Online Slots: Probability and RTP

At this stage you can ignore all the common myths about slot machines, “this machine is ready to pay out”, “this machine is rigged”. All slot machines are based on the law of probability and use random number generators so each time you hit spin your odds of hitting that jackpot remain the same. So you could hit 3 jackpots in a row or like the Lion’s share machine in Las Vegas not pay out for 20 years!

Probability: Back to Basics

Let’s roll a 100 sided die, the chance of me hitting a 100 are 1 in 100 or 1/100 = 1%. This is the law of probability and if I roll a dice long enough I will on average hit 100 once in every hundred rolls.

KEY POINT: Casinos use these probabilities in determining their total Return to player (RTP)

KEY TERM: RTP = expected return to the player in the long run expressed as a % e.g 92% RTP. But anything can happen in the short term!

RTP = (Total amount paid out in winnings) / (Total amount bet)

So back to my dice, knowing the probability I could offer you the chance of placing a £1 bet on the roll of a ten sided dice giving you the chance of winning a £100 Jackpot if a 100 comes up or nothing on any other number.

If 100 customers play 1 game each I would expect to pay the Jackpot out once and could work out my RTP

RTP = (£100) / (100 x £1) = £100/£100 = 100%

This also tells me by that by making this offer in the long run I would not make any profit as it would be paid back to the player, so I need to amend one of two things :

  1. My probability of winning, or
  2. My jackpot amount.

Let’s change the probability of winning.

I will now use a 120 sided die meaning the chance of hitting a 100 are now 1 in 120 or 1/120 = 0.83%

On average I would now need 120 customers to play before I can expect the jackpot to be hit and my new RTP would be:

RTP = (£100) / (£1 x 120) = £100 / £120 = 83 %

This is good news for me as now I can expect to make a profit on my game. For every £100 gambled I can expect the player to win £83 (£100 x 83%) and keep £17 myself or a 17% house edge.

KEY TERM: House edge is the expected amount of money a slot machine is expected to retain expressed as a %. This can also be calculated as 1 – RTP.

Now let’s change the Jackpot amount.

Sticking with my hundred sided die I now only offer the player £90 if they hit the jackpot. As with the first example I can expect on average the Jackpot to be hit once every 100 rolls. My new RTP would be

RTP = (£90) / (£1 x 100) = £90/£100 = 90%

For every £100 gambled I can expect the player to win £90 and keep £10 myself, 10% house edge.

WHAT HAS ANY OF THIS GOT TO DO WITH SLOTS I HEAR YOU ASK!

Understanding these principles is key as they form the basis of all slot machines and more importantly their RTP and Jackpots.

Let’s take my 100 sided die and replace it with a reel with the numbers 1 to 100 on, bingo, a 1 reeled slot machine. The only difference is real slot machines have symbols as they look nicer but behind every symbol is a number.

Let’s add another 2 identical reels and I have built myself a 3 reeled slot machine.

Now let’s set my Jackpot. I want to pay a jackpot on a spin where the 3 10’s are shown on the one winning line.

The odds of this happening can be calculated as:

100 on Reel 1 x 100 on Reel 2 x 100 on Reel 3

= 1/100 or (1%) x 1/100 or (1%) x 1/100 or (1%)

= 1/1000000 or 0.0001%

This means I would now expect the jackpot to be hit once every 1,000,000 spins. I want my machine to be set at a 90% RTP. I am therefore going to charge £1 per spin and set my jackpot at £900,000!

RTP = (£900000)/ (1000000 x £1) = £900000 / £1000000 = 90%

So now you know how a slot machine works and how they are able to offer large jackpots from small initial outlays.

Often modern slot machine will have virtual reels with 256 numbers on each. The chance of getting 100 on each reel is 1 in 16,777,216!

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