Human Sex Determination: Psychic Sperm and the Gambler’s Fallacy…..

Carl Sagan supposedly once said that randomness is clumpy. Those three words have become one of my favorite go-to quotes, particularly when teaching residents and medical students who are often overly impressed with improbable runs of similar diagnoses or exam findings. I love this quote because it is so simple and yet reveals so much about our experience with observing the natural world. Sagan’s ability to offer up insightful nuggets of rational thought, even if he didn’t actually produce this gem, was unmatched and his efforts to bring science and reason to the public have been sorely missed. If you haven’t read any of Sagan’s works, I highly recommend The Demon-Haunted World: Science as a Candle in the Dark.

If you have a coin, and a few hours to kill, record the results of a long run of flips and you’ll see what Sagan meant about the nature of randomness. You will inevitably observe clusters of heads or tails that might seem improbable, but eventually the outcomes will average out to about half of the flips being heads and half resulting in tails. The more trials that you perform, the closer the outcomes will approach 50% for each possible result, assuming you aren’t gaming the system by using a trick coin.

I don’t think that very many people would argue with the fact that on average a coin flip is random chance, although there are still people out there who think that the Earth is flat and that Justin Bieber is a reptilian humanoid. But because of a deeply rooted cognitive bias, the gambler’s fallacy, we frequently fail at recognizing that randomness is clumpy. We accept the established overall odds, but our acceptance wavers in the face of short runs that go against our expectations. This error in logic can lead to the belief, for instance, that after five heads in a row there is a higher than 50% chance that the next flip with land on tails as if to magically even things out.

In my line of work as a pediatric hospitalist, I frequently experience other healthcare professionals making this mistake in a variety of circumstances. There is a known likelihood of bacteremia when an infant less than 28 days of life is evaluated for fever, for example. Despite this, it is common for physicians and nurses to lament, upon seeing fever as the triage chief complaint, that they are due for this life threatening infection after a number of recent febrile neonates have had negative blood cultures.

The cognitive bias which results in this commonly employed logical fallacy is, as is often the case, the result of an inappropriately employed mental shortcut. These shortcuts, known as heuristics, can be very helpful but sacrifice accuracy for efficiency of thought. In the case of the gambler’s fallacy, the representative heuristic is to blame. If someone is aware of the fact that a result has a known frequency of occurring, they often mistakenly make the assumption that short runs will be representative of long runs. They believe that a run of ten or twenty should be equally split between heads and tails in the same way that a run of a million would be. But, once again, randomness is clumpy and short runs often have surprisingly unbalanced results.

A concept that is very closely related to this is the clustering illusion. Humans excel at failing to appreciate how variable a small sample of a larger population of random or almost random events can be. We see a streak or a cluster, rather than a random clump, and assign more meaning to them than they deserve. This phenomenon can be seen at play in sports when we determine that a player has a “hot hand” but more notoriously in bogus disease clusters.

Cries of cancer clusters are common in the media. Cancer Alley, a stretch of the mighty Mississippi between Baton Rouge and New Orleans, is one such cluster that achieved widespread coverage in the late 1980’s but has largely been shown to be an illusion. There is even a Wikipedia page specifically on cancer clusters.

I recently had a somewhat heated exchange with a relative of a friend on Facebook. My friend, a mother of three boys, was expecting her fourth child and had not yet found out whether this baby was a boy or a girl. She expressed her desire for a girl and her uncle commented that the new baby would almost certainly be female because the odds were highly in favor of such an outcome. While it is true that the odds of having 4 boys in a row are somewhat low at 1 in 16, this was a classic example of the gambler’s fallacy. I responded, an argument ensued, and nobody went home happy.

So what were the odds of my friend’s child being a girl? There are two ways to approach this problem with one of them being right and one feeling right to many people because of the representative heuristic. Readers of Science-Based Medicine should of course know that what feels right on a gut level is often completely wrong. First though, some basics on the determination of sex in humans are in order.

Unlike alligators, the sexes of which are determined by the temperature an egg is exposed to at a critical period of development, whether a human infant is born as a male or female is determined by genetics. The sex of most mammals, humans included, is determined by an XX/XY system that most of you are probably fairly familiar with even if you don’t remember all the specifics.

Modern humans, individuals with genetic syndromes aside, have a genome which consists of 23 paired chromosomes. The two that determine an individual’s sex are, not surprisingly, called sex chromosomes. Females generally have two X chromosomes (XX) and males have both an X and a Y chromosome (XY). It is widely considered that human zygotes are inherently on the path towards being female at conception and that, if present, a single gene located on the Y chromosome alters this course resulting in male offspring…usually. Sex determination is very complex and there are certainly instance where the genotype (XX or XY) doesn’t match the phenotype (outward appearance) but these are quite rare and beyond the scope of this post.

Most cells in the human body are identified as diploid, which means that they contain the above-mentioned 23 pairs of chromosomes. Well, this isn’t entirely accurate, as most cells in and on the human body are bacterial and they can have up to 4 chromosome copies depending on the growth conditions at the time. But we’ll keep moving.

Reproductive cells like sperm and ova, known as gametes, are haploid in that they only contain one set of the 23 human chromosomes. This makes sense because they will combine to form a diploid zygote at conception. The female ovum always contains an X chromosome. It is the male sperm which ultimately will determine sex because an individual sperm can carry an X or a Y chromosome. Which, if any, sperm fertilizes the impatiently waiting ovum is a crapshoot and it works out to a roughly 50/50 split between male and female embryos.

Of course there is some nuance to this. There is the possibility of a minor influence by environmental factors, or factors inherent to sperm carrying X versus Y chromosomes, which may lead to a slightly increased chance of male versus female offspring in some women, or a slightly higher rate of male or female births across some populations, but these differences are not meaningful. And unless you are making use of gender selection via technology, such as with IVF, the myriad other means of encouraging the birth of a preferred sex will not alter the outcome. And studies looking at large numbers of families have shown conclusively that even in the case of families with long runs of male or female children, the chance that a subsequent child will be male or female remains pretty close to 50/50.

So in the case of my friend with 3 boys and a baby on the way, the likelihood of having another boy was 50%, not 6.25%. And the chance of finally having a girl was 50%. But let’s further explore the notion so strongly argued by my friend’s relative, that the sex of previous children impacts the sex of future children. As I have already explained, there is a perfectly reasonable cognitive bias to blame for this fallacious logic, the misuse of the representative heuristic. But for argument’s sake let’s assume that he was right.

What would the mechanism for this phenomenon be? How would past results impact future results of a seemingly random process like sex determination? Could the male “apparatus” somehow be affected by the owner being cognizant of the sex of his mate’s prior children, thus initiating a physiologic process that selects an X- or Y-chromosome-carrying champion to breach the defenses of the female genital tract and fertilize the ovum in a more controlled fashion? Or could the female genital tract somehow alter conditions such that an X or Y chromosome might have a higher chance of success? None of this makes sense.

Or maybe something supernatural is going on? We should keep an open mind, right? If you believe in a higher power then I guess you have your answer. Perhaps there is a mysterious effort underway by a technologically advanced observing alien race to manipulate the human species but still attempt to maintain at least the appearance of randomness over multiple pregnancies? Or is this some diabolical scheme where sentient sperm must act to prevent our awareness of a grand conspiracy which only works if there is a roughly equal number of male and female offspring? Are they psychic and able to probe the inner recesses of the male mind or simply plugged into the nervous system via nanotechnology? We may never know the answer but there is something I do know: don’t anthropomorphize gametes, they hate that!

Oh, and it was a girl.

One last interesting tidbit. Right now the world is on the edge of its seat waiting to see what the sex of Prince William and Duchess Kate’s baby will be. There actually is some evidence to support that it will most likely be a little girl. Morning sickness seems to serve as a predictor for having a female infant, but not just any morning sickness. A study out of the department of epidemiology at the University of Washington found that women with severe hyperemesis gravidarum that required hospitalization were 50% more likely to have a girl. But obviously this would only be helpful after the sex has been determined.

Posted in: Basic Science, Critical Thinking, Obstetrics & gynecology

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28 thoughts on “Human Sex Determination: Psychic Sperm and the Gambler’s Fallacy…..

  1. windriven says:

    “Oh, and it was a girl.”

    And I’ll bet your friend’s relative did a whooping victory dance.

    Superstition trumps science and technology in every tiny mind.

  2. WilliamLawrenceUtridge says:

    I was all set to scream “OH YEAH, WHAT ABOUT REGRESSION TO THE MEAN, SMART-GUY!!!!” Then I realized, that’s just the name we use when the short-term trend ends – it’s the statistical inevitability, not a physical law.

    Back to skeptic’s school I go…

  3. Adam says:

    A comment, a question, and an anecdote related to the gambler’s fallacy and gender:

    When explaining to people why the odds of getting a head after flipping 99 heads in a row is still 50%, I point out that while the odds of getting 100 heads in a row are incredibly small, they are exactly the same incredibly small odds as flipping 99 heads in a row and then getting a tail – and the reason for this is that in order to get the 99 heads in a row in the first place, you’ve got to beat all the odds.

    Regarding gender selection, as the parent of 3 boys, we’ve had a lot of discussions on this topic in my house. One theory that we’ve come across is that, at the risk of oversimplifying, “male” sperm swim faster but die out sooner, while “female” sperm swim slower but live longer. So if the egg is already released and waiting for the sperm, the odds are higher (but certainly still far from 100%) of ending up with a boy, and if the sperm are there prior to the egg being released, the odds are higher of ending up with a girl. And if a woman consistently finds herself “in the mood” at the same point in time relative to when she ovulates, she is more likely to have one or another gender. Is there actually any evidence of this (that X or Y sperm swim faster/slower or last longer)?

    And finally an anecdote… when we were expecting our first child, my aunt claimed to have a foolproof method for predicting the gender of the baby. She then paused briefly and said, “Well, I was 3 for 3 with this method in my last job, but of the three pregnant women in my new job, I haven’t gotten one right yet.” So there you go: a foolproof method with a 50/50 chance of being right :)

  4. anthro49 says:

    Are you telling me that it’s just a random clump that after having one lovely daughter, I spawned three stereotypically Dennis The Menace little boys?

    Oddly enough, I never suspected otherwise, but then I read The Demon-Haunted World at a relatively early age.

    The rather amusing postscript is that my daughter, who complained loudly all her life about her fate grew up to have—–A daughter and then two boys. Just random? Sure…Our family is obviously cursed.


  5. Harriet Hall says:

    An obstetrician I knew could infallibly guess the sex of a baby in utero. He would tell the mother one sex and write the other sex in the chart, so if the mother accused him of telling her wrong, he would show her the chart and say she must have mis-heard him. :-)

    1. calliarcale says:

      My dad had a similar approach. He’d tell the expectant parents his prediction, and then write it down on a piece of paper and seal it away. Or at least, that’s what they thought. When the child arrived, if his spoken prediction was correct, he took credit. if his spoken prediction was not correct, he insisted that it was and produced the sealed note to prove it, which lo and behold would be correct. Of course, he wrote down the opposite gender to what he said out loud. ;-)

  6. Robert Feinberg says:

    And then there’s this:
    Mammals Can ‘Choose’ Sex of Offspring, Study Finds

    1. windriven says:

      “The scientists assembled three-generation pedigrees of more than 2,300 animals and found that grandmothers and grandfathers were able to strategically choose to give birth to sons, if those sons would be high-quality and in turn reward them with more grandchildren. The process is believed to be largely controlled by the females, Garner said.”

      Hmmm – perhaps the reportage is weak or perhaps I’m unusually obtuse today but this strikes me as head-banging, bat-shit crazy woo. We are being asked to believe that the ‘grand animals’ were able to predict the quality of their offspring in advance and based on that prediction tweak the knobs so that males would result if sufficiently high quality was preordained.

      Moreover we are to believe that this “process is believed to be largely controlled by the females.” Now I understand that environmental factors in the female reproductive tract are thought to have a slight impact on the relative survival rates of male v female sperm but this seems a rather large leap from there. Or maybe the suggestion is that Greta says, “hey Hans, I’ve consulted with the owl and she tells me that our next foal is going to be of outstanding quality so turn off the female sperm faucet so that it will be a male.”

  7. It is worth going into additional details about the probability calculation as it depends on the way the question is phrased. Consider the following two questions:

    (1) A family has two children. The first of them is a boy. What is the probability that the second is a boy?


    (2) A family has two children. Given that one of them is a body, what is the probability that the other child is a boy?

    The answer to the first is 1/2. However, the answer to second is 1/3. To see why this is, consider all the possible options of having two children (B = boy, G = girl)


    However, since we know that one of them is a boy, the fourth option (GG) is excluded. That leaves us with three options (BB, BG and GB). One of them is consistent with the question (BB).

    If we look at the case discussed in the blog post, we see that if the question is analogous to the first scenario (which seems to be the case here), the probability of getting a girl is 1/2. If it had been analogous to (2), the probability of a girl is 4/5 (only options are BBBB, BBBG, BBGB, BGBB, GBBB, only BBBB is the option for 4 boys). Now, I am not saying that the uncle was using Bayesian statistics (as presumably, he knew that the _first_ three were boys, not just any three out of four children). In fact, it seems that he was performing the Gambler’s fallacy.

    1. Harriet Hall says:

      If you want to get really confused, see
      See the section “information about the child.” When you are given the additional information that the boy was born on a Tuesday, that seemingly irrelevant information changes the probability that the other child is a boy. I struggled with this for a long time before I understood.

  8. Sean Duggan says:

    Robin Baker’s Sperm Wars postulates the “environmental factor” and includes some figures showing a moderate effect based on perception of economic position. Oddly enough, the bias seemed to work out with females being more likely in times of economic hardship. Of course, Robin Baker’s work is far from lacking controversy with his talk of prostitution and rape being encoded in our genetics as ways to further spread one’s genes.

    1. calliarcale says:

      I read something suggesting that it could have to do with nutrition. The idea was that the female reproductive tract was somewhat less welcoming to male embryos if the mother was less well nourished. There was something to do with blood sugar, but for the life of me I don’t remember the details. It was of course speculative, but it was an interesting idea since it would explain why sex ratios favor females in times of hardship and in wealthy societies that put a premium on weight loss; perhaps females in our society are more likely to be trying to lose weight when they happen to conceive. They furthermore pointed out that this could have an evolutionary advantage as this sort of environment would favor polygyny (one male with three female partners means the same number of offspring can be produced without feeding as many adult mouths). All speculative, of course, but an interesting idea.

  9. Angela says:

    For me, that 1/16 stat for bbbb is what fails me. I think it and jump straight to “isnt that like a 15/16 chance of having a girl?” I fail to intuitively see that the chance of bbbg is also 1/16, and there are no other combinations possible now that you have three boys in a row. So, it’s 1 of two possibilities.

    It took a lot of conversations with a math major (i was art history) for me to see the difference between odds and current probability.

  10. “Carl Sagan supposedly once said that randomness is clumpy.”

    No, that’s from Abelson’s Laws. “Chance is lumpy.” Get it right, scientists.

    1. Clay Jones says:

      Which was written in 1995, one year before Sagan died.

    2. starskeptic says:

      Source please…

      1. Clay Jones says:

        For what? Sagan being the originator of that line? I couldn’t find one, just other people saying he said it.

      2. Clay Jones says:

        1995 was when Abelsons published that similar line.

  11. Rachel Irene says:

    What a synchronicity, I’m mid-way through a Demon Haunted World right now.

  12. Dr. Pullen says:

    What. I always thought, Third time never fails” was gospel in 50-50 or near that random events. :.) Thanks for reinforcing statistical facts and helping us avoid this “human nature” faulty logic.

  13. BillyJoe says:

    Did he really think that that odds of a couple with no children having 4 boys in a row is the same as the odds of a couple with three boys having another boy next time round?

  14. Clay Jones says:

    Yes, he very much did. And he angrily kept referring to how his statistics teacher in college would be laughing at me.

  15. sao says:

    While getting an X and a Y from the father is random, there are many mechanisms where one or the other could be favored. Genomic imprinting is a process where the expression of the gene is a function of its source of the gene (ie father or mother). Most of them in humans are related to embryonic growth and the placenta. So, if the father had an X which had some less than healthy alleles for placental growth, conceptions of girls might be less likely to implant and produce an effective placenta (and successful pregnancy). The result would be a family tendency towards boys.

    You could argue that each successive repeated value increases the likelihood that the odds are not, in fact, 50-50, just as too many repeated heads and too few tails increases the odds that the coin you are tossing was doctored. Whether or not people accurately judge when the odds have changed or when the odds are merely lumpy is another question.

  16. shamshad says:


    Sir I have many question about the genetics of human I am talking about the sex ratio of male and female in human being. I read in books of genetic I will read the human being has 46 chromosomes and 23 pairs in these 23 pairs 22 are not involved in sex determination. Only the last one 23rd pair involve in sex determination. Male has XY pair and female has XX pair. These chromosomes separated after the meosis. Sperm contain X and Y chromosomes and the egg contain X chromosomes only. X and Y chromosome containing sperms are equal in number.
    These all things I read from the books because I have lot of interest in genetics but my question are these
    1:- if the fertilization of egg by the sperm is chance then why in older era or 70 to 80s the count of male is higher than the female?
    I was selected 20 houses from my village it is very backward and poor and 0% chances of ultrasound before baby birth or killing of girl because the nurse who does the cases of delivery tell me that she said in my practicing life of 35 year no one case comes when any one mother wants to kill her daughter. So these 20 houses has only 7 girls and 36 boys or male keep in mind these are the one generation before me data.
    2:- Diet of male and female before and after the marriage.
    If the male diet is mostly depends on the natural resources and he is stronger than the female why it’s happen the female give the birth to male young one and vice versa. I will also study lot of those families which have more boys and lot of those families hawing more girls.
    3:- stress or tension on the male and female after marriage.
    Why it happens if the female is in stress and weaker than the male and the male is strong and don’t care about the tensions why in this case the female in more than 90% chances gives the birth of male young one. And vice versa
    4:- why the population of male in villages which are apart from the cities and whose population mostly depends on the natural food resources is higher than the females.
    Why the population of male in most of the villages is higher than the cities in cities most of the families have on average 4 girls and only one boy but in case of villages the case is totally opposite villages has more male population than the female.
    5:- condition of male and female before and after the marriage.
    Why in most cases if the female is dominant of male and the male is recessive then the 1st young one is male if she remain dominant on male then she has more female child but if the female after marriage become recessive due to certain reasons then 50% chances has to give birth male to young one.
    6:- environmental conditions.
    I in older eras when environmental conditions are harsh and only strong persons can survive in these conditions so males are the best survivors of these conditions. So females give birth to only male baby. So the number of males is so much high in these conditions. But mostly people think that the killing of women or baby girls is so much high just like in Arab just before Islam.
    But I give you several hundred examples of those villages where ultrasound and killing of baby girls is zero. But these villages have so much high number of boys. I am give you several hindered examples of those persons who are drunker and take drugs and they have healthy wives so they have baby girls. I have several examples of those people hawing weak and sick wives and strong and healthy husbands have baby boys.
    Please tell me what answer of these questions is.

    If the human sex determination is depends on the by chance method of sperm fertilization if the sperm contain X chromosome then girl birth is takes place. But in case of Y chromosome male is produced. But I don’t think so because if the process is not depends on the other things and fertilization is by chance process then why in older era the count of males are so high. i have several cases in which strong points are present when the food or diet, stress, environmental conditions, conditions of male and female before and after marriage.
    i don’t think that these things are directly involved in sex determination but these things create environment to fertilize what chromosome to the egg.

    I give you an example we are 5 brothers 2 brothers are poor and live in village and totally depends on the natural resources they wheat bread with milk and grow on vegetables both are married both have 6 boy and only 3 girls.
    But my one brother live in city and his wife is strong and dominant she has all girls and no one is boy.
    Please give me the answer of these questions.
    My English is not so good please ignoring my mistakes of grammar and spell thanks.


    Select 3 males and 3 ladies and check the results after marriage keep in mind in these persons 1 male life in city and 2 are lives in village. But in case of females or ladies 1 is lives in city but 2 lives in two different villages. These all persons are closely relative to me they don’t about this experiment. I will set some assumptions about this experiment. That experiment is 5 year long to check the results.
    Conditions of brides
    Couple 1
    1st male lives in village but that village has all facilities of cities they have no natural food source.
    His wife is strong dominant eats healthy food lives neat and clean.

    Couple 2:-
    2nd male lives in village and grow own vegetables eats healthy food and has cows so they drink milk.
    His wife is sick and she is very weak she is recessive.
    Couple: – 3
    3rd male lives in city and totally eat and drink and lives on artificial foods
    His wife is weak and unhealthy but after the birth of 1st baby she becomes dominant over male.
    1st baby 2nd baby

    1st couple girl girl

    2nd couple boy girl

    3rd couple girl girl

    Unexpected result: – unexpected result to me in this experiment is 3rd couple 1st baby girl.
    But all other results are about my assumptions.
    Experiment number 2:-…………………………………………….
    Please sir help me please sir.

    1. Harriet Hall says:

      The sex ratio is not a random 50/50: more boys are born than girls. The statistics for India are not out of line with the rest of the world.
      It is not legitimate to reach conclusions based only on one’s personal observations. Properly controlled statistical studies must be done. For instance in your “experiment” there were more girls, but if more families had been observed the total number of boys might be greater. Clusters (such as a village with a higher than average prevalence of boys) are to be expected and are often observed and misinterpreted. It is premature to speculate about how diet, stress, environment, etc.might have changed the sex ratio before it has been established that the sex ratio has indeed been changed.

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