3 ideas
Krishna tells Arjuna (Gita 2.47) that a person's jurisdiction extends only to the act itself, never to its results, and that one should neither make results the motive nor withdraw into inaction. The mechanism separates what is controllable (choice, effort, execution) from what is not (outcome). Once they are separated, fear of failure loses its grip on the decision.
The Gita names this discipline karma yoga and describes it as acting while holding success and failure in the same regard, calling that evenness itself yoga (2.48). What this adds to the action-fruit split is the actor's inner state: steadiness that does not rise or fall with the result.
The Gita traces a causal chain (2.62–63): dwelling on objects breeds attachment, attachment breeds desire, thwarted desire breeds anger, and anger produces delusion, loss of memory, and destruction of discernment. Craving a particular result therefore actively degrades a person's ability to decide well. Yudhishthira shows this at the table: each loss makes his need to recover the stakes more urgent, and each wager is worse than the last.