What is the ruling on the wager "whoever does not travel, his wife is divorced," and does it count as a divorce, and what is the expiation for whoever does not travel?

What you mentioned about wagering on divorce can be interpreted in two ways:

1. That the divorce is contingent merely on the absence of travel. If the travel time was specified and the period elapsed without you both traveling, then the divorce is binding for both spouses. Each of you can reconcile with his wife before the expiration of her waiting period, provided this divorce does not complete the three divorces. However, if the travel time was not specified, then the divorce does not occur unless travel becomes impossible, for example, due to death. Engaging in such a wager is disliked (makruh).

2. That the intention of the wager is that whoever does not travel must divorce his wife. This wager is invalid, and failure to fulfill it does not result in divorce. Consequently, each of your wives remains in your marital bond. According to some scholars, one must offer an expiation for an oath (kaffarat yamin), while others say it is not necessary. As a matter of piety and precaution, it is better to offer an expiation for an oath to avoid scholarly disagreement.