HOW DOES Bookmakers simple princes of the example

Bookmakers operate solely for profit. And, contrary to popular belief, the bookmaker profit depends not on the number of lost bets, and by correctly exposed factors. What is "right"? This means that for any, even the most unexpected outcome of the event, the bookmaker must remain at a profit. Consider how the coefficients are formed. First, analysts determine the teams' chances. This is done in many ways, which can be divided into two groups: analytical and heuristic. Analytical - it's mostly statistics and mathematics (probability theory), heuristic - a peer review. One way or another by combining the results are output probability event outcomes. For example, as a result of the activities of analysts and experts should be based on probabilities derived: 1 X 2 55% 30% 15% Although the probability of mathematics expressed in a number from 0 to 1, for a more "smooth" species we write it in percentage. Translating probability coefficients, we obtain 1 X 2 1.82 3.33 6.67 This - "fair odds", ie "Pure chance", but these factors are never in the line, because in this case the bookmaker receives profit. In line odds on the event will look like this: 1 X 2 1.65 2.90 5.00 Turning to the probabilities, we have: 1 X 2 60% 35% 20% Sum of probabilities is not 100% and 115%, and this difference is 15% and there is a bookmaker profit, profit margin, which he lays at odds on. Since receiving rates on this line, bookmaker sees that the sum of the players bets are distributed between the three outcomes as follows: 1 X 2 75% 15% 10% That is, in each set all the players in the amount of hundreds of thousands of dollars, $ 75,000 was delivered to win 1, $ 15 000 for a draw and $ 10 000 - to win 2. Most of the players most often puts a known favorites, compiled on the basis of outcomes of most of ekpressov . What do you get with every bookmaker embedded hundreds of thousands of dollars by players in the event of different outcomes? the outcome of consumption bookmaker (payment of winnings) net profit bookmaker 1 $ 123,750 - $ 23,750 X $ 43,500 $ 56,500 2 $ 50,000 $ 50,000 So we see that if the favorite wins, that, according to the logic, it happens more often, the bookmaker will suffer losses. If we assume that the teams' chances were calculated correctly, then 100 matches 55 complete victory for the favorite and losses bookmaker in the amount - $ 130 625 25 - draw and profit bookmaker $ 141,250, and 20 - the defeat of favorite and profitable bookmaker $ 100,000, ie . after a hundred matches the bookmaker a profit $ 241,250, but at the risk of $ 130 625 (for each delivered millions of players). But nevyigryshi favorites that bring profit in this situation bookmakers, are not uniformly distributed, ie, It may well be the case that in a hundred games a favorite to win one hundred percent (even in the next hundred will not win in 90, which statistically give the same probability distribution of 55% - 25% -20%), and loss bookmaker will be $ 237,500 per delivered a million players (though even in the next hundred matches its earnings of $ 482,500)! It is totally unacceptable for business, and the bookmaker is obliged to exclude even the theoretical possibility of such a situation. To do this, he must artificially understate the rate on the favorite. The bookmaker does not know in advance exactly how distributed bets, but knows for sure that the players will "load" on the favorite, so insurance overstates the likelihood of the favorite winning. There he can have two situations: either overestimate the probability so that it is in terms of percentage is greater than the proportion of bets on the favorite, or so that it will be lower. Suppose a bookmaker decided to put the following factors: 1 X 2 New probability distribution 85% 18% 12% new coefficients 1.18 5.55 8.30 Then, with the same distribution of the sums of rates will be: the outcome of consumption bookmaker (payment of winnings) net profit bookmaker 1 $ 88,500 $ 11,500 X $ 83,250 $ 16,750 2 $ 83,000 $ 17,000 As you can see, here for whatever the outcome of the match, the bookmaker will make a profit! If in 100 matches victories and failures favorite distributed "as planned", it will amount to $ 138,225 for each embedded player, in the worst case (100 out of 100 - the favorite wins) - $ 115,000 at best (100 out of 100 - defeat favorite) - $ 170 000 for each delivered a million! Now let's see what happens if overestimated the probability of victory was the favorite as a percentage still lower than the corresponding share of rates. Assume, as follows: 1 X 2 New probability distribution 72% 25% 18% new coefficients 1.39 4.00 5.55 What is the distribution of profits at the same rate we will have proportions? the outcome of consumption bookmaker (payment of winnings) net profit bookmaker 1 $ 104 250 - $ 4250 X $ 60,000 $ 40,000 2 $ 55,500 $ 44,500 As you can see, again, there was an option of losses for the bookmaker. Therefore, the bookies always prefer to overestimate the favorite, than to underestimate, or even in comparison with the real his chances, as compared to the distribution coefficients, which set the players with their bets, which always put on the favorite of most of the rates than it should be according to the likelihood of its victory. Odds and probabilities corresponding to those used in Example proportions rates, taking into account the profit margin, would have to be: 1 X 2 probability distribution 80% 20% 15% coefficients 1.25 5.00 6.67 And here it does not matter, in fact distributed teams' chances, whatever the outcome of the bookmaker will make a profit in the amount of 6.25% of the amount of money set by the players, that is the main thing - to know how to distribute their bets players! In reality no real chance of any allocation of funds to calculate exactly the players is impossible, there is always some error. Therefore, as has been said, the bookmakers are trying to initially underestimate the odds on favorite to guarantee a profit, ie, determine the chances of teams and add to the calculated probability of the favorite winning 15-20%. And as they become available interest rates, depending on their real current distribution coefficients vary to profit was the highest.