If you’ve found this page while looking for the basics of lucky numbers you can read about them here.
This section gets fairly complicated so feel free to just trust that playing Lucky Numbers with 5 x 6p tickets is profitable with a bonus.
If you’re interested in the mathematical proof behind this then please read on.
Lets start by looking at the odds of winning on Lucky Numbers:
We can start by calculating the odds of all 3 lucky numbers winning, we have 3 lucky numbers and there are 90 bingo balls so the probability of all 3 winning is calculated by:
3/90 x 2/89 x 1/88 = 0.00000851 (or 1 in 117,480) – pretty much as close to zero as you can get
There a 3 different combinations that can result in 2 Lucky Numbers winning, these are:
Win Win Lose (WWL)
Win Lose Win (WLW)
Lose Win Win (LWW)
To calculate the odds of 2 balls winning we have to calculate the odds of each of these circumstances and add them together
WWL = 3/90 x 2/89 x 87/88 = 0.00074
WLW = 3/90 x 87/89 x 2/88 = 0.00074
LWW = 87/90 x 3/89 x 3/88 – 0.00074
0.00074 x 3 = 0.00222 (or 1 in 450 chance)
Finally we need to calculate the odds of 1 Lucky Number Winning, again there are 3 combinations that can result in this:
Win Lose Lose
Lose Win Lose
Lose Lose Win
We again need to calculate the odds of each of these occurring, we can then total them to get the overall probability:
WLL = 3/90 x 87/89 x 86/88 = 0.0318
LWL = 87/90 x 3/89 x 86/88 = 0.0318
LLW = 87/90 x 86/89 x 3/88 = 0.0318
3 x 0.0318 = 0.0955 (or roughly 1 in 10)
We’ve now got approximate odds of winning on lucky numbers, lets see what the outcome is if we assume we play lucky numbers 117,480 times at 30p each, apart from the fact we’ll have spent over £35,000 (£35,244 to be exact).
Total = £15,438
We can use this 6.2% as the overall house edge of lucky numbers when played in this way to calculate the profitability of bingo bonuses when played on lucky numbers.Note: If we ignore chance of winning 3 lucky numbers due to how rare it is this 6.2% changes to 7.0%Virtue fusion sign up bonuses have a number of different variations, but as almost all of them have 100-300% of deposit bonus and a 1-4 x Bonus wager requirement.
Lets look at the worst case, a 100% bonus with a 4 x WR.
We deposit £50 and get a £50 bonus
We then have a £200 WR (£50 x 4)
We calculated earlier that on average we lose 6.2% of all wagering on Lucky Numbers (using this approach!) and can therefore calculate the amount we can expect to lose on average when completing the wager requirement:
£200 x 6.2% = £12.40
We therefore know that on average we will lose £12.40 over the course of £200 wagering.
This puts us in a position where we:
WR loses: -£12.40
Overall: £87.60 a profit of 37.60
We’ve now proven the profitability of playing Lucky Numbers using bonuses and this approach.
Remember many sites have more than 100% bonus or have less than 4 x WR, either of these just makes this even more profitable. 300% Bonus with a 1 x WR makes over £130 profit off a £50 bonus.