Is there a place for cold calculation
Is there a place for mathematical calculation in games, lotteries, where it is still customary to rely on luck - with this question we turned to Dmitry Dagayev, deputy vice-rector, Associate Professor of the Department of Higher Mathematics of the National Research University Higher School of Economics and a teacher of the course "Game Theory" on Coursera.
- Decision about, whether to sit down at roulette, whether to pick up bones or cards, depends on two components. First of all, this is the mathematical expectation of the result of the game - how much on average you can get in this game. for instance, if the lottery ticket with probability 0,1 will bring a win 10 dollars, and with probability 0,9 - nothing, then the expected winnings of participation in the lottery are 1 dollars. Secondly, is the player's attitude to risk. If a player is risk neutral, then if the price of the lottery ticket is higher 1 dollar, he won't sit down to play the above lottery, and for less 1 dollar will play with pleasure. If the player likes risk, then he will be ready to pay more for such a lottery ticket 1 dollar. Anyway, to make a decision, a rational player needs to be able to calculate the expected result. So yes, the mathematical analysis of the game must be started even before, how did you sit down to play this game, - says Dmitry.
- Interesting, how game theory interprets the concept of "luck".
- Imagine, what did you agree with a friend to throw 10 once a coin. If dropped 10 eagles, a friend promised to buy you a football ticket. The number of heads dropped is a random variable, and the loss 10 eagles are a very unlikely event (its probability is approximately equal 0,001). Nevertheless, the probability of this event is not zero. Onset of an unlikely event, which brings a win, in this case, dropping out 10 eagles, just can be interpreted as luck.
- Is it possible to participate in lotteries, advertising games, adhering to some strategy? What strategies can these be??
- Sure. Suppose, that you and your friend are flipping a coin, if heads come up, you win, on a tails - friend. Let's assume, that before each flip you can choose the size of the bet or decide to stop the game, and a friend is forced to make this decision. Then you can try to beat your friend as follows. The first time you bet one dollar, if you won, then finish the game, if lost, then double the rate. If you won the second time, then stop the game (and you win, earning 2-1 = 1 dollar), if lost, then double the rate. This is what you do until then, until one day you win. The moment you hit heads, you end the game, and your total winnings will be 1 dollars. This strategy allows you to "guaranteed" to earn 1 dollars. Many casinos deny entry to players, who use similar strategies. I put the word "guaranteed" in quotes for the reason, what is deception: in reality, the partner may not agree to double bets after each win, or you may not have enough money for the next bet. So you won't be able to win guaranteed..
- Advertising games, lottery tickets, draws - is there any classification for this, based on the probability of winning? Where luck is more likely?
- There are professional lottery organizers, they also include casinos. They will always be profitable in the long run simply for the reason, that all casino games have a negative mathematical expectation for the player. To play such games in order, to earn, definitely not worth it. Besides, there are marketing promotions, in which the mathematical expectation may well be positive. Participation in such promotions is safer for your budget.
The probability of winning the main prize in the most famous lotteries Megamillions - 1 to 175 711 536 PowerBall – 1 to 175 223 510 EuroMillions – 1 to 116 531 800 Eurojackpot - 1 to 59 325 280 The Primitive –1 к 139 838 160 The slogan 6 of 45 1 to 8 145 060
Calculation vseloterei.com
