My book says the following:
In case of poor braking conditions, e.g. a wet runway, it is desirable to reduce the V1 for safety reasons, thus increasing the distance available for abandoning the take-off.
However, in a sample examn question the answers are as follows:
On a dry runway it is recommended to decrease V1 to the lowest value
On a contaminated runway it is recommended to choose the highest value for V1.
(runways are not slippy)
In your first paragraph, it is talking about poor
braking conditions; i.e wet and/or slippery runways. In this scenario, the general school of thought is to minimise your exposure to a high speed abort where the braking conditions are poor - i.e it is (generally) safer to reach your GO position as quickly as you can, get airborne following engine failure and come around and land with full length available. This school of thought can also apply to dry runways as well (i.e the first option in your exam question), to avoid high speed aborts which are generally considered more dangerous than getting airborne and coming around for a full length landing.
The second option in your sample question refers to
contaminated runways (that are specified as not slippery); which is an
acceleration issue, not braking - in fact in an abort case the contamination actually helps with braking. So what this is saying, it's best to have the highest V1 because following an engine failure, if you GO you have to 'push' the aircraft through the muck on the runway on 1 engine up to rotate speed; whereas if you STOP, you have the muck on the runway helping you stop. In this scenario, in general it's saying its best to maximise your time available to STOP, vice GO in the scenario above.