# Blazing Blackjack: A Major Jackpot

A recent post by Cardiff Casino on Twitter caught my attention. It’s always exciting to see the picture of a big jackpot displayed for everyone to see. As you can see from the picture above, the top jackpot stands at more than 68,000 Pounds¹. To be sure, that is life-changing money for most people. But how fair is it? Most casino side-bets like this are usually a sucker’s bet. Is there a level where it makes sense to play this jackpot? Here’s what we know:

- It costs 1 Pound to play this side-bet
- The top jackpot is 68,000 pounds and requires you to draw 3 7 of Diamonds as your first three cards.

We can use some probabilistic math to figure out the probability of us drawing a single 7 of Diamonds from a deck of cards. The formula is the following:

We can see that we have less than a 2% chance at drawing a card that is exactly the 7 of Diamonds. But in order to win this jackpot, we need to draw three of them in a row. While this number will be slightly affected by the number of decks that a casino uses in this game, we can treat the drawing of this card as an independent event since there is always 1 7 of Diamonds per deck. At this point, we have the following formula:

Yes, the above is a very small number; there is a very, very low probability of being dealt 3 7 of Diamonds in a row. What does this mean in real terms of odds? You will only be dealt 3 7 of Diamonds about 1 in 140,608 hands. Also note that in order to keep yourself drawing to the third 7 of Diamonds, you need to start with 2 of them in your hand. That will only happen about 1 in 2,700 hands.

The Blazing Blackjack jackpot only becomes a fair proposition when it is above 140,608 Pounds!

So while it’s great for a casino to promote their games, you should be aware of the odds before you start dreaming of that top prize.

### Blazing Blackjack Jackpot: Exposed Cards

If you’ve played blackjack then you know that you never actually draw 3 cards in a row directly. You start with 2 cards and then other players make their decisions to draw or stay. The dealer also exposes one of their cards for all of the players to see. Let’s assume that you manage to draw two 7 of Diamonds as your starting hand. So what happens to your odds if you see a 7 of Diamonds that is not in your hand? That particular card is very valuable to you and certainly affects your odds, right? For this formula we will assume a 6-deck shoe so there are 6 7 of Diamonds that we are interested in. We will also assume that after our initial draw of 2 cards, we see a 7 of Diamonds in another player’s or the dealer’s hand.

You can see that our probability has dropped quite a bit! Losing that 7 of Diamonds is an expensive proposition because if even 1 7 of Diamonds is lost, then the odds of winning is about 1 in 339,000!

**¹**For the purposes of this article, we can ignore the currency and the exchange rate since the probabilities remain the same regardless of which currency you use.