Torrent Gear

How to calculate the mathematical expectation of a bet

1) What is EV and why is it counted

EV (Expected Value) - the average financial result of a long-distance bet.

EV> 0 - the rate is beneficial on average.

EV <0 is the entertainment price/margin.

EV = 0 - fair play without advantage.

Base template:

EV = Σ (payout _ i × p_i) − rate.
Where 'p _ i' is the probability of the outcome 'i', payouts are net winnings (profit, not bet return), "bet" is your risk in the money.

2) How to translate coefficients into probability (sports)

The key is the implide probability (probability "wired" in the cap).

Decimal coefficients: 'p = 1/k'.

Examples: k = 2. 00 → p=50%; k=1. 80 → p≈55. 56%; k=3. 00 → p≈33. 33%.

Fractional: 'p = denominator/( numerator + denominator)'. (5/2 → p=2/7≈28. 57%)

American:

Plus: 'p = 100/( A + 100)' (A = + 150 → p≈40. 00%)
Minus: 'p = A/( A + 100)' (A = − 150 → p≈60. 00%)

Important: the sum of the implide probabilities of all market outcomes> 100% is the margin. For an honest assessment, compare your subjective probability'p 'with a marginal one.

3) EV in sports betting: formula and examples

For a single bet with decimal cap 'k' and your probability score 'p':

EV = (k−1) × p − (1−p).

Equivalent: EV = k· p − 1. (here 1 is your bet)

Example 1 (minus): k = 1. 90, p=50%. EV = 1. 90×0. 50 − 1 = −0. 05 (− 5% of the rate).

Example 2 (plus): k = 2. 20, p=50%. EV = 2. 20×0. 50 − 1 = +0. 10 (+10%).

Express trains: multiply k and p by event; volatility is rising, and EV is often falling due to total margin.

4) EV in casino games

Roulette (European)

Bet 1 cu on "red":

p (win) = 18/37, payout 1:1 → net profit + 1 when winning.
EV = (+1)×(18/37) + (−1)×(19/37) = −1/37 ≈ −2. 70%.

Slots

Calculating through a full set of outcomes is difficult; use RTP:

EV on the back = − edge × Turnover, where edge = 1 − RTP.
Example: RTP = 96% → edge = 4%. Per 1000 units of turnover, the average EV ≈ − 40 units.
For one EV bid at% ≈ − edge.

Blackjack

With the basic strategy "effective RTP" can be ~ 99% +.

The EV of one distribution depends on the rules and your decisions. Base: EV ≈ − edge. Deviations from the basic EV → strategy are lower (worse).

5) EV bonuses and vager (when "plus" is possible)

The main idea: wagering costs money - this is the turnover of × edge allowed games.

Wagering tax: 'Cost ≈ Bonus × Wager × edge'.

Net EV bonus: 'EV _ bonus ≈ Bonus − Cost' (excluding restrictions and risk of bankruptcy).

Example: Bonus 100 cu., Vager × 30, games with RTP = 97% (edge 3%).

Cost ≈ 100×30×3% = 90 → EV_bonus ≈ +10 у.е.

If % edge=4 → Cost=120 → EV_bonus ≈ −20 c.u.

Additionally, consider the bet limit, prohibitions on high-RTP games and the likelihood of "not living" to the end due to variance.

6) How to estimate your probabilities (p)

EV is only as accurate as your probability estimates:

History and data (team/player statistics, model).
Market conditions (margins, line shifts).
Error humility: EV sensitivity to p change is often high.

Mini check:

If'k· p> 1 '→ EV> 0. If a little more than 1 - the edge is fragile, it can be "eaten" by the commission/taxes/valuation error.

7) Quick calculation templates (copy and substitute)

Single sports bet (decimal k):

'p = your probability estimate'
'EV = k· p − 1 '(in fractions of rate)

Market 1 × 2 (no draw):

Home: k1, Guests: k2 → implide p1 = 1/k1, p2 = 1/k2
Margin ≈ p1 + p2 − 1
Your score is p1, p2 → EV_home = k1· p1 − 1; EV_away = k2·p2 − 1

Roulette (any equally likely set with payments):

EV = Σ (profit _ i × p_i) where p_i = number of winning sectors/37

Slots/any RTP product:

`edge = 1 − RTP`
'EV% ≈ − edge'on bet; per series: 'Total ≈ − edge × Turnover'

Wager Bonus:

'Cost ≈ Bonus × Wager × edge'
'EV _ bonus ≈ Bonus − Cost'

8) Frequent errors in calculations

They confuse profit and payment. In formulas, use net profit (k − 1), not k.

Ignore margin. Implide probabilities must be summed> 100%; excluding margin, EV will be overstated.

Take RTP "from advertising," not actual. The same slot is 96/94/92% - look for the figure in your casino.

Do not consider variance. Positive EV does not guarantee profit in one session; need distance and bankroll.

Fees/taxes. Reduce actual EV (especially in plus strategies).

9) EV and bankroll management

At EV <0: limit turnover (time limit/stop loss), choose higher RTP/lower margin.

With EV> 0: Scale the bid carefully. Kelly theory (for binary outcomes approximately):

'f ≈ (k· p − 1 )/( k − 1) 'is the bankroll share of the bet.
In practice, they use Kelly's share (½ or ¼) to reduce the risk.

10) Checklist "in 60 seconds"

1. Find out the cap/rules/actual RTP.

2. Convert the cap to an impulse probability; count the margin.

3. Give your p (honestly!) and calculate EV = k· p − 1.

4. For bonus - 'EV _ bonus ≈ Bonus − (Bonus × Vager × edge)'.

5. Consider fees/taxes and volatility (bet size, distance length).

6. The solution: to bet only with EV> 0 (and sufficient confidence), otherwise - to play as entertainment with a predetermined "price."

Expectation is a compass. It turns emotions and marketing into numbers. Having learned to quickly count EV and check your probabilities, you stop guessing "lucky - unlucky" and start making decisions systematically: where there is an advantage - play disciplined, where there is no advantage - control the budget and treat the game as conscious entertainment.