According to Rule 40(e) from the rules of the previous convention:

If no candidate shall have received such majority, the chairman of the convention shall direct the roll of the states be called again and shall repeat the calling of the roll until a candidate shall have received a majority of the votes entitled to be cast in the convention.

What’s not known is how much time is allotted between each “roll of the states” to allow nominees time to campaign.

Now let’s consider Rule 40(b):

Each candidate for nomination for President of the United States and Vice President of the United States shall demonstrate the support of a majority of the delegates from each of eight (8) or more states, severally, prior to the presentation of the name of that candidate for nomination. Notwithstanding any other provisions of these rules or any rule of the House of Representatives, to demonstrate the support required of this paragraph a certificate evidencing the affirmative written support of the required number of permanently seated delegates from each of the eight (8) or more states shall have been submitted to the secretary of the convention not later than one (1) hour prior to the placing of the names of candidates for nomination pursuant to this rule and the established order of business.

Since it’s likely that only Cruz and Trump will go to the convention having won eight states, then delegates for Rubio and Kasich are unbound and can vote for anyone they want. Cruz might even win on the first round of voting if 100% of the unbound delegates vote for him. He would certainly win on the second round of voting. (See my previous post explaining that a significant percentage Trump’s delegates are not actually Trump supporters, and would in almost all likelihood vote for Cruz in a Trump v. Cruz matchup.)

However, apparently the RNC is allowed to change the candidate eligibility rules before any voting takes place. They would have to do that if they wanted anyone besides Cruz or Trump to compete. (We determined in the previous paragraph that Cruz would win without a rule change, thus the real reason for the rule change would be to stop Cruz and not to stop Trump who already lost.)

Even if they change the rules, remember there are 2,472 delegates, and they each get to make up their own minds as to who they will vote for. A bunch of guys in the legendary “smoke-filled room” can’t decide who the delegates vote for.

How long does a contested convention take? In 1880, James Garfield was finally nominated on the seventh day of the convention, after 36 ballots.