Chapter 2
Odds imply a probability. Multiplying legs multiplies those implied probabilities too, so they fall quickly as legs are added. When every price carries a margin, as the invented prices in problem 10 do, that margin compounds in the same way.
Problems 7–12 · 2 warm-up · 3 steady · 1 stretch
What probability do decimal odds of 2.00 and 1.25 imply?
Answer 50% and 80%.
Four legs are each priced at 1.25, an implied 80% each. What do the combined odds imply for all four together?
Answer About 41%: four legs that each look likely combine to less than an even chance.
Three legs imply 60%, 70%, 75%. What is the combined implied probability?
Answer 31.5%, a little under one in three.
Each leg is a two-way market priced 1.91 on both sides (invented). Without any margin, each side would be 2.00. Compare a 4-leg accumulator at 1.91 with the margin-free version.
Answer The 4.7% margin per market becomes about 16.8% over 4 legs.
Every leg implies 70%. After how many legs does the combined implied probability first fall below 10%?
Answer At 7 legs.
A leg is priced at 1.50, an implied 66.7%. Does that mean it will win two times out of three?
Answer No. Implied probability is a way of reading the price, not a statement of how often the leg will win.