#Variance of coin flip how to

(Please note that in terms of the Game #2 we can talk about one attempt or one round that consist in the successful toss of the three tails in a row and in any other failure to do so.) 2. If I found somebody willing to play them with me, then I would earn in average a dollar out of each toss. First, the expected value is positive ( +EV), hence both games are advantageous for me (or their operator) in the long run. Several things arise from the calculations. One more comment on the calculations above: the probability of winning times the profit + the probability of losing times the loss. Now we have everything we need to calculate the expected profit (EV) of both games: The probability of losing is the remainder from one (100%), thus 0.875 (or 87.5%). As for the 2nd game, I need to toss the tails 3 times in a row. Very briefly: the odds of winning and losing in the first game are 'Fifty-Fifty', thus the probabilities are equally (1/2) = 0.5.

The probabilities serve as the weights for possible dollar profits or losses. To arrive at the EV we also need to determine the probabilities of winning and losing in both games. The decision making, which of the games is better from the long-term prospective, will be aided by the Expected Value (EV), which is a sort of an estimate of a mean profitability of both games (a long-term average). Calculation of Expected Profit or Value (EV)Īs for the Game #2 we can see that it is not so easy to determine by eye-balling whether the game is advantageous or not. If I manage to do so, you will give me $15, and if I fail, I will give you $1 for each unsuccessful attempt (that is when the heads comes out straight away or after one tails or after two tails in a row).

Game #2: It is coin flipping again, but this time, to make it more interesting, I will have to toss the tails three times in a row.

At first sight it is obvious that it is a good business for me, but we will get to the point later on. If the 'heads' comes out, I will give you $1, and if the 'tails' comes out, you will give me $3. Imagine that we took a simple coin and played the following two simple games with it.

#Variance of coin flip how to

The Example or How to Get the Variance Right If this is a new topic to you, then you will be certainly enriched. This article will show the step-by-step calculation of variance and give you a better understanding of its meaning and use in practice. The basic information on variance, but also on the way how the good or bad luck may be measured, you can find on the page Variance & Dollar EV Adjusted. The frontiers between which the player's profit moves are called the variance (VAR). However he may also be lucky and earn more than the expected average. There may be a period of bad luck, when his profitability is lower than expected (that is lower than his long-term average).

Hence the poker player may expect some rate of profitability with some sort of likelihood. by ROI – Return of Investment) gets crystalized. The more hands are played by a player, the more his profitability (measured e.g. Variance is a statistical measure that shows how the short-term earnings deviate, or may deviate, from the expected long-term average profitability.