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Also if the daily amount is less, is it just a proportion, i.e. shows up every 3 times for 33% of max, etc..?
Does click-thru increase if the ad is shown less than the max, or is the click-thru maximized at the max daily spending?
Not sure what you are asking for number 3, but I'll give you my 2 cents.
In my experience, click through is maximized for specific phrases only, be they shown at the maximum rate or not.
Of course, I am a tightwad: I figure if I have to pay to get people in the door, they'd better dang well buy something. So the measurements I really look at are Conversion Rate and ROI. In my mind, I would rather have less traffic with a higher percentage of that traffic buying something than have lots of people clicking into my site.
In other words, instead of bidding on 'widgets' and having my ad showing up for 'blue widgets' and 'pink widgets', I bid only on the specific phrase 'blue widgets'...if I have only blue widgets to sell. And, I look at my ROI when I bid: it may not behoove me to max out the daily spend if I can't get a good return.
But, if you are looking just to get people in the door so people become aware of the site and to increase the site's brand recognition, then you'd get more bang on a more general phrase.
In theory, you'd have more clicks on the maximum bid.
But you have to ask: are those really the clicks you want?
If you look at the statement you receive occasionally you see Overdelivery Credits, which is where Google have delivered more than you said you wanted, in which case they give you the credit for those clicks.
I'd suggest that your better to be shown all the time, but to restrict the amount of traffic by bidding less per click, using exact match and negative keywords.