losses do not change anything in the general intention to make a profit. In the case of longer loss periods, it must be possible under tax law for the lack of profit-making intent to establish from further evidence that the taxpayer only pursues the activity for personal reasons and inclinations related to his lifestyle . With a given risk, entrepreneurs must also take advantage of opportunities to win, because otherwise, under tax law, if there is no intention to make a profit, hobby is assumed.

If one follows the broad definition of risk for speculative risks, then risk management measures not only mean that the risk of loss is wholly or partially eliminated, but also that opportunities for profit are completely (with risk avoidance and risk transfer ) or partially (with risk reduction and risk diversification ) waived.

The job of the value analyst is to increase the odds, not the profit.

literature

• Literature on chances of winning in the catalog of the German National Library

Individual evidence

1. ^ Karl Hax, Fundamentals of Insurance , 1964, p. 26
2. ↑ Hans-Jürgen Wieben, Credit Rating and Risk Management , 2004, p. 40
3. ↑ Hans Friedrich Eckey / Reinhold Kosfeld / Christian Dreger, Statistics: Basics - Methods - Examples , 2000, p. 3
4. ↑ Dieter Urban / Jochen Mayerl, Applied Regression Analysis , 2018, p. 400
5. ↑ Volker H. Peemöller / Joachim Kregel, Basics of Internal Auditing , 2010, p. 194
6. ↑ BFH, judgment of November 19, 1985, BStBl. 1986 II, p. 289 = BFHE 145, 375
7. ↑ Marcus A. Gunkel, Efficient Design of Risk Management in German Non-Financial Companies , 2010, p. 79
8. ↑ Albert Bronner / Stephan Herr, Simplified Value Analysis with Forms , 2003, p. 7

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