CS2 Overtime Math: A Conditional MR3 Model and Its Limits
Overtime should be priced from the applicable rules and current state, not from a presumed psychological bonus. This guide contains a reproducible conditional model. Its transition probabilities are invented inputs, not observed professional win rates. There is no private sample establishing a sixty-two-percent comeback effect or evidence that bookmakers systematically omit it. A tied score can prompt a forecast review, but it does not establish an even matchup or an underdog edge by itself.
The round-count example assumes MR12 regulation reaches twelve-twelve, followed by MR3 overtime: three rounds on each side, first to four wins the period, and a three-three split starts another period. These are the rules of the model, not a claim that every event uses the same cash, timeout or technical configuration. Valve's supplemental rulebook explicitly says it is not the complete event rules and directs readers to the organizer. Check the actual event and market terms before applying any totals identity.
With this structure, regulation uses twenty-four rounds if tied. A decisive first overtime adds four, five or six rounds, making totals twenty-eight, twenty-nine or thirty. A tied first period uses six rounds but does not finish the map. A second period therefore ends the map no earlier than thirty-four. These are conditional counting results for a normally completed map. Forfeits, administrative settlements or a market that excludes overtime need their own definitions. Do not describe a requested bet as settled just because the current score implies one branch of the model.
Budget and state paths
Within a half, cash and surviving equipment can affect future options. Use the actual reset, income, equipment and purchase conditions instead of a universal ten-thousand-dollar rule or an outdated weapon-price list. The budget below is purely arithmetic: a player who spends a stipulated amount has a specified remaining balance after a stipulated income. A teammate's drop or saved weapon can change the feasible purchase. A lost opening round therefore does not universally remove the AWP from the entire team. Saving before a later round can still have value under the relevant rules.
The transition tree keeps a memory of previous outcomes in the three-round half. The input for round two depends on whether round one was won. The round-three input distinguishes all four two-round histories. Enumerating the eight paths produces a distribution over zero through three wins. This is a state-dependent model, not three independent Bernoulli rounds. Each probability is labeled hypothetical. Calling one side favoured here refers to the chosen inputs, not a measured current map advantage or a guarantee of a full buy.
For the second half, the illustrative model gives the opponent the same transition tree from its own perspective. It additionally assumes the halves are independent. A cash reset does not prove that assumption; team strength, tactics and information can remain shared. Combine the two distributions or enumerate all sixty-four potential paths. Stop counting played rounds when either side reaches four. A calculation using all potential rounds can recover the period winner, but stopping at the winning threshold is necessary to obtain the distribution of actual period length.
Ties and overtime totals
In this particular mirrored example, the chance of a three-three tie is the sum of squared half-distribution probabilities. The result is about twenty-five point six six percent. It is not a universal professional tie rate and does not follow from polarization alone. Independent fair rounds would give thirty-one point two five percent. Different state transitions can move the tie probability in either direction. The example proves the result of its own assumptions; it does not establish that binomial methods always overprice multiple overtime.
At a live twelve-twelve score under the stated counting rules, Over twenty-seven and a half is already certain for a normally completed map. Over twenty-eight and a half excludes a four-zero first period. Over twenty-nine and a half includes six-round first periods and repeats. Over thirty and a half requires the first period to tie. Before the match, those probabilities also need the probability of reaching overtime and its conditional state. Do not copy the live probability into a pre-match ticket or infer positive EV solely from a large quoted payout.
A repeated-period formula needs another assumption: each period has the same win, loss and tie probabilities and is independent of earlier periods. Then eventual winner probabilities sum the geometric series of ties. If side order, fatigue or new information changes the next period, update the state instead. A fixed-input series calculator does not implement this entire conditional half tree. The calculations are provided explicitly rather than attributing unsupported state-dependent functionality to the local tool. Entering a narrative about tilt is not a measured transition estimate.
Using the model
Before considering a ticket, write the current score, starting sides, event configuration, market definition, transition inputs and accepted odds. Keep probability uncertainty separate from quote margin. De-margining a market gives a reference estimate, not true probability. Neither the existence of a timeout nor a comeback score establishes a fixed adjustment. Broadcast delay, acceptance and possible settlement mismatches remain execution questions. A pause does not make a live entry risk-free, and an unconfirmed price is not an available return.
Use sensitivity checks instead of a single confident number. Compare the invented state tree with a simpler independent baseline and alternative feasible transitions, recording the reason for each. Evaluate exposure jointly with any existing map or totals position; correlated tickets do not diversify merely because their names differ. If the rules or probabilities are unclear, pass. No universal stake cap, minimum-price threshold or guaranteed psychological edge is justified by this worked model. Its useful output is a traceable calculation with boundaries that a reader can inspect.
Worked conditional calculations
Invented conditional half tree, A's perspective
P(W1)=.56
P(W2|W1)=.72; P(W2|L1)=.36
P(W3|WW)=.78; P(W3|WL)=.55
P(W3|LW)=.50; P(W3|LL)=.22
path probabilities:
WWW=.314496; WWL=.088704; WLW=.086240; WLL=.070560
LWW=.079200; LWL=.079200; LLW=.061952; LLL=.219648
half distribution H(k wins):
H(0)=.219648; H(1)=.211712; H(2)=.254144; H(3)=.314496
P(at least two half wins)=.568640
Second half: opponent B has the same tree from B's perspective
halves independent by assumption; enumerate 8*8 potential paths
stop played rounds as soon as A or B reaches four period wins
P(A wins first period)=.3717179392
P(B wins first period)=.3717179392
P(tie 3-3)=sum_k H(k)^2=.2565641216
independent fair six-round tie baseline=20/64=.3125
neither tie rate is an observed professional frequency
At 12-12, normal completion under this MR3 model
P(total 28)=P(period decided after 4)=.26138112
P(total 29)=P(period decided after 5)=.2410344448
P(total 30)=P(period decided after 6)=.2410203136
P(first period tied, later total at least 34)=.2565641216
sum of these branches=1
P(Over 28.5)=1-.26138112=.73861888
P(Over 29.5)=.2410203136+.2565641216=.4975844352
P(Over 30.5)=.2565641216
pre-match P(Over 30.5) additionally needs the probability of reaching OT
If entire periods repeat independently with these same probabilities
t=.2565641216; a=b=.3717179392
eventual P(A wins)=a/(1-t)=.5
P(at least m periods)=t^(m-1)
changing the next-period state invalidates this constant-repeat shortcut
Invented cash arithmetic, not current weapon prices or event configuration
starting cash C=10000; chosen loadout cost=7150; loss income=1400
remaining next-round cash=10000-7150+1400=4250
stipulated desired purchase cost=5750; shortfall=1500
this one-player shortfall does not rule out saved gear or teammate drops
confirm actual reset, prices and income before using a real budget model.Valve: CS Major Supplemental Rulebook, scope and event rules
