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

Probability of 3 Lucky Numbers Winnings

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)

Probability of 2 Lucky Numbers Winnings

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)

Probability of 1 Lucky Numbers Winning


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).

Based on probabilities we can expect to win the following lucky numbers:
3 balls – 1 time (117,480 x 0.00000851)
2 balls – 261 times (117,480 x 0.00222)
1 ball – 11,223 time (117,480 x 0.0955)
This means we win:
£300 x 1= £300
£15 x 261 = £3,915
£1 x 11,223 = £11,223
Total = £15,438
Overall Lucky Numbers Winnings
We’ve not yet factored in the Bingo winnings that can be won on top of the Lucky Numbers winnings, Virtue Fusion don’t publish their exact house edge on Lucky Numbers but typically House edge varies from 10-50% (sometimes this is expressed as RTP or 50%-90% return to player)
For the purposes of this example let’s use a worst case estimate that the house keeps 50% of bingo spend (House edge of 50% RTP of 50%).
This means that of the £35,244 we spent we can assume we’ll get half of it back as bingo winnings:£35,244 / 2 = £17,622
By adding the Lucky numbers winnings to the Bingo Return we can calculate the overall return:
£15,438 + £17,622 = £33,060
This means that after spending £35,244 we can expect to lose £2,184 a loss of about 6.2%.
Lucky Numbers overall RTP

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)

Lucky Numbers Wagering Requirement

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:

Deposit: £50

Bonus: +£50

WR loses: -£12.40

Overall: £87.60 a profit of 37.60

Lucky Numbers Mathematical proof

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.

To test this out, sign up to one of our recommended Virtue Fusion sites below


NameBingo SiteDeposit / BonusClaim BonusComments
Betfair bingo£20 / £30Claim Bonus2 x £15 Bingo and £10 games bonus
Boyle Sport Bingo£5 / £20">Claim Bonus
bucky bingo£10 / £40Claim BonusAdditional 5% cashback on deposits each month
Deal or No Deal Bingo£10 / £30Claim Bonus
gala bingo£10 / £40Claim Bonus
mecca bingo£10 / £40Claim Bonus
paddy power bingo£5 / £20Claim BonusRegular Free Bingo Games
totesport bingo£10 / £25Claim Bonus
Vernons Bingo£5 / £25Claim Bonus
William Hill Bingo£10 / £40Claim Bonus

For more details on all Virtue Fusion bonuses that allow Lucky Numbers click here.

4 thoughts on “The Maths behind The Lucky Numbers Bingo Strategy

  1. Hi Matt,

    This site looks great, really useful and interesting. One question though: in your list of bingo bonuses you state the wagering requirement. I’ve signed up to a few of them (gala and totebingo) and there is no mention in any of the terms and conditions of the offer that there is a wagering requirement. Does that mean they’ve removed the WR and I can withdraw my winnings?


    1. Hi Dan,

      Glad you like the site!

      I’ve just checked and it looks like I made an error in the table, thanks for highlighting it. They both have a 2 x Bonus wager requirement so you should need to wager that before withdrawing. Having said that on all Virtue Fusion sites you can withdraw your cash balance but that will reduce your Bingo Bonus balance to zero.

      I’d recommend:
      If you have a bingo bonus (that’s above say £1) do some more wagering to meet the WR it will then move into your cash balance
      If your whole balance is in the cash balance and the bingo bonus is zero, just withdraw it all.

      Hope that helps, let me know if any questions.

  2. Hi Matt

    Having followed your Virtue Fusion guide here I’ve deposited a total of £65 with a few Bingo halls and have withdrawn more than £150. Still waiting for my 1 in 117,480 win for matching all 3 lucky numbers but this method is definitely a winning formula!

    Thanks for all this fantastic information. Keep up the good work buddy!


    1. That’s great news, glad you’re enjoying it and finding it profitable. Let me know if any questions or if you find any other techniques not listed on the site.

      P.S You might be waiting a while for the 1 in 117,480 🙂

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