Any seasoned bettor knows that betting on your favorite team is a bad idea. On the other hand, lotteries are so popular all over the world, although people believe that it is quite difficult to judge the likelihood of such rare events as the occurrence of a few specific numbers from a large set. Such an opinion boils down to distorted perceptions resulting from what are known as the effects of possibility and certainty.

Many players do not measure the value of a bet by its expected value (EV), but instead consider what they assume about the potential profit. For example, try to estimate your chances of winning a million dollars in this format.

While all options here represent the same quantitative change (5% improvement), they produce different qualitative experiences — in other words, each option generates a different emotional response. Option (a) moves you from zero chances of winning to real ones. And although they are extremely small – with a probability of 0.05 – the transition to the realm of the possible is a decisive trigger for positive emotions. This feeling is known as the effect of opportunity, which usually leads players to become overly convinced of the lucky ticket this time, and is the driving force behind lottery participation, which, for a small cost, offers the chance of huge winnings.

Options (b) and (c) tend to elicit less dramatic emotions. Even though c (b) actually doubles your chance of winning, it still doesn’t provide a quality impact – it doesn’t click the same mental buttons.

With option (d), the result goes to certainty (100%), which, in turn, leads to the opposite effect of possibility. It is known as a certainty effect, which means that in the absence of EV calculations, results that are close to certainty tend to be underestimated in relation to their probability.

** The vividness of thought and the riot of imagination of the players **

Despite the benefits of weighting the probabilities, players still tend to bet on Team A over Team B just because they intuitively believe Team A is more likely to win, rather than a higher value calculation.

In addition, research has shown that the objective use of probability in assessing outcomes is diminished when the subject evokes a vivid emotional representation of the outcome, or the wording of the rate requires special attention.

Regarding our lottery example, who hasn’t had something like this idle discussion with friends or family: “What would you do if you won the lottery?” This is an example of spawning a vivid fantasy of an unlikely outcome. This inevitably leads you to believe in excess of the possibility of hitting the jackpot.

For the same reason, betting on your favorite team or player is a bad idea, as your emotional attachment produces brighter projections of the desired outcome, and far outweighs the actual probability of the desired outcome.

** The importance of correct wording **

When the rate is formulated in understandable terms, it is easier to calculate the expected value – estimated or designed – so the weighting will be close to probability or equal to probability. However, subtle variations in how bets are formulated can be relevant to interpreting them correctly.

** “One of the golden rules of betting is that any bet must be judged in terms of expected value.” **

For example, direct markets can be formulated as either “player A versus others” or as a long list of all participants, including player A (for example, player A: 3.201, player B: 9.454, player C: 11.232, etc.) .).

The first option offers a simplified representation of the problem for player A, which leads to a cognitive advantage in his probability of success. The second option – although it is exactly the same probability – seems a more difficult prospect, simply because the opponents that Player A must overcome are listed. This leads to an insufficiently balanced estimate.

** Focus is as important as emotion **

Likewise, focus is critical to correctly estimating probability. Typically, you can see the following rates:

“Will team A score?”

Odds Yes / Odds No

“Will Team B score?”

Odds Yes / Odds No

Players’ judgments are overly balanced when they focus on each option individually rather than a combination of both:

“Will Team A and Team B score?”

Odds Yes / Odds No

One study in 1999 by Craig Fox and psychologist Amos Tversky clearly demonstrates this. They asked a group of American basketball fans to rate the individual odds of eight NBA playoff quarter-finalists.

Judging without resorting to correct calculation often leads to underestimation of probability. Since the focus was solely on assessing the odds of only one team, and NBA fans had a vivid impression of each team, the aggregate probability of outcomes was vastly outweighed – by as much as 240% – for the eight teams. It is clear that the correct overall result should have been around 100%.

When asked to simply rate the odds of winning the Eastern Conference or Western Conference, the resulting probability was very close to 100%. This was due to the fact that both options elicited less emotional response and were equally specific.

** Rare events: “hole in the group” **

The infamous upheaval in the betting world was carried out by two players in 1991 (it became known as the “hole in the group”). It clearly illustrates how the inability to visualize a rare event and judgment without resorting to correct calculation leads to an underestimation of probability.

A couple of players, after intensive analysis of statistics, calculated that the chances of hitting the ball in the hole from the first time in one of the European golf tournaments averaged about 2.25. Armed with this knowledge, they went on a tour of the country, targeting independent bookmakers and requesting odds for their chosen competition. These small operations were not of interest to professional risk assessors, so bookmakers in this case. just relied on intuitive judgment.

Bookmakers believed that hitting one particular hole on the move was quite rare because they had little or no experience with what was happening on the golf course. As a result, the quotes for such an event ranged from 4.00 to 101.00. It was a great example of underestimating a rare event, and resourceful bettors made a great profit from it.

One of the golden rules of betting is that any bet must be judged in terms of the expected value – the probability-weighted average of the result.

Unfortunately, gamblers tend to assign odds to betting options based on their ratios to probabilities, resulting in probability and certainty effects that can end up being very costly.