two halves 16.80 completed by two players pays 8.40 each. The room's books are unchanged, and two players each hold half of what one player expected. For a player who values a certain, smaller prize, this is the friendlier rule.
Bingo Desk / The numbers
Round 04
Shares, splits and rollovers, shown as figures
This page is the desk\u2019s arithmetic. Four rounds, four rules, and the same columns for each: what the room took, what it paid, and where the difference went. The point is not that any of it is unfair - it is that the four rows do not add up to a payout ratio, and a player who divides one round by its own takings will get a number that means nothing.
Room ticket
- Sheet
- BD-56-05
- Subject
- The arithmetic
- Rows
- four rounds
- Point
- a single round is not a ratio
A share4 room types: the prize is a stated percentage of the tickets sold in the round
A floor1 room type: a share with a guaranteed minimum the operator adds to
A fixed sum3 room types: a printed prize the operator owes whatever the room sold
Direct answerA share room pays a stated percentage of the round's takings, a fixed-prize room pays the same sum whatever the round took, and a tied round either splits the prize between the winners or carries it into the next round as a rollover. Across four representative rounds the money taken was 84.00, the money paid to players was 69.00 plus 1.00 into a linked jackpot, and the operator kept 14.00.
Taken: 84.00Paid: 69.00Linked jackpot: 1.00Retained: 14.00
How each row is worked
The ledger at the foot of the front page carries the four rows; this page shows where every figure came from and what a reader would have to reproduce it.
- A 90-ball evening room whose prize is a share. 240 tickets at 0.10 taken = 24.00. The room pays 70%. 24.00 x 0.70 = 16.80 to the full house, and the operator keeps 7.20. Nothing was guaranteed, so a quiet round would simply have paid less.
- A guaranteed-prize room. 120 tickets at 0.10 taken = 12.00. The room's promise is a fixed 15.00 full house, so the operator pays 3.00 from its own money. The row's net is negative by exactly that amount.
- A rollover room. 180 tickets at 0.10 taken = 18.00, of which 70% is 12.60. The previous round was tied, so its 12.60 was carried in and the full house paid 12.60 + 12.60 = 25.20. The row's net is negative, and the honest reason is that the rollover was funded by a round that is not in this table.
- A jackpot-linked room. 300 tickets at 0.10 taken = 30.00. The room's own full house was set at 12.00 - a smaller share than the others, because 1.00 of the takings is contributed to the network jackpot rather than paid in the round. Net 17.00.
Reading the two totals honestly
The four rows together took 84.00 and paid 69.00, plus 1.00 into a jackpot that will be paid in some later round. Dividing the paid figure by the taken figure gives 70.00 / 84.00 = 83.3%, which is higher than the 70% share the first and third rooms are sold on. That is not an anomaly and not a trick: the ratio is above the share because a guarantee and a rollover both push money into a round from outside it, and the outside money is real but invisible in a four-round view.
What a player can correctly conclude is narrower and still useful. Round by round the payout moves a long way in both directions; over a long run the share, the guarantees and the rollovers have to be funded out of the same ticket price, and the price is set where they are. A single round's ratio is a sample, and a four-round ratio is a slightly larger sample, and neither is the room's RTP.
The ledger, as arithmetic (illustrative)
90-ball share room: 240 x 0.10 = 24.00; 24.00 x 0.70 = 16.80 paid; net +7.20
Guaranteed-prize room: 120 x 0.10 = 12.00; fixed prize = 15.00 paid; net -3.00
Rollover room: 180 x 0.10 = 18.00; 18.00 x 0.70 = 12.60; + 12.60 carried in = 25.20 paid; net -7.20
Jackpot-linked room: 300 x 0.10 = 30.00; 12.00 paid; 1.00 to the jackpot; net +17.00
Tickets sold across the four rounds: 240 + 120 + 180 + 300 = 840
Taken: 24.00 + 12.00 + 18.00 + 30.00 = 84.00
Paid to players: 16.80 + 15.00 + 25.20 + 12.00 = 69.00
Into the linked jackpot: 1.00
Retained by the rooms: 84.00 - 69.00 - 1.00 = 14.00
Paid out as a share of what was taken: 70.00 / 84.00 = 83.3%
Row-by-row net: +7.20 - 3.00 - 7.20 + 17.00 = 14.00, which is the same figure arrived at from the other direction - which is the check worth doing on any ledger a reader builds.
What a tie does to the arithmetic
A tie is the one event that changes the numbers without changing the rules. Two full houses on the same call, in a room whose rule is to split, produces two prizes of half the value. Under a rollover rule the same event produces no prize at all, and a larger one later. The expected value across the two events is the same; what differs is how the value is spread across players and across time.
split
rollover
carried The same 16.80 is carried into the next round and paid as 33.60 to one winner. The room has paid out the same amount later, and one player in the next round receives double. For a player who values a large prize and is indifferent to when it arrives, this is the friendlier rule - and it is the rule that makes a room's advertised prizes look large.
claim order
who was first The first valid claim takes the whole prize. Where a room uses the claim order rather than a split, the value is decided by a player's reaction to a number the room has just called, which is the only place in this product where speed has any value at all.
What this page does not claim
- It is not a measured rate of return. Four illustrative rounds priced by hand are a demonstration of structure, not a measurement of any room. A room's real figure over a year is a different exercise and belongs to the operator's published data, not to a hand-written table.
- The percentages are examples. Shares of 60% to 80% are ordinary and a room might pay a different figure per pattern type within the same round. The structure survives the variation; the numbers do not.
- A guarantee is not a loss to the operator on every round. The 3.00 shortfall in row two is offset by the surplus in row four and by every full room elsewhere in the day. Treating one guaranteed round as an operator's loss would be reading a single row of a longer book.