Deer aren't equipped to fight and defend themselves. They have 2 defense mechanisms; freeze and bolt. When they sense a threat they first freeze hoping their camouflage will keep them from being seen. If they sense they've been made, they bolt and run for their lives.
Unfortunately, when they take off running, it's a full tilt panic run hoping to outrun whatever might be chasing. In that state they're mentally (what little they have) on the threat behind, and not on what may be ahead. In any case, they couldn't consider a bicyclist a threat, and will try to jump over or past you.
Can you predict when they'll bolt, not really, but it will usually happen after they've tried the "freeze" method first. So if you see a deer happily grazing or walking, odds are you're OK. But if you see one in that frozen stance, he may hold that or bolt.
Also be aware that bicycles are pretty quiet, and it's easy for one to "sneak up" on an animal, and set it into panic mode when he suddenly senses your approach.
My advice is that if you see deer in the area you should make sure they know you're coming from a long way off.
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WARNING, I'm from New York. Thin skinned people should maintain safe distance.