What is the word for reserving something for yourself before others do? [duplicate]

The word you're hearing is actually dibs:

2: claim, rights
// I have dibs on that piece of cake

Etymonline says it's a

children's word to express a claim on something, 1915, originally U.S., apparently from earlier senses "a portion or share" and "money" (early 19c. colloquial), probably a contraction of dibstone "a knuckle-bone or jack in a children's game" (1690s), in which the first element is of unknown origin. The game consisted of tossing up small pebbles or the knuckle-bones of a sheep and catching them alternately with the palm and the back of the hand.

Although "bagsy" and "dibs" are the two terms I know best, another phrase that has a similar meaning is "two's up".

I first heard it on an episode of the UK TV show "QI" hosted by Stephen Fry. From the Transcript of Series 4, Episode 4:

Stephen
Yeah. Yeah. [working class accent] "Two’s up on your burn."

Phill
Two’s up on your burn?

Stephen
"Two’s up."

Phill
I swear I’m getting an erection.

Stephen
I have to say when I first arrived in prison, I was a little discombobulated by the entire experience, as you can imagine; you have to give your finger prints and take your clothes off and it’s all very . . . It’s just like public school, it’s lovely. But the . . . the first person who came in; he said, "Two’s up." I said--[looks upward wonderingly]--"Is it? What? Where?" [working class accent] "Two’s up. Two’s up, mate. Two’s up. On your burn."

"Two’s up" means when you’ve finished your cigarette, you give it to the guy who’s first to say "two’s up" to you. And he gets the rights. It’s like saying "bags have your fag end," basically. And then they collect about six of those and then they make a new cigarette out of it.

And, from the Urban Dictionary, the currently top definition has:

Two's up is a very old Yorkshire expression meaning, "Save me a small amount of what you're currently consuming" It was originally used by miners who were hungry and wanted a piece of pie from one of their more fortunate colleagues. It became more popular in the 70's and meant "share your cigarette with me":

"I've left my fags at home, two's up on your rolly (hand rolled cigarette)"

And finally, the site ARRSEPedia (an informal, not 100% serious Wiki about anything connected to the British Army) has:

Popular amongst capwearing bus-stop dwellers, meaning to leave half of a cigarette for someone else. A chav equivilent of puting dibs on something.

(It should, perhaps, be noted that both the Urban Dictionary and ARRSEPedia include alternative, somewhat less salubrious, uses for "two's-up", although the meaning is broadly similar).

The Oxford English Dictionary explains that to "get dibs on something" is to announce that one is making a first claim on something, the earliest recorded usage dating from 1932. Interestingly, the associated word dubs which relates to announcing a claim to two marbles knocked out of the playing ring, is recorded as being used more than a century prior to dibs. Not surprisingly, given the sound of dubs, it derives from the earlier cry of doubles.

A related word you may encounter is "shotgun", which is effectively "calling dibs" but pertaining to the (desirable) front passenger seat in a car.

It has nothing to do with weapons, but it used to.