How to Work Out a System Bet: 2/3 and 3/5

To calculate a system bet, count the combinations, divide the total stake between them, multiply the decimal odds within each payable line and multiply that product by the unit stake. Add the line returns, then subtract the full total stake, not just the stakes on winning lines.

Your money is split across separate accumulators. A 2/3 system has three combinations, so a total stake of $30 gives each line a $10 unit stake. Each winning line produces a gross return, including its returned stake; a losing line returns nothing. Net profit is what remains after deducting all $30 staked.

These examples use hypothetical cash stakes in dollars to match the screenshots, not to imply any UK bookmaker currency or availability. Stakes are equal across lines, odds are decimal, and bets are win-only, with no taxes, promotions or deductions. Results are wins or losses unless the separate void example says otherwise. The calculator rounds each line return to two decimal places before adding them; bookmaker rounding may differ.

How many combinations are in an m/n system?

An m/n system includes every possible m-selection accumulator from n selections. A 3/4 therefore contains four trebles, not three.

The combination count is C(n,m) = n! / [m!(n-m)!]. A factorial means multiplying the integers from that number down to 1: for example, 4! = 4 × 3 × 2 × 1. By definition, 0! = 1.

The chart shows line counts, not payouts. It includes both fixed-size systems and named full-cover formats that combine different accumulator sizes.

The inline visualiser below counts combinations and cost. It accepts 3–8 selections and combination sizes of at least 2; it has no odds or payout inputs.

If w selections win, the number of payable lines is C(w,m), or zero when w < m. This applies to a fixed-size system with binary win/loss results, without voids or bankers.

Total stake and unit stake: which amount do you enter?

A $30 total stake spread across three combinations means a $10 unit stake. Entering $30 as the unit stake instead makes the system cost $90.

Use s = T / N and T = s × N, where s is the unit stake, T the total stake and N the number of combinations. The field convention depends on the actual betting slip, not the country.

Before confirming, check the accepted combination count, unit stake, total stake, odds and minimum unit stake. If division produces an awkward amount, check the permitted input precision and the final total shown on the slip.

Worked 2/3 calculation: three doubles

With selection A at 2.00, B at 1.50 and C at 1.70, a 2/3 system contains AB, AC and BC. A $10 unit stake makes the total stake $30.

Multiply the odds within each double. AB has combined odds of 2.00 × 1.50 = 3.00, so its return if it wins is 10 × 3.00 = 30.

When exactly two selections win, only their double pays. When all three win, all three doubles pay, giving 30 + 34 + 25.50 = 89.50.

One winning line produces a return, but not necessarily a profit. If only BC wins, you receive $25.50 after staking $30 across the whole system.

With exactly two winners, this example breaks even when the winning pair's odds product equals 3 and makes a net profit when it exceeds 3. That is conditional arithmetic, not advice to increase the odds or a prediction of success.

For a same-budget comparison, a straight treble staked at $30 has combined odds of 5.10. It returns $153 if all three selections win and $0 if any loses. See the detailed system bet versus accumulator comparison for the distinction.

Worked 3/5 calculation: ten trebles

A 3/5 system contains ten trebles. With all five selections at 2.00 and a $10 unit stake, the total stake is $100 and each payable treble returns $80.

The complete combination list is:

ABC, ABD, ABE, ACD, ACE, ADE, BCD, BCE, BDE, CDE.

Each treble has combined odds of 2.00 × 2.00 × 2.00 = 8.00, giving a return of 10 × 8.00 = 80.

Four winners produce C(4,3) = 4 payable trebles. Their returns total 4 × 80 = 320; subtracting the $100 total stake leaves $220 net profit.

The shortcut R = s × C(w,m) × o^m works only with equal odds o, equal unit stakes s and ordinary win/loss results without voids or bankers. When w < m, the return is zero. With unequal odds, the winner count alone is insufficient: you must identify the actual winners and calculate each payable line.

How do Yankee and Lucky 15 calculations differ?

A Yankee combines 11 lines of different sizes, while a Lucky 15 adds four singles. Neither is the same as a fixed 2/4 system, which contains only six doubles.

These standard structures are listed in William Hill's bet types guide.

A Trixie therefore differs from a 2/3 system by including the treble as well as the three doubles.

With a $1 unit stake and all four selections at 2.00, the following returns apply. The total stakes are $11 for the Yankee and $15 for the Lucky 15. No bonuses are assumed.

With all four winners, the Yankee returns 6 × 4 + 4 × 8 + 16 = 72. The Lucky 15 adds $8 from the four singles, making its gross return $80 and net profit $65.

For more detail, see the Yankee guide and Heinz, Super Heinz and Goliath guide. Their standard line counts of 57, 120 and 247 also appear in the count chart above.

How to check the calculation in the calculator

Open the round-robin calculator, choose the combination size and turn singles off before entering the unit stake. For the 2/3 example, you need doubles only.

1. Choose “Decimal”.
2. Set three selections with odds of 2.00, 1.50 and 1.70.
3. Select only “By 2s” and turn “with singles” off.
4. Enter 10 in “Stake per parlay”.
5. Confirm that “Total stake” shows 30.
6. Select “Pro” to view the three combinations.

Three decimal odds inputs showing 2.00, 1.50 and 1.70Local calculator interface: the odds used in the 2/3 example.

Stake per parlay set to 10 and total stake showing 30The local interface shows a $10 unit stake and $30 total stake; combination-size controls are not visible in this crop.

Pro view showing three combinations at odds of 3.00, 3.40 and 2.55, with conditional returns of 30, 34 and 25.50Local interface in “Pro”: each amount is the return if that combination wins, not confirmation that all three won.

Read the all-win gross return of $89.50 and net profit of $59.50. With exactly two winners, the gross return ranges from $25.50 to $34 and net profit from −$4.50 to +$4. The amount depends on which pair wins; this is neither a confidence interval nor an outcome forecast.

To reproduce the 3/5 example, enter five odds of 2.00, select only “By 3s”, keep “with singles” off and enter 10 in “Stake per parlay”. This gives ten combinations and a $100 total stake. The named Yankee preset reproduces 11 lines.

The calculator supports 2–12 selections, decimal, fractional and American odds, and one or multiple combination sizes. It has no actual-winner selection, void, banker, each way or promotion controls, and no probability model.

How does a void selection affect the calculation?

In this void model, the selection stays in every original combination at technical odds of 1.00. Do not delete the original lines or redistribute their stakes.

FON's Russian-language rules, §4.6, specifically describe this treatment for systems. Tower's English-language rules, §2.25, also specify technical odds of 1.00.

Return to the original 2/3 system: A wins at 2.00, B wins at 1.50 and C is void. Each original line still has its $10 unit stake.

The gross return is $65 and net profit is $35 after deducting the original $30 total stake. There is no additional refund outside these line returns. If all three selections are void, every line settles at odds of 1.00 and the total return is $30 under this model.

English excerpt from Tower Betting Rules section 2.25 describing settlement at odds of 1.00Source: Tower, Betting Rules 2.0, §2.25, original English text. No effective date is specified.

The bookmaker's sport and market rules determine when a selection is void. Cancellation and a push have different causes, even where the applicable settlement uses odds of 1.00.

Each way bets, quarter handicaps, half wins or losses, dead heat and Rule 4 require their specific settlement terms. Rule 4 deductions apply to winnings excluding the returned stake under the market rules; they are not a universal reduction to decimal odds. A simple win/loss/void model cannot replace those terms. In an ordinary equal-unit each way bet, the total stake doubles and the win and place parts are calculated separately—it is not simply double the payout.

How does a banker change the combination count?

A banker is a required selection in every included combination. If it loses, all those lines lose; it provides no guarantee of success.

For a fixed-size system, the count is C(n-b,m-b), where the b mandatory selections are included within m and 0 ≤ b ≤ m ≤ n. The banker principle is described in Marathon's rules, §8.28.

A 2/4 system with A as the banker retains only AB, AC, AD: three lines rather than six. At a $10 unit stake, it costs $30. If A loses, all three lines return zero.

Operator notation can differ, so check the accepted combination list. The recommended calculator has no banker control.

How to reconcile the payout with your betting slip

Check the payout against the original accepted combination list and the applicable bookmaker rules. A matching winner count alone does not establish that the calculation is correct.

Work through:

• the actual unit stake and total stake;
• the accepted combinations and odds;
• each selection's final result;
• the applicable void rules;
• per-line rounding;
• bonuses and free bet terms;
• each way place terms;
• dead heat and Rule 4;
• payout caps.

The accepted slip and applicable operator rules control settlement. These calculations show money flow for stated results; they do not prove profitability, predict probabilities or guarantee recovery of losses. If your next question concerns format choice and risk rather than arithmetic, continue with the guide to when to use a system bet.