One of the most common arguments used against evolution is that of probabilities. Someone will calculate the probability of a protein or a collection of biomolecules and show that the probability that it was formed by chance is 1 in a number so large that it takes an impressive number of digits just to write it down. The conclusion offered is that the probability is so low that anyone who believes in evolution must be ignorant and so biased toward evolution that they cannot think straight. Many people like to quote Herbert Yockey’s article “A calculation of the probability of spontaneous biogenesis by information theory”, in *Journal of Theoretical Biology, ***67**:377–398, 1977. He shows how many different combinations of amino acids are possible and he concludes that abiogenesis is impossible since the probability is on the order of 1 in 10^{65} that even a simple protein could form at random. Therefore evolution cannot even get started. Another favorite approach is to quote Fred Hoyle who, in a sidebar called “Hoyle on Evolution” in *Nature*, Vol 294, page 105, Nov. 12, 1981, cites the number 1 in 10^{40,000 }as the odds of abiogenesis. Furthermore, Hoyle reportedly said the odds were comparable with the chance that “a tornado sweeping through a junk-yard might assemble a Boeing 747 from the materials therein”.

Much has been written to show the fallacies of this line of argument. The point I wish to emphasize in this post is the importance of feedback in thinking about probabilities. I have previously pointed out in a post on January 7, 2018 and in a letter to the editor in March 2012, the error in using combinations to derive probabilities. Evolution is a gradual process of change involving a high degree of parallelism and many steps, as I have shown in my review of the book *Introduction to Evolutionary Informatics*. Perhaps the most important element is that of feedback. It is not just the existence of many steps in evolution, but the role of feedback at each step. Survival to procreate is the crucial feedback factor that distinguishes any population of organisms or molecules. That is a feedback mechanism that provides active real-time information about the direction for evolution.

The importance of feedback has been shown mathematically by Herbert S. Wilf and Warren J. Ewens in their article “There’s plenty of time for evolution” in *PNAS*, December 28, 2010, vol. 107, no. 52, pp 22454–22456. They conclude that while combination-based probabilities scale exponentially, if there is any feedback those probabilities scale logarithmically. That is, for N elements, each selected from x possible values, the number of combinations scales as 1 in x^{N}. However, with feedback at each step, the probability of success scales proportionally to 1 in x log(N). That is a very large difference. But their math isn’t easy to follow. A good way to illustrate the importance of feedback is to consider a familiar game.

The game of Mastermind, or any of the many variations of it, demonstrates the tremendous impact of feedback. In the game, two players each secretly select a short sequence of elements such as colors, numbers, letters, or words. Then the other player is challenged to guess that selection. For instance, one player may select the number 53882. The other player has a 1 in 100,000 chance of guessing it at random. This is equivalent to the scenarios that Yockey, Hoyle, and others would calculate. If this were the approach used in the game, both players would tire and starve long before the game was over. However, the game becomes interesting when some feedback is introduced. At each guess, the first player responds with some elementary feedback about the guess. Depending on the specific rules being used, it may be how many digits are correct, whether they are in the right position, or even which ones are correct, etc. With this feedback, the second player can usually guess the answer in about ten or fewer guesses. This makes the game challenging and interesting and possible. The probability drops from 1 in 100,000 to nearly 1 that the answer will be obtained.

In evolution, the feedback in each generation is the determination of which subset of the population will be the source of procreation for the subsequent generation. Unlike Mastermind, no intelligent being is required to make this determination. It includes all the individuals of that species that survive in the current environment and are able to reproduce. On average, this will tend to include a disproportionate number of those most likely to survive in a slowly changing environment. With a large amount of parallelism and continual feedback, the probability of attaining the combination of molecules necessary for life is very high.