31 Sovereignty of God. Ultimate success comes from God and not from human efforts. The contrast here is between the plans and efforts for the battle (“the horse is made ready for the day of battle”) and the true acknowledgment of the source of victory (“the Lord”; see Pss 20:7; 33:17).
21:31 / Antithetic. Preparations for war (horse) can and should be made, but ultimately all depends on the Lord (1 Sam. 17:47), who alone is wise (Sir. 1:8). See also Psalms 20:7; 28:7; Jeremiah 9:23. This proverb specifies the more general saying in verse 30.
31 This verse is related to v 30 in that it provides a concrete example of a face-off between humans and God. Even wars, which seem to be humanly accountable and which humans only too readily prepare for, do not escape the overarching causality of the Lord, without whom victory cannot be achieved.
Ver. 31 continues the thought of the preceding verse. As human wisdom, so likewise is human strength and reliance on human aid and might nothing; comp. Ps. 20:7 (8); 33:17.—The horse is made ready for the day of battle. The participle expresses the permanence of the matter; therefore, lit. “stands prepared, is prepared” (Hitzig).—With b compare also David’s language to Goliath, 1 Sam. 17:47: “The battle is Jehovah’s;” i.e., on Him depends the decision of the war, its favorable issue, its victorious result.
21:31. Human effort, like human wisdom (v. 30), has its limitations. It is useless to fight against God (v. 30), or without Him (v. 31). Soldiers may use horses in battle, but the superiority of a cavalry unit against foot soldiers is no guarantee of victory. That comes only from the Lord, who can turn battles His way in spite of man’s efforts (cf. Pss. 20:7; 33:17).
21:31 Men may go to elaborate plans to insure military success, but victory on the day of battle comes from the Lord alone. It is better to trust in Him than in horses—or in nuclear weapons—(see Ps. 20:7).
Plumptre summarizes verses 30 and 31 as follows:
Verse 30: Nothing avails against God.
Verse 31: Nothing avails without God.
21:31 A soldier can do all within his ability to prepare for battle (20:18), but in the end no preparation can override God’s power. Victory is in God’s hands.
21:31 prepared … victory. This is not a condemnation of adequate preparation but rather of reliance on it for victory, instead of on the Lord (cf. Ezr 8:22; Ps 20:7; Is 31:1–3; Hos 1:7).
21:31 but to Yahweh belongs the victory Yahweh—not human preparation—determines outcomes. See note on 20:24; note on Psa 20:7.
21:31 The verse takes for granted that people will make suitable preparations to reach their goals, while recognizing that the result depends on God.
 MacDonald, W. (1995). Believer’s Bible Commentary: Old and New Testaments. (A. Farstad, Ed.) (pp. 846–847). Nashville: Thomas Nelson.
 MacArthur, J. F., Jr. (2006). The MacArthur study Bible: New American Standard Bible. (Pr 21:31). Nashville, TN: Thomas Nelson Publishers.
 Sproul, R. C. (Ed.). (2005). The Reformation Study Bible: English Standard Version (p. 907). Orlando, FL; Lake Mary, FL: Ligonier Ministries.