From the various sources I consulted, one of the most likely origins for the term "draw"–meaning a match or game that finishes with an equal score–originated in warfare terminology.
The excerpt below for "drawn" conjures images of sword fights and the barbaric penalty, hang drawn and quartered, that awaited men found guilty of high treason whereas women were burned at the stake.
From 1786, The Spelling and Explanatory Dictionary of the English Language by Rev. John Bentick A.M.
Drawn, a. unsheathed, evicerated, equal
From 1828, A Dictionary of the English Language - Volume 1, by Samuel Johnson and John Walker
To DRAW, (draw) v.a. pret. drew; part.pass. drawn
to leave a fight unfinished, as a drawn battle;
DRAWN, (drawn) part. Collected;
pulled out; equal; where each party takes his own stake; open; put aside, or unclosed; eviscerated; […]
From 1818, in an earlier edition of the aforementioned text, the bellicose theme of the verb draw is reiterated but Johnson also refers to removing stakes (wagers, bets) for its past participle form.
To DRAW [emphasis in bold mine]
36. To withdraw from the combat; to leave a fight unfinished; as, when both sides claim the victory, it is called a drawn battle.
3. Equal; where each party takes his own stake.
Below is the source and the words by Joseph Addison, whom Johnson partially cited, in his entry for drawn.
The Present State of War, and the necessity of an Augmentation, Consider'd
“At present, if we make a Drawn Game of it, or procure but moderate advantages, we are in a condition which every British heart must tremble at the thought of.” (1708)
An earlier instance of drawn game is found in the following publication:
The Roman History Written in Latine Faithfully Done Into English by Titus Livius (printed 1686)
But the Consul met them by the way, where a fierce Battel was fought between them, with uncertain event; and though it were indeed but a drawn Game, yet the rumor went that the Romans were worsted, because several Persons of Quality, and Colonels, and one Commissary-General of their side were slain, and especially, for that the Consul himself was wounded. Fame, which always makes bad News worse, had so augmented the loss, that the Senate were in no little pain and perplexity, and resolved to have a Dictator chosen; nor did any Man doubt but Papirius Cursor, the greatest Warrior of that Age, ought to be the Man;…
From 1733 The History of England - Vol 2 by Rapin de Thoyras (second edition)
I believe this suffices to shew, it was a drawn Battle, which afforded no real matter of triumph either to the King or the Parliament. Indeed, three or four days after the battle, the King took Banbury Castle where was a Garrison of eight Hundred Foot, and a Troop of Horse. But if the Circumstances of taking this Place be well considered, it will be found, that it was far from being a consequence or effect of victory.
From a collection of letters, printed in 1718, the publication of Philosophical Letters Between the Late Learned Mr. Ray and Several of His Ingenious Correspondents, Natives and Foreigners, contains one missive dated 1698/9
This Day a large Tyger was baited by 3 Bear Dogs, one after another. The first Dog he kill'd; the second was a Match for him, and sometimes he had the better, sometimes the Dog; but the battle was at last drawn, and neither car'd for engaging further. The third Dog had likewise sometimes the better, and sometimes the worst of it; and it came also to a drawn battle. But the wisest Dog of all was a fourth, that neither by fair Means, nor foul, could be brought to go within reach of the Tyger, who was chain'd in the middle of in the Middle of a large Cock pit. The owner got about 300l. for this Show, the best seats being a Guinea, and the worst 5s. The Tyger used his Paws very much to cuff his Adversaries with, and sometimes would exert his Claws, but not often; using his jaws most, and aiming at under, or upper Sides of the Neck, where Wounds are dangerous. […]
I hope you will pardon this tedious Narration, because I am apt to think ’tis very rare that such a Battle happens, or such a fine Tyger is seen here. I am, &c
The following instances of drawn match are of a far less violent nature, the last of which appears to support the OED's speculation that draw (meaning tie) is derived from withdraw
Rupertismus By John Cleveland (1651)
With their wide listening mouth from the great Peers
That ran away in triumph. Such a foe
Can make them victors in their overthrow;
Where providence and valour meet in one,
Courage so poised with circumspection
That he revives the quarrell once againe
Of the Soules throne, whether in heart or braine,
And leaves it a drawn match: whose fervour can
Hatch him, whom Nature poach'd but Half a Man
His trumpet, like the angel's at the last,
Makes the soul rise by a miraculous blast.
Rushworth's Dialogues. Or, the Judgement of Common Sense in the Choyce of Religion (1654)
By William Rushworth
(as some expresse, if their mind be truly reported: For I desire not to Search other mens books for their defects, if their vertues entice me not to read them) So far as to render the contradictories equally and indifferently ballanc'd, leaving it a drawn match, whether the mysteries of Christian Religion, on which depends the worlds Salvation, be true or fals.
New Academy by Richard Brome (1659)
Cash Your father Lightfoot, you forget again.
There’s a drawn match made*: for the monsieurs
Have ta’en their money again and you have still
Your maidenheads, I hope. But to have heard
The coil† they kept, the wrangle†, and the stir†,
And how the young blades put the old one to’t,
Would ha’ perplexed you more* than keeping of
Your maidenheads from men you love.
Clicking on the first asterisk, the page provides this insight:
The failure to bring things to a conclusion means that there was no 'winner' and Strigood has therefore lost his fee for providing the young French gallants with English virgins to deflower. See OED drawn, ppl. a 3: Of a battle or match: Undecided.
The origin of this usage is said to be uncertain, but here the possibility suggested of derivation from 'withdrawn' is appropriate. Finding the young women to be trapped and without intention of becoming prostitutes, the gallants withdraw.