Is there a connection between better, which is sometimes employed as a noun, among other parts of speech, and the noun bettor? This post explains their etymological origins and lists and defines related words.
Better is primarily an adjective, from Old English bettra (and, previously, betera), meaning “superior.” It can also mean “more advantageous or favorable,” “improved,” or “greater than half” (as in “the better part of an hour”). The adjective better pertains to doing something to a greater degree or with higher quality or can replace more (“She was doing better than twenty miles per hour”) or preferably (“It’s better left where it is”).
As a verb, better means “make more acceptable or complete” or “improve on” (as in “The runner will try to better his personal record in the event”). It also serves as an auxiliary verb, one that supports another verb, as in “You had better get going,” sometimes with the first verb elided.
The noun better means “advantage” (“Don’t let him get the better of you”), “something superior” (“We expected better of her”), or “someone of higher rank or status” (“I was told to respect my betters”).
Better is also a variant of bettor, meaning “someone who makes bets.” The origin of bet, meaning “wager” (as a noun) or “wage” (as a verb), is uncertain, but it could be from abet, meaning “incite” or “urge on.” More likely, however, it is from the obsolete English word beet, meaning “make good” and related to better. Either way, it began as criminal slang; the affirming phrase “You bet” (even more informally, “You betcha”) is also slang, though not of unsavory origins.
Two additional words based on better are betterment, meaning “an act of becoming or making better” or referring to an instance of property improvement, and the adjective bettermost, meaning “superior.” Better, however, generally suffices as a comparative that stands between good (which supplanted the Old English word bot, meaning “advantage”) and the superlative best. (Bot does survive in the phrase “to boot,” meaning “in addition.”)