cursor adrI5CaS
Sometimes a word has a slightly different meaning in Science than in common usage. Thus a "force" in physics has a different meaning from that implied in "forcing yourself to give up smoking" or an evil "force".
In its everyday sense "altruism" denotes an act which results in the actor making some kind of a sacrifice to help someone else. It is inherent in this definition that the actor is aware of these costs and benefits and to whom they acrue, while choosing to act.
To a sociobiologist who studies nonhuman organisms (birds, insects, etc.), such a definition would be useless since we cannot read the minds of these creatures and know what they think or feel for certain. Therefore a different definition for altruism was adopted by biologists. It is based on the outcome of the action not its intention. For example an animal wishing to help its neighbor, feeling discomfort in the process and continuing the process in spite of the discomfort but actually benefiting from the interaction at its neighbor's expense, would be altruistic by the first definition but not by the second one. Impressing someone by means of an expensive gift of an addictive drug would be an example of this.
Therefore, these gains and losses to the two interactants are not necessarily in pleasure, but rather in FITNESS. Here's another word! It might mean brute force or healthy condition in the gymnasium, but in evolutionary theory it is a measure of evolutionary success. There have been several definitions. They have each been tried one by one to preserve Darwin's theory as the picture became more complicated. The kind of fitness used in the definition of altruism is what is called "personal fitness" or "reproductive success" or simply "RS". It is measured as the number of offspring an animal or plant produces with its own reproductive system in its lifetime regardless who rears or rescues them. These are weighted by risks taken in their production. Thus a hypothetical bear may have twice as large a litter if she refuses to hibernate and carries on feeding. However, if there is a 50% probability she will die with the cubs before Spring if she tries this stunt, then bears who try will have the same RS as those who don't.
Your RS like the other two kinds of fitness also takes into account "interest rates". A human who waits to be 50 years old to reproduce might have to have 5 kids to do as well as another who had 1 kid at age 14. This is because that 1 could be reproducing at an early age and a grandparent by the time the 5 were born. The 5 might not get born because their would-be parent might meet with an accident.
So to simplify things, biological models are often limited to semelparous organisms like corn plants or praying mantides who are all the same age. They all reproduce together at the ends of their lives and then all die together. In other words they have non-overlapping generations so RS is measured as the number of offspring produced at the end of life (period).
RS takes into account extra offspring produced due to windfalls (e. g. a windstorm knocks down many persimons and a hungry wolf finds them) as well as extra help given a would be parent by others (e. g. a hungry pregnant wolf gets fed by her sister).
Classical fitness, or Darwinian fitness, doesn't take windfalls into account, due to the thought that the animal's genes didn't earn the bonanza.  Help from neighbors is similarly dismissed.
Your inclusive fitness, like classical fitness does not increase with bonanzas you experience from the help your kin give to you. But it does increase with the help you give to others!
This is so because inclusive fitness is tallied up by counting "offspring-equivalents" the individual rears or rescues regardless who their parents are.
Your grandchild would count as 1/2 of an offspring-equivalent (i. e. 1/4 of a self-equivalent because offspring are 1/2 self-equivalents). A  niece or nephew is also 1/2 an offspring-equivalent. Thus an act causing you to leave behind seven grandchildren and three nieces and nephews, as opposed to ten grandchildren and no nieces and nephews, would leave you no better or no worse off. This is so even though committing the act would lower your classical and personal fitnesses.
If committing the act got you seven grandchildren and four nieces and nephews as opposed to ten grandchildren then it would be the prefered strategy. In 1964 William D. Hamilton, then at the London School of Ecomomics, who discovered personal and inclusive fitnesses, predicted that inclusive fitness would be the thing maximized by natural selection. Of course this is true of personal fitness too, and it is clear from the above example, that sometimes an animal's inclusive fitness is higher than its personal fitness. The point is that an animal has more control over its inclusive fitness and by maximizing that, it will maximize the expected value of its personal fitness. In other words cases where the animal suffers a low personal fitness due to sacrifices made will on average be compensated (sometimes over sometimes under but on average just right) with gifts from others. In the case of those species of ants with truly sterile workers the compensation would go not to the worker but a queen somewhere in the population with her genotype.
This is not mystical but just a consequence of statistics. One can look at the offspring-equivalents as good for their own sake as carriers of the actor's genes, or as prommises that the actor will be compensated. Each system is an equally good predictor of evolutionary success. This is reminiscent of the concept used in Vedic cultures of "Karma" (Sanskrit for energy, motion, action) where an altruistic act lands the actor good karma which in turn can be looked at as good for its own sake (the satvassic approach) or a promise of a future reward (the rojassic approach). Thus personal fitness is a rojassic (pertaining to king, kingliness, selfishness) concept and inclusive fitness is a satvassic (pertaining to light, penetration, transparency, altruism) concept. The only reason for appealing to The Vedic Tradition (pertaining to cultures such as Hinduism and Buddhism) is to resolve an apparent discrepency in the apparent equivalence between the personal fitness and inclusive fitness approaches. This is taken care of in Vedic Philosophy by the concept of "group karma". In Population Genetics the argument goes as follows: if in my life I raised 10 nieces and nephews and had no own offspring, then I have increased the sum of all the inclusive fitnesses in the population by 5 and the sum of all the personal fitnesses by 10. Shouldn't both increments equal each other? Well in fact they do, becase although each niece or nephew has 1/2 of an offspring-equivalent in her/him, she/he also has 1/2 of a stranger-equivalent too. So the 10 individuals I reared correspond to five offspring and five strangers. Hamilton put all the stranger-equivalents together in a catchall called "diluting effect". This is because strangers are made of on average representative samples of the gene pool. Parts of a relative made of representative samples of the gene pool are thought of as a diluting agent diluting the genes which are replicas of the altruist. This is such a complex way of looking at it that I prefer to think of the stranger equivalents as being meted out equally to everyone in the population. This is the kind of "white lie"  that might arise by saying I reared one offspring and one stranger instead of saying I reared two nieces.
Then If I reared the 10 nieces and nephews as above, my inclusive fitness would come out not as 5 but 5+C, where C is the total number of stranger-equivalents reared by everyone this generation divided by the population size. And everyone gets a C tacked on to his inclusive fitness and C is the same for everyone in the generation. C is the "group karma" component. Thus in a world where mostly everyone is altruistic a mean individual would get more out of society than he/she puts in riding on a good group karma so to speak.