Green’s Dictionary of Slang

(orig. US) a general excl. of affirmation or agreement.

1905		Brownsville Dly Herald (TX) 24 Nov. 2/2: ‘Betcha it’s a boy or girl — hey?’ ‘Betcha tain’t’.
1913		Day Book (Chicago) 2 Aug. 24/2: Betcha they couldn’t keep him awake on a bet, or even a brass tack.
1916		Richmond Times (VA) 9 Jan. 37: [cartoon caption] Mit dis hand up she go two bones I betcha!
1928		R. Carr Rampant Age 43: Skeeter’ll be hot rocks when he’s a Senior, betcha.
1932		D.,W. Lovelace King Kong 19: ‘[A]nd I’ll betcha Ignatz here’d think the top of a cocoanut tree nineteen times wonderfuller’.
1945		Craig (CO) Empire Courier 25 July 2/4: You’ll all agree to that, I betcha! [DA].
1955		Amer. Motorcyclist June 30: She is headed for Miss Motor Maid 1970, I betcha.
1967		Life 20 Oct. 34: It’s an experience for him, but . . . he’s kinda bored, I betcha.
1968		S. Gore Holy Smoke 74: Big mob land now, orright. Betcha!
2000		Guardian 29 Apr. 3: Nah, you’re all right. I’ll betcha.