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So if I have two humsters and they start to reproduce themselfs then how much generations of hamster's family it takes to get first bad mutations?

The info here does not help to find answer https://www.reddit.com/r/askscience/comments/32x33j/how_do_animals_like_hamsters_and_snakes_avoid_the/

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    $\begingroup$ I think you're more likely to see problems related to recessive alleles than mutations. If the hamsters keep inbreeding, the odds of getting a hamster with two copies of bad recessive genes goes up, so you're more likely to see genetic diseases based on that instead of new mutations. But I don't know anything about the frequency of hamster recessive alleles, so I can't estimate the odds of seeing a genetic disorder in each generation. $\endgroup$
    – user137
    Commented May 21, 2018 at 8:22
  • $\begingroup$ @user137 Good point about recessive alleles! $\endgroup$
    – NoWar
    Commented May 21, 2018 at 9:04
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    $\begingroup$ Is the question aimed only at mutations (which involve changes in individual genes), or also at genetic changes including recombination and crossover which only involve changes in gene frequency and location? Both types of changes occur in every generation. Changes due to recombination and crossover are more likely to be harmful when both parents have a larger number of "bad" recessives. $\endgroup$
    – S. McGrew
    Commented May 21, 2018 at 13:04

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Everybody carry deleterious mutations anyway

Your two hamsters most definitely already carry a number of deleterious alleles at segregating sites (segregating sites = polymorphic sites). Also, I will not talk about inbreeding depression in your population coming from only two individuals which will be very important but I will only answer your specific question. In short, I will assume your are not interested in segregating sites...

Probability of an offspring to carry a new deleterious mutation

The vast majority of new mutations are deleterious (Shaw et al. 2003). I don't know of estimates of mutation rate in hamsters but in mammals (and in all eukaryote species anyway generally speaking; e.g. see this post and this post or directly bionumbers#mutationrate), the genome-wide mutation rate is of the order of 1 to 100 mutations per offsprings.

If the couple of hamsters have $x$ offsprings, then the probability to have at least one new mutation in at least one offspring is given by the cumulative exponential distribution

$$P = 1-e^{-U x}$$

, where $U$ is the genome-wide mutation rate. With $U=50$ and $x=1$ (one offspring), this probability is $P = 1-e^{-50} = 1 - 1.9 \cdot 10^{-22} ≈ 1$.

In short

In short, to a fair level of approximation, every new offspring carry at least one deleterious mutation that was not present in either parent.

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