Which element is critical for a wager to be legally recognized?

The key element for a wager to be legally recognized is the mutual agreement on wagering conditions. This means that all parties involved in the wager must understand, accept, and agree to the terms of the bet. This agreement is essential because a wager fundamentally relies on the consent of the participants to the specific conditions under which the bet is made.

Without this mutual agreement, the wager lacks the essential foundation of a contract, which would render it unenforceable in a legal context. The clarity and assurance that all parties are in accord on the conditions foster transparency and fairness in the betting process.

In terms of the other choices, the involvement of professionals in betting isn't necessary for a wager's legal recognition since amateurs can also enter into legally valid wagers. Similarly, while documentation of all bets might be useful for record-keeping, it is not a fundamental requirement for a wager to be recognized as valid. Lastly, minor participation in bets does not relate to the legal recognition of the wager itself, as age regulations and the requisite capacity to enter a contract are dictated by law rather than the nature of participation. Thus, the critical aspect remains the mutual agreement on the conditions of the wager.