An accumulator, sometimes referred to as a roll-up, is a bet with multiple selections. It works in exactly the same way as the double or the treble (win, place or each-way) but is a term generally used when more than three selections are involved. Technically doubles and trebles are also accumulators but the term accumulator largely refers to any bet with four or more selections. More specifically, an accumulator with four selections is referred to as a 4-timer (or 4-fold, differing terminology with exactly the same meaning). Five selections would be a 5-timer, six selections would be a 6-timer and so on.
Accumulators are very popular because the payouts can be massive for a very low initial stake. This, however, simply reflects the unlikely nature of landing a successful accumulator. Accumulators (or ‘accas’) are common for horse racing and especially football, where the outright outcomes of many matches are chosen, amongst others.
E.g.) A quick example of how the odds of accas can quickly spiral; 6 timer - 6/4, 7/4, 2/1, 4/6, 9/4 and 11/4. The odds for each selection are very attainable as win singles but, as a 6-timer, represent 10/4 x 11/4 x 3/1 x 10/6 x 13/4 x 15/4 = 643500/1536, -1 = 641964/1536, which is 53497/128. A £1 6-timer at these fairly innocuous odds would pay out £418.95.
A non-runner on one selection means the entire stake goes onto the remaining selections that are still ‘running’, i.e. a 7-timer becomes a 6-timer, a 4-timer becomes a treble etc.