Two partitions of final scores
A round handicap and a round total use the same final score but ask different questions. A handicap cares which team finishes ahead and by how much. A total cares how many rounds were played. Similar winning patterns do not make the contracts identical. Define both winning sets before comparing price or margin. The examples below use a specified first-to 13 regulation model with a 12-12 tie, followed by a hypothetical MR3 overtime block. Overtime counts in the stated markets. These are teaching settlement assumptions; confirm the actual contract before using them.
1. Market Definitions Under MR12
Against that grid, the core markets settle as follows:
- Favorite -2.5 rounds: the favorite must win by 3 or more. In regulation that means 13-10 or better.
- Favorite -3.5 rounds: the favorite must win by 4 or more. In regulation that means 13-9 or better.
- Over 21.5 rounds: at least 22 rounds must be played. In regulation the loser needs 9 or more rounds, so the map ends 13-9 or closer. Every overtime map cashes the Over automatically.
- Under 21.5 rounds: 21 rounds or fewer. The map must end 13-8 or wider, in either direction.
At 13-8, Under 21.5 wins regardless of the winning team. A−3.5 wins only if A is the winner, since the margin is 5. At A 13-9, the total is 22 so Under 21.5 loses, while A−3.5 wins by a 4-round margin. At A 13-10, A−2.5 wins but A−3.5 loses. At A 13-11, both negative handicaps lose although A wins the map. In the chosen overtime block,16-12 covers both spreads,16-13 covers only−2.5 and 16-14 covers neither. All three are Over 21.5.
A constructed distribution, not a simulation result
The following probability table is invented to demonstrate score partitioning. It is not output from a correlated-round simulation, not a measured map profile and not calibrated to a named team. It assigns all overtime mass to the first block for simplicity. Unlisted legal scores have zero mass in this teaching model. Each pair shows A’s score and B’s score, followed by its probability. Check that all weights sum to 1 before using them. A different score distribution can produce different handicap and total prices even with the same overall map-win probability.
Hypothetical final-score probability masses, A score:B score
13:4 .090;13:5 .055;13:6 .070;13:7 .080;13:8 .080
13:9 .085;13:10 .080;13:11 .080
16:12 .015;16:13 .020;16:14 .025
4:13 .025;5:13 .020;6:13 .025;7:13 .030;8:13 .035
9:13 .040;10:13 .045;11:13 .055
12:16 .015;13:16 .015;14:16 .015
sum=1;P(A wins)=.68
P(A-2.5)=.575;P(A-3.5)=.475
P(Under21.5)=.510;P(Over21.5)=.490Equal probability is not identical settlement
Let U denote Under 21.5 and H denote A−3.5. Their probability difference is P(UwithoutH)−P(HwithoutU). In the chosen model, UwithoutH consists of B’s13-8 or wider wins, mass 0.135. HwithoutU consists of A 13-9 and A 16-12, mass 0.100. Hence P(U)−P(H)=0.035. If those exclusive masses happened to be equal, the probabilities would match, but the tickets could still settle differently on individual outcomes. Equal probabilities do not make contracts logically equivalent or create an arbitrage.
Teaching-model probability identity
P(U21.5)=P(A regulation margin>=5)+P(B regulation margin>=5)
P(A-3.5)=P(U21.5)-.135+.085+.015=.475
P(U21.5)-P(A-3.5)=.510-.475=.035
Equal exclusive masses imply equal probabilities only.
They do not imply the same winning scorelines.
Fair-price references:1/.475=2.105263157895
1/.510=1.960784313725Use the offered side price, not a margin ranking
A smaller complete-market overround does not guarantee that your chosen side has better EV. Consider hypothetical quotes A−3.5 at 2.20 and B+3.5 at 1.60. Their overround is 7.954545%. Under 21.5 at 1.90 and Over 21.5 at 2.00 have only 2.631579% overround. Nevertheless, under the constructed probabilities the spread has EV+4.5% and the Under has EV−3.1%. This counterexample defeats a mechanical rule to route every blowout opinion into the lower-margin total. Compare p×d−1 for the actual side and subtract additional cash costs once.
Hypothetical quotes, same constructed probabilities
spreadOverround=1/2.20+1/1.60-1=.079545454545
totalOverround=1/1.90+1/2.00-1=.026315789474
EVspread=.475*2.20-1=.045
EVunder=.510*1.90-1=-.031
Lower total-market margin does not establish superior side EV.The chosen distribution also has mass 0.205 where A wins but A−3.5 loses. Relative to all maps that is 20.5%; conditional on A winning, it is 0.205/0.68≈30.147059%. Those are different denominators. Do not describe one as “one in five winning maps.” An observed collection of close wins also does not prove a team closes badly: opponent strength, overtime and selection matter. A favourite can win exactly as forecast while a correctly understood handicap loses. That is an ordinary losing state, not a settlement error.
Estimate scores honestly
Real score probabilities require evidence or a validated model of round states. Economy, side, roster and map version can create dependence; they do not imply fixed preferred markets for Nuke, Ancient or Mirage. Do not manufacture pistol conversion percentages or assign a universal normal spread to every map. Respect the stopping rules, including 12-12 and the chosen overtime format. If later overtime blocks are possible, keep their exact margins rather than placing every long-overtime result in a bucket that automatically loses a spread. Aggregate only states sharing the same settlement for all contracts being compared.
The final record needs the score distribution and its source, the exact included-round rules, complete opposing quotes, timestamps, probability uncertainty, accepted stakes and all related map exposure. Test the winning sets against concrete scores before calculating EV. Then examine alternative plausible distributions, especially the exclusive cells separating spread and total. CLV can document a benchmark price change but cannot validate the constructed probabilities. If the sign of EV depends on unsupported score weights, retain the uncertainty and pass. A clean partition is necessary for a comparison, but it is not evidence that the probabilities are right.
Buying both markets is not automatically a hedge. In the teaching distribution, A−3.5 and Under 21.5 both win with mass 0.375, only Under wins with 0.135, only the spread wins with 0.100 and both lose with 0.390. With 100 staked on each at 2.20 and 1.90, respectively, the combined position can lose 200. Its conditional expected profit is 1.40, simply the sum of 4.50 and−3.10 from the two tickets. More winning combinations do not imply lower joint risk. Calculate the state-payoff table rather than adding separate Kelly recommendations or assuming a total protects every favourite loss.
Hypothetical combined stakes,100spread and100under
Both win:.375;net=220+190-200=210
Only Under wins:.135;net=190-200=-10
Only spread wins:.100;net=220-200=20
Both lose:.390;net=-200
Expected profit=.375*210+.135*(-10)+.100*20+.390*(-200)=1.40Keep integer-line pushes and administrative settlements separate from this binary example. A refunded stake is not a lost stake and does not belong in the same probability bucket. If overtime is excluded, rebuild both winning sets on the regulation score and apply the specified 12-12 treatment. Do not assume that an overtime final score preserves the same handicap result as the regulation tie. This check should happen before comparing any prices, because a beautifully calculated probability for the wrong contract remains unusable.
