On a familiar Hobbesian picture (whether it was that of Hobbes, I know not), a sovereign is needed to enforce the laws in order for moral behavior to become rational, where rationality is equated with self-interest, and once there is a sovereign, it is rational to strictly adopt morality. Gauthier, instead, thinks we can get by with the fact that by strictly committing ourselves to the moral code, we will likely lose out—we'll get caught.
I do not know that either picture is sufficient to show that it is rational to become moral. For, it seems, a smart person with the executive virtues might instead of adopting morality, will adopt almost-morality, such as a disposition to act morally unless one has a better than 99.9% chance of gaining at least twenty million dollars without getting caught. We can imagine the almost moral financier who goes along, as morally as everybody else, cooperating with others, obeying traffic laws, punctiliously handling her clients moneys—as long as less than $20 million is at stake or as long as the chance of getting caught is 0.1% or higher. It seems that from a self-interest perspective, she might do better than just by adopting morality, though on the other hand Gauthier might point to the psychic costs of monitoring for the possibility of getting $20 million dollars with a chance of getting caught under 0.1%. On the other hand, the wishful thinking might add some spice to the person's life. And maybe the person has a pretty good antecedent chance of eventually being able to work the swindle. So, I think, on Gauthier-like and thumbnail-Hobbes-like considerations, it might sometimes only be rational to adopt almost-morality.
But there is a better way to argue for adopting morality. Say that a view is "serious" provided that there is some evidence for it. On all serious non-religious views, all life's payoffs are finite. On some serious religious views, adopting morality increases the chance of an infinite positive payoff, and on some of these also infinitely increases the size of a possible infinite positive payoff (e.g., by moving one from one level in heaven to another, thereby resulting in greater bliss for eternity). On some serious religious views (there is an overlap between these and the former), adopting morality decreases the chance of a negatively infinite payoff, and on some of these also infinitely decreases the size of a possible infinitely negative payoff (e.g., my moving one down to a lower circle of hell). On some serious religious views, the effect of adopting morality on infinite payoffs is inscrutable. On some serious religious views, there either are no infinite payoffs (e.g., religious views that have no afterlife) or the infinite payoffs are only finitely affected by whether one adopts morality (e.g., reincarnationist views on which everyone eventually achieves the same level of bliss, so that how one lives only affects how many lives it takes to do that).
But on no serious religious views is it the case that the effect of adopting morality decreases the chance of a positive infinity payoff, increases the chance of a negative infinity payoff, infinitely decreases a positive infinity payoff, or makes infinitely worse a negative infinity payoff. Putting the above together, and using some coherent way of handling infinities mathematically, and assuming that at least one of the serious religious views on which there is an increase of a probability of a plus infinity, or an infinite increase of the size of a plus infinity, or a decrease of the probability of a minus infinity, or an infinite decrease of the size of a minus infinity given adoption of morality is a view that has non-zero probability, and assuming that non-serious views cancel out or are overwhelmed probabilistically by serious ones, we get the conclusion that self-interest requires that we should adopt morality, rather than almost-morality or any other alternative.
I do want to consider one objection. According to orthodox Christianity, salvation is a fruit of God's grace rather than something we achieve by our own willed effort. Now, one might argue from this fact that it is not the case that I decrease the chance of God giving me the grace of conversion when I adopt the way of life of the pimp over the way of life of a philanthropist. If so, then whether I adopt morality or not will not affect the chances of infinite (whether positive or negative) payoffs. That's fine. But there is no Christian view on which it is the case that we in fact increase the probability of a positive payoff by adopting the way of life of the pimp. Granted, God loves the pimp, but God also loves the philanthropist. The probabilities that God will offer such-and-such a grace to a person are, on these grace-based views, inscrutable. One might worry that the philanthropist is more prone to self-righteousness than the pimp. But just as, according to Christian doctrine, God loves the exploiter, so too does God love the self-righteous. (Of course he hates the exploiting and the self-righteousness, both for the effect on victims, and for the effect on the vicious person.)
But that objection is only relevant if the above-described Christian view is the only one with non-zero probability. (There are some complicated theological and probabilistic questions about some of the arguments in the previous paragraph—it might turn out to be compatible with a grace-based view of salvation that morality, being itself a fruit of grace, increases the chance of salvation, or prepares the way for the acceptance of grace. Also, once one has received grace, by acting seriously immorally, one rejects grace. While God might offer it again, perhaps we cannot count on it.) And if that is the case, then one has other rational reasons to be moral—reasons internal to that Christian view, such as that by being moral, one acts lovingly towards the God who died for one's sins, and lives more fully as a member of the body of Christ. It does not matter for the argument whether a religious view on which morality improves the chance of an infinite payoff is true. All one needs is non-zero epistemic probability.
A more serious objection is with regard to the content of that morality. But among the serious religious views, first there will be agreement that one ought to be moral, so striving to figure out what is moral and striving to do that will be prudent, and, second, there will be agreement on various, though not all, aspects of what being moral entails. In such a case, it will be more prudent to choose the safer route (thus, if one serious view says that contraception is immoral, and no serious view says that contraception is morally required, then one shouldn't contracept).