There is a new TV show called “Red or Black?” on ITV1. It is a guessing game in form of a TV competition, and Ant & Dec are its presenters. In each episode, they start by 1000 people, and in each level of the game, they ask them “Red or Black?”. Then there is an event based on luck to determine which choice is going to win, red or black, and the ones who chose it will rise to another level. This goes on until finally 1 person remains, and in the final level there is again a 50 – 50 percent chance that he or she wins £ 1000000.
Now, apart from “What on earth is this? Just flip a damn coin!”, there are two facts in this program which are visible from the first episode. One is, the losers of higher level, have a lot more disappointment than the losers of lower levels. Secondly, if on the last level red has won, the participants are more willing to choose black.
One: Now, the first fact seems trivial. Of course people that are closer to a million Pounds are more disappointed for losing the bet. But let’s look at it from another angle: Didn’t those who enter the competition know that this was a 1 in a 1000 chance? If they knew this from the beginning, if they expected it, why are they “more” disappointed on higher levels?
To better illustrate this, let’s compare “Red or Black?” to another hypothetical game: Imagine a simple game, in which 1 person is randomly chosen from 1000 people, and is given the same chance of final choice between Red or Black by lottery. This game is fairly the same as the original “Red or Black?”, but only the process of reaching to the final stage is different.
Those who lose in our hypothetical game will be disappointed, but all equally, and just a little, compared to the people losing in a high level of “Red or Black?”
These two games produce the same results, they both choose 1 person randomly who may or may not win a million pounds. The only thing is, in the process “Red or Black?” creats much more disappointment and psychological stress.
There may be a number of reasons, but all of them must be related to the structure of the game. The main reason is, as “Red or Black?” goes on, the contestants think they are closer to the 1000000 pounds, and indeed they are: it’s more probable to be the winner among 2 people, than it is among 64 or 128. So, each stage creates a new level of expectations for the remaining contestants, and by remaining in the game they win a higher chance of having the prize.
Yes, they don’t “actually” win anything by remaining in the game, they win one more chance. What a colorful sight! Too bad it is an illusion…
This also creates higher opportunity costs for time the participants are spending, and if that does not seem much, the cost of their stress is. My conclusion, compared to the hypothetical example is that, this game is economically inefficient for the participants. And therefore, it is safe to say that those who lose on higher levels of “Red or Black?” actually lose more!
Do I have a general point here? Yes: There may be many games (including different economic systems) that produce similar or the same results. But we should not forget that the way of doing things also affects the players, and creates different hidden costs. Take US and Scandinavian countries for example. They are all developed countries, but which one is more efficient in terms of welfare of their population?
Second: Imagine you are playing with a coin. You have already flipped it once, and it was Heads. If you wanted to flip the coin again, which one do you think is more likely to come: Heads or Tails?
The answer is none of them, they both have an equal chance of showing up: The probability is always the same: 50 – 50. The fact that we think “It has been 2 times Black already, this time it should be Red!” Is just a trick that our minds play on us. In these kind of games, what has happened has got nothing to do with the probability of what is about to happen.