The Mathematics Behind Your Favourite Casino Games

Casino play, whether land based or online is essentially about having fun and trying to make some money whilst youíre doing so. Most people donít manage to turn their passion for casino games into profit, but this doesnít mean that itís not achievable. To give you the best chance of understanding some of your favourite casino games (and hopefully tilt the odds of a positive return on investment in your favour too) weíve taken a quick look at how the maths behind some of the games works out.

One element of online casino gaming which requires some thought is the bonus. Sign up offers and welcome bonuses present an opportunity to maximise profitability. The best way for you to understand the maths behind beating wagering requirements can be found via johnslots handy guide.

The House Advantage

The bitter truth is that all casinos have a house advantage. Itís how they were designed to make money and ensure profitability over a sustained period. This is true whether youíre in Las Vegas , Manchester or sat in your bedroom playing an online service. The trick here is to identify games which have a slimmer built in house advantage and manipulate this to your benefit. Table games like blackjack, craps & poker tend to have a low house advantage. Baccarat offers a low house advantage of 1.06% on the bankerís hand & 1.24% on the playerís hand.

The Slots

Gone are the solely mechanical slot machines with machine arm, nowadays even slots in physical casinos are computer controlled. Each machine tends to contain a random number generator software which controls the reels in relation to the pay line.

The highest number of reel positions on a slot machine is directly relative to the number of reels. If there are 3 reels with 20 symbols, the total number of spinnable combinations is:

20x20x20x20 = 8000

The number generation software for this machine would cycle between 1 and 8000 with only a certain number of combinations (usually just one) yielding a winning spin. In order to maximise potential returns, players are known to Ďloadí machines with as many coins as possible when first beginning play. It is known that physical machines wonít pay out their jackpot if empty so picking a popular machine and coin loading - this lack of action is prevented. This also goes some way to explain why slot experts tend to play multiple machines at once. Although this looks like a pretty rogue practice, itís very common.

Slot machines online operate in a similar way, with software controlling the RNG which decides the outcome of each spin. Return to Player percentages within UK casino slot games tend to range between 80-94%. This means that if you play with £100, on average (over time) youíll get between £80 and £94 back.


Also known as Chemin de fer, Baccarat is a well known table game for up to 15 players (smaller tables seat around 6-7). Player and dealer bets are cycled and bets placed on outcomes of cards in each hand totalling as close to 9 as possible. Aces are classed as low, counting as 1, picture cards & 10s count as zero.

House advantage on the player bet is 1.24% with an even money payout (1/1). The same payout applies to the banker's hand but with a 5% house commission. Therefore, a £10 bet on the dealer's hand (winning) would return £9.50. The house advantage on the bankerís bet is 1.06%. Payout on tied hands is either 8 or 9-1 but has actual real odds of 10-1. This makes the tie bet a bad value bet in theory.

The erratic nature of Baccarat makes it a difficult strategy game. Just like slot machines, this one is to be played for fun primarily. Itís pretty hard (nee impossible) to tilt the odds in your favour.