Safest Betting Strategy - Math & Probability

Описание: Before we make a bet, the risk and profit ratio is normally an important factor we need to think about for our plan. This means we usually need to accept some risks of loss for a bet in which the winning probability is not 100%. Is there a way to design a risk-free betting plan under certain conditions? The answer is yes, and you can manage it easily based on some simple mathematical calculations.

For example, let's assume that the two teams to attend the soccer world cup final are Brazil and Germany. You have two friends, Alice and Bob, who support Brazil and Germany respectively. Alice thinks that Brazil will win the game and its probability to win is 60%. On the contrary, Bob believes that Germany will be the winner and its chance of winning is 60%. Are you able to design a betting plan to place bets with both of them so that you can make money for certain?

Now it is time for the answer. You can make the following bet with Alice. If Brazil wins, you’ll pay her $2.5. On the other hand, if Germany wins, she’ll pay you $3. Alice will be happy to agree with this bet because her expected profit on this bet is 2.5 x 60% - 3 x 40% = $0.3, or 30 cents. Then you will make the same bet with Bob that you’ll pay him $2.5 if Germany wins, and he’ll pay you $3 otherwise. Bob will also agree with this bet because his expected profit on this bet will also be 2.5 x 60% - 3 x 40% = $0.3, or 30 cents. So, both Alice and Bob will have expected positive profits based on their own winning odds. As the designer of this bet, you also have the expected positive profit, which is that you will get 3 - 2.5 = 0.5 no matter which team will win the game.

In fact, as long as Alice and Bob have an expected winning odds over 50% for their preferred team, there is always a way to design a bet that will give both of them positive expectation and you positive winnings at the same time. In the world of investment, hedge funds normally use similar strategies all the time to secure their profits.