you can alter that by changing the weight of certain banners in the campaign. If I recall, a banner can belong to multiple campaigns, and an advertiser can manage multiple campaigns.
So, if you set the weight of your favorite banner to 3, and the rest are 1, then, your favorite banner will come up 3 times as frequently. Still somewhat random.
What I have done in the past is run a bunch of impressions, 5000-10000 of each banner, then, weed out the lower clicking ones. There is a better way to do this which I haven't engineered yet.
After a while, you get a stack of banners that pull clicks. Then you can use that info when building galleries, freesites, etc. so that you know which banners pull better.
You can run multiple campaigns on the same page (i.e. your 'three' image scenario above), but, there used to be something called grouping that would prevent duplicate banners in different campaigns from being displayed in the same pageview. Or, you could manage it yourself by putting distinct banners in each campaign, and having each 'spot' be a campaign.
Once you play with it you'll start picking up the tricks.