Help! Bingo side bet odds.

At my local bingo hall, they offer a side bet called Lucky Ball.

Lucky Ball allows you to start with 1 bingo ball number right off the get-go literally every round, thus increasing your chances of getting bingo. Costs $5. They offer 36 bingo cards for $25, and a decent amount of my competition plays less than 36.

The crowd varies from 50-100 people. They offer 12 games paying at least $100 per game depending on crowd size. The other 4 special games vary in payout from $150 to $600.

They also sell extra bingo cards each round (blatantly terrible bet, and every time someone buys one my odds get worse).

Two of the games doesn't use N's (double corner cluster and letter X down and out), and another game doesn't use B's or O's (little picture frame).

What is the house edge on Lucky Ball?

Is it better to get a Lucky Ball as a B, I, N, G, O, or are all numbers the same value?

Is Lucky Ball ever a mathematically sound bet?

Do you need more details to answer my question more thoroughly?

With all due respect, I don't appreciate the irrelevant comment you provided. It's not helpful! Please help me to figure out the odds on this side bet or say nothing. If you want me to address a gambling related question you have in exchange for that information, I'll gladly consider.

Quote: Bowler377

With all due respect, I don't appreciate the irrelevant comment you provided. It's not helpful! Please help me to figure out the odds on this side bet or say nothing. If you want me to address a gambling related question you have in exchange for that information, I'll gladly consider.

The spammer and his message have been removed.

Quote: Bowler377

Do you need more details to answer my question more thoroughly?

Questions:

One - when you buy a lucky ball, can you apply it to any of your cards?

Two - do you have to determine the lucky ball in advance, or is it just that you can call Bingo when you are one number away, regardless of what it is?

Three - what constitutes a win in Double Corner Cluster? (I assume X "down and out" is just filling both main diagonals, and "little picture frame" is the eight numbers surrounding the free space - correct?)

Thank you very much for your quick response.

Lucky ball applies to every bingo card you have for every game.
You have to determine your Lucky Ball in advance before you buy bingo cards.

If your lucky ball is the only number you need for bingo that hasn't been called, you win.

Double corner cluster means you must have 2 clusters, one in one corner, and another at a different corner. Example:

OOXOO
OOXOO
XXXXX
OOXOO
OOXOO
.
These are the 4 different places you can have a corner cluster on a bingo card, and you need 2 of them. You don't need all 4 corner clusters.

X down and out means if you're one number away from a full X you win. Example:

OXXXX
XOXOX
XXOXX
XOXOX
OXXXO

Notice how in the top right corner we are missing only one O for a complete X of O's. That is sufficient for a bingo in X down and out.

You are correct about Little Picture Frame. Yes, it is the 8 numbers surrounding the free space.

Quote: Bowler377

Thank you very much for your quick response.

Lucky ball applies to every bingo card you have for every game.
You have to determine your Lucky Ball in advance before you buy bingo cards.

So, in other words, when you buy a Lucky Ball, you specify a number - for example, "I want Lucky Ball 57", and it is as if every appearance of G-57 on your cards was, in effect, another Free space.

My gut response is to get a Lucky Ball in the N column, as you now need only 3 to win a regular game instead of 4, but I will have to do some simulations to see how accurate that statement is; an N number is worthless in an X or Corner Cluster game.

Quote: ThatDonGuy

My gut response is to get a Lucky Ball in the N column, as you now need only 3 to win a regular game instead of 4, but I will have to do some simulations to see how accurate that statement is; an N number is worthless in an X or Corner Cluster game.

Wouldn't that N number also be less likely to be on your card since you only have 4 numbers in that column as opposed to 5 numbers?

I did some simulations based on four possibilities: no lucky ball, a B/O number, an I/G number, and an N number.
It turned out that the values for B/O numbers were pretty much identical to the ones for I/G numbers.
The following table shows:
(a) The number of balls called;
(b) The percentage chance of winning in that many balls or fewer, with no lucky ball;
(c) The percentage chance of winning in that many balls or fewer, with a non-N lucky ball (e.g. B-1);
(d) The percentage chance of winning in that many balls or fewer, with a non-N lucky ball (e.g. N-33);
(e) The percentage chance of winning in that many balls plus 1 or fewer, with no lucky ball, to make it easy to compare to the lucky ball numbers.

It turns out that there doesn't appear to be that much of an advantage with an N lucky ball over a non-N one - almost certainly not enough to counter the loss of the advantage in losing the lucky ball in X and Corner games. Your best bet appears to be choosing an I or G number, as those are the only columns that appear in every special game you mentioned.

As for "is it worth it," it may come down to, "How many other cards in the game have it?"