Slot Machine Simulator
|B7 B7 Db||0||2500||5000|
|B7 B7 B7||0||500||1000|
|R7 R7 Db||0||300||600|
|R7 R7 R7||0||150||300|
|A7 A7 Db||0||250||400|
|A7 A7 A7||0||100||200|
|3B 3B Db||120||120||120|
|3B 3B 3B||60||60||60|
|2B 2B Db||80||80||80|
|2B 2B 2B||40||40||40|
|1B 1B Db||40||40||40|
|1B 1B 1B||20||20||20|
|AB AB Db||20||20||20|
|AB AB AB||10||10||10|
|-- -- Db||4||4||4|
|-- -- --||2||2||2|
|Symbols: Db=Double, B7=Blazing 7, R7=Red 7, A7=Any 7,|
3B=Triple Bar, 2B=Double Bar, 1B=Single Bar, AB=Any Bar, -- blank
This is a simulator of a Blazing 7s slot machine, using the actual PAR sheet from the manufacturer which specifies the symbols on each reel. There are no graphics, it just does a bunch of spins and tells you the results.
Number of coins played:
|Multiplies the probability of each winning combo by the payout for that combo to get the payback for that combo, and sums all such paybacks to get the total payback for the machine. This shows that I did the programming correctly, because I get the same result as the par sheet.|
Spin a bunch of times and see what return you get.
Number of sessions: Number of spins per session:
Jackpot's portion of total return
In most slots I've seen, the jackpot comprises <1% of the total return. But Blazing 7s is tricky. Since the payback on the machine is 92.70% for three coins and 92.52% for two coins, you might conclude that the jackpot is only 0.18% points of the return. In reality, if you played three coins but there was no jackpot prize, the return would be reduced by 1.8% points. What's going on?
Well, if you look carefully at the paytable, you'll see that wins aren't multiplied for multiple coins on most wins, which is unusual for a slot. So, on wins up to Triple Bars, those wins contribute more to the total return on 2 coins, and less to the total return on 3 coins. That depresses the overall return fer 3 coins vs. 2. To make up for that, for all prizes higher than Triple Bars, there's a bonus for playing 3 coins. Usually there's a bonus for only the top jackpot, but on this slot the six top prizes contain a bonus for 3 coins. It might not look like there is because each prize, is doubled, but it shouldn't be, it should be only 50% higher. Take a look at the prize for three of Two Any 7's plus the Double symbol. If the prizes were distributed evenly across the number of coins, they would be 100, 200, and 300 for 1, 2, and 3 coins respectively. However, instead of 200 and 300 for two and three coins, it's 200 and 400. This bonus for six of the top prizes makes up for the fact that it's shortchanging 3-coin players on the lower pays, relative to the 1- and 2-coin players.
So how do we figure how much the jackpot comprises of the total return? We simply multiply the odds of getting the jackpot times the size of the jackpot, divided by the number of coins played. From reels 1 to 3, there are 2, 2, and 1 symbols respectively that can trigger the jackpot, among 72 stops total for each reel. So the odds of hitting the jackpot are 2/72 x 2/72 x 1/72, which is about 0.0000107. Multiplying that by the 5000-coin prize gives us 5.35% points, and dividing by 3 coins played gives us about 1.8% points.
So, without a jackpot, this game at three coins would be 92.7% - 1.8% = 90.9%. Ouch.
*Calculated Machine Return According to Symbol Frequency*
It's possible to estimate the payback of a machine by doing lots of spins, recording which symbols hit, and then using the frequency of the hit symbols to calculate the payback, but it takes lots of spins. Assuming you could record 800 spins per hour and played for a full week (40 hours), then here are the results for the Blazing 7s slot, according to the sim I just ran, for 1000 attempts and 1 coin played:
- 50% chance of being off by within ±0.7% points
- 10% chance of being off by within ±1.4% points
- 1% chance of being off by within ± 2.2% points
When you run the spin simulation, the program does the same thing, recording which symbols landed on the payline, whether they were winning combinations or not, for each session. Once a session is over, it uses that frequency data to calculate what the payback on the machine would be, assuming that the frequency we observed was in line with the expected frequency. That's where I got the figures I just mentioned. We do see that estimating the payback that way, rather than looking at the raw return, is much more accurate. Actual returns are in a much wider range than those predicted by using the symbol frequency.