The chance of winning is the chance of winning multiplied by the amount of the prize. For example, if the chance of winning a prize worth NIS 1000 is 1%, the chance of winning is NIS 10;
The profit expectancy is the expectation of winning minus the cost of participating in the lottery. Thus, in the example above, if the price of a lottery ticket is 3 NIS, the profit expectancy is 7 NIS.
- Group participation in the lottery, in which each participant purchases a ticket and the profits are distributed among all the members of the group, does indeed increase the chances of winning – the greater the chance of winning any prize the more people hold the right to receive a share of the profit in the lottery tickets.
However, at the same time, group participation in the lottery reduces the amount of the winnings, since the prize received will be divided among all the members of the group. Therefore, group participation in the lottery (with the full amount paid by the group members invested in the purchase of lottery tickets, without a "commission") does not change the expectation of winning.
We will present this in a follow-up example of the above example: if the chance of winning a prize worth 1000 NIS is 1%, the chance of winning is 10 NIS. In a group of 10 participants, for each of whom a ticket was purchased for the benefit of the group, the chance of winning the prize increases from 1% to 10%, so that the chance of winning for the entire group is 100 NIS. However, the prize is divided among all ten participants. Accordingly, the chance of winning for the participant is, again, 10 NIS.
Obviously, if only part of the amount is invested in the purchase of lottery tickets, then the expectation of winning decreases accordingly. For example, if half of the cost borne by the group members is reduced as a commission and tickets are purchased at only half of the cost amount, then in the above example only 5 tickets will be purchased, and not 10; In any case, the chance of winning the prize will decrease from 10% to 5%, and the expectation of winning for the participant will be NIS 5 and not NIS 10.