Accumulators: the bookmakers’ star product
Bookmakers push accumulators hard, and there is a reason. Every match carries its own fee, and combining them stacks the fees up. With the typical fee in our data, a single bet costs 6.3% of the stake; a 3-match accumulator, 18%; a 5-match one, 28%. And a single miss loses everything.
Technical Why the margin compounds
If each leg i has odds oi and overround m, its true probability is roughly pi = 1/(oi(1+m)). The accumulator pays Πoi with probability Πpi (assuming independent matches), so its expected return is Π(oipi) = (1+m)−k. The effective edge is 1 − (1+m)−k, which grows almost linearly with k. With m = 6.7%, the median margin of the 235,796 matches analysed in The odds.
Streaks mean nothing
Even someone who wins half their bets will go through streaks of six, seven or eight losses in a row in a season. They have not lost their “touch”: that is what chance does. The danger lies in how people react. Betting more to win back losses (“chasing losses”) turns a normal bad streak into a hole. Chasing losses is one of the clearest signs that gambling is becoming a problem.
Technical How the streaks are simulated
Each season is a sequence of n independent Bernoulli bets with win probability p. We simulate 5,000 seasons and record the longest losing run in each. For n = 100 and p = 0.5 the typical longest run is about log2(n) ≈ 6–7, and almost one season in three reaches 7 or more.