A ticket is a chance, and chance is linear
A bingo ticket carries no opinion about anything. It is a random set of numbers inside a round that other people are also buying into, and the only thing a player controls is how many of them they hold. This page is about what that buys, what it does not buy, and why every room in the world puts a cap on it.
- Sheet
- BD-56-03
- Subject
- The ticket
- Buys
- chance, in a straight line
- Capped
- yes, per player and round
What is printed on a ticket
The layout differs by variant and the meaning does not. A ticket is a grid of numbers taken from the pool the room uses, with some cells blank, arranged so that each row and column contributes to the patterns the room pays for. In a ninety-ball room a ticket holds fifteen numbers in nine columns and three rows; in a seventy-five-ball room it is a five-by-five grid with the centre often free. The numbers are assigned by the room rather than chosen by the player, which is the first thing that separates bingo from a lottery ticket a player fills in.
Because the assignment is random, every ticket in a round starts equally likely to be the first to complete the pattern. That equality is the whole reason the room's size is part of the value of a ticket: if all tickets are equally likely and one of them must win, then a player holding one ticket in a room of sixty holds one sixtieth of the chance, and the same ticket in a room of two hundred and forty holds one two-hundred-and-fortieth.
Why more tickets buy chance and nothing else
This is the part that is worth being precise about, because bingo is frequently described as though holding more tickets were smarter rather than simply larger.
linear The chance multiplies
Five tickets in a room of sixty is a five-in-sixty chance of the win, which is eight and a third per cent, against one and two-thirds per cent for one ticket. The chance rose by exactly the same factor as the spend.
flat The cost per point of chance does not move
One ticket at 0.10 buys 1.67 percentage points for 6 pence each; five tickets at 0.50 buy 8.33 points for the same 6 pence each. There is no discount for buying more, and no penalty either - which is what "linear" means.
capped The room stops it somewhere
Every room caps the number of tickets a single player may hold in a round. The cap exists because a player who could buy every ticket in the room would hold a certain win and take the pot with their own money, minus the operator's share - a transaction with no purpose and a cost to the operator.
shared The prize does not multiply
Buying more tickets raises the chance of winning and does not change the size of the prize, because the prize is set by the tickets sold in the room rather than by the tickets one player holds. More tickets, same prize, proportionally more chance to be the one who takes it.
What a ticket does not give you
- No ownership of a position. A ticket cannot be sold, transferred, hedged, cashed out or held after the round. Nothing in the series' other mechanics - an early settlement, a cash-out offer, a lay on an exchange - exists in a bingo room.
- No influence on the draw. Fewer players in a room raises the value of each chance and does not change the numbers. A room whose size a player can predict is a room whose prize a player can predict; nothing about it is a system.
- No memory between rounds. Numbers are drawn afresh, and a number that was called last round has no bearing on this one. Any pattern a player believes they see across rounds is the ordinary appearance of randomness, which is why this desk publishes no strategy and no pattern.
- No value before the buy-in closes. A ticket bought into a room that then sells almost nothing is worth almost nothing in a share room, and worth the stated sum in a room whose prize is fixed. Same ticket, same price, different value - the prize page is about that difference.
The one number a player really controls
Ticket price is set by the room. Room size is set by the other players. The prize rule is set by the operator. The only variable a player sets is the number of tickets, and the arithmetic above shows that this variable buys chance at a flat rate rather than buying value. That makes it a decision about how much to spend rather than a decision about how cleverly to spend it, which is why the honest version of this page ends in the cost of the hour rather than in a technique.