Slot Math Question: Matching non-consecutive symbols on an active payline.

Hi all!

I'm a newbie to slot math and have found your forums of great assistance when needing to double-check my figures. One thing has remained stubbornly difficult to nail, so I'm hoping you pros can help me figure this out.

We've got bonus symbols that match anywhere on an active payline (non-consecutive match is valid). If you are playing multiple lines and successfully match 3 or more bonus symbols on more than one line, only one bonus game is triggered (at the highest # of symbols matched on any payline).

Here is how I am calculating the expected probabilities of matching bonus symbols on a line:

yR1 = number of bonus symbols on Reel 1 (so yR2=# on Reel 2)
nR1 = number of non-bonus symbols on Reel (so nR2=# of non-bonus symbols on Reel 2)
tR1 = total number of all symbols on Reel 1 (so tR2=total positions on Reel 2)


Match-5: (yR1*yR2*yR3*yR4*yR5)/(tR1*tR2*tR3*tR4*tR5)

Match-4: ((yR1*yR2*yR3*yR4*nR5)+(yR1*yR2*yR3*nR4*yR5)+(yR1*yR2*nR3*yR4*yR5)+(yR1*nR2*yR3*yR4*yR5)+(nR1*yR2*yR3*yR4*yR5))/(tR1*tR2*tR3*tR4*tR5)

Match-3: ((nR1*nR2*yR3*yR4*yR5)+(nR1*yR2*nR3*yR4*yR5)+(nR1*yR2*yR3*nR4*yR5)+(nR1*yR2*yR3*yR4*nR5)+(yR1*nR2*nR3*yR4*yR5)+(yR1*nR2*yR3*nR4*yR5)+(yR1*nR2*yR3*yR4*nR5)+(yR1*yR2*nR3*nR4*yR5)+(yR1*yR2*nR3*yR4*nR5)+(yR1*yR2*yR3*nR4*nR5))/(tR1*tR2*tR3*tR4*tR5)

The first question would be: does that look correct for calculating the probabilities?

The real devil is coming in when looking at expected returns, especially in how to balance them across variable numbers of lines played. For instance, on scatter matches, you multiply the total bet (line bet times number of lines played) times the scatter wins in order to balance the bet against the fact that scatter matches happen regardless of lines played. With the pay-any-on-an-active-payline way of matching the bonus symbols, the probability of playing across multiple lines is less than the number of lines played * the per-line probability, due to overlapping of matching line positions.

How can I balance the probability and returns of bonus symbol wins on a per-line basis for multiple-line play? Any help you can provide would be most appreciated. Thanks!

Hi,
Im no expert but it looks ok to me, and multiple lines dont matter as the odds on each line is the same wether you play one line or 20, just the win frequency increases.

Its easy to plot all your figures on a speadsheet to get the overall % return on a 5 reel slot if you know all the info.

Quote: Shannon

Hi all!

I'm a newbie to slot math and have found your forums of great assistance when needing to double-check my figures. One thing has remained stubbornly difficult to nail, so I'm hoping you pros can help me figure this out.

We've got bonus symbols that match...

Who is "we"?

Quote: MathExtremist

Who is "we"?

Very good question. This is why I chose to pass on this thread.

Hi Loveslots20,

Thank you for that. I see how you're thinking, I'm just not sure it's correct when the bonus symbols are spaced out on the reels. So once bonus symbols appear on a reel, any lines starting in the other two visible positions on the reel have less of a chance of getting enough non-consecutive symbols to acquire a winning match. I can see how this might not matter, but something is off on the actual return vs. what is expected on my spreadsheet and I keep banging my head against the wall trying to figure out what it is. I'll keep working on it. Thanks again!

Hi MathExtremist,

"We" is my friend and I - my friend is writing the code and I'm doing the figures on the spreadsheet. We're trying to figure out how to do a simple virtual slot to put into a social game, but we're not slot designers so it's starting from scratch. I'm enjoying the challenge of it, but starting to wonder if my amateur approach is missing something big. I thought that this might be the place to get some help from people who do know what they're doing in this arena.

Thanks, CrystalMath, for letting me know why you passed. My apologies if I mis-stepped.

OK. Your calculations look correct. It is possible, then, to have 3 match on one line and 4 or 5 match on a different line during the same game, right? Of course, this depends on the line layout.

Thanks! I just breathed a small sigh of relief. So yeah, the way we have it set up is that you can get match-3 on one line and a match-4 on another line, but only the highest match "counts". So if you are playing nine lines per spin, and match both 3 symbols on one line and match 4 symbols on another line, only the match-4 gets counted. These are being used to initiate a bonus game, so match-3 gives you a 1x multiplier to the bonus game payout, but a match-4 would give you a 2x multiplier (the difference in payouts for each match are in the spreadsheet). To compensate for this, is it fair to multiply the winnings by the total bet (so 1 coin on each of 9 lines would be 9x the bonus game payout)?

Quote: Shannon

Thanks! I just breathed a small sigh of relief. So yeah, the way we have it set up is that you can get match-3 on one line and a match-4 on another line, but only the highest match "counts". So if you are playing nine lines per spin, and match both 3 symbols on one line and match 4 symbols on another line, only the match-4 gets counted. These are being used to initiate a bonus game, so match-3 gives you a 1x multiplier to the bonus game payout, but a match-4 would give you a 2x multiplier (the difference in payouts for each match are in the spreadsheet). To compensate for this, is it fair to multiply the winnings by the total bet (so 1 coin on each of 9 lines would be 9x the bonus game payout)?

Hmmm that sounds very like slotomania type of slot math!

And that method would affect the overall % if your are discounting a lower win that is on a seperate winline at the same time.

When you pay only the highest win per line thats ok but when its highest win over all the lines thats very different story and has to be factored in as far as I know.

The way my slots work is that you pay more for hitting more than 1 feature combination at the same time.

eg if the ave feature value is £25 ( yeah im in uk lol ) for 3 symbols ok for most other people $25 for a 3 if two different lines are hit at the same time it should pay x2 etc thats the best method for slot math AFAIK

Quote: Loveslots20

Hmmm that sounds very like slotomania type of slot math!

Ha, I'll have to go play some more Slotomania to see how they're handing it, then. But since I don't know if they have balanced math, I'm not sure if their rules are appropriate to follow.

Quote: Loveslots20

eg if the ave feature value is £25 ( yeah im in uk lol ) for 3 symbols ok for most other people $25 for a 3 if two different lines are hit at the same time it should pay x2 etc thats the best method for slot math AFAIK

Ah, so you add the average values of the two wins together? I wondered if that was the right route to go. So if you win a match-4 at $50 average value but had also hit a match-3 at $25 value, you'd give them the match-4 and payout at $75(times the line bet)?

Thanks again!

Assuming I am reading this right, I wouldn't design a bonus trigger like this personally. If you are going to make non-consecutive bonus symbols count, I think you're better off making the bonus trigger as scatters.

Why? Because players will easily get confused on why sometimes 3 bonus symbols will trigger the bonus and why some others won't.

For example on a 25-line machine (O = bonus symbol):

XXOXX
XOXXX
XXXXO

is a success (upside down V is an active payline)

but

OXXXX
XXXOX
XXXXO

is not.

To the casual player, I feel this would be confusing.

If the bonus symbols have to be on an active payline, you really should force them to start from the farmost left reel, imo.

Quote: tringlomane

Assuming I am reading this right, I wouldn't design a bonus trigger like this personally. If you are going to make non-consecutive bonus symbols count, I think you're better off making the bonus trigger as scatters.

There are 3 ways to trigger a bonus with bonus symbols that I have worked with. You can have them as a scatter (3+ anywhere in the 15 locations), as a line-scatter (3+ anywhere on a line), or as a line-pay (3+ from left-to-right). These are all okay. It's just a matter of what the company wants for their slot.

Quote: tringlomane

Assuming I am reading this right, I wouldn't design a bonus trigger like this personally. If you are going to make non-consecutive bonus symbols count, I think you're better off making the bonus trigger as scatters.

Why? Because players will easily get confused on why sometimes 3 bonus symbols will trigger the bonus and why some others won't.

For example on a 25-line machine (O = bonus symbol):

XXOXX
XOXXX
XXXXO

is a success (upside down V is an active payline)

but

OXXXX
XXXOX
XXXXO

is not.

To the casual player, I feel this would be confusing.

If the bonus symbols have to be on an active payline, you really should force them to start from the farmost left reel, imo.

This is where slot designers add anticipation sounds. It trains the player very quickly what will and will not trigger a bonus.

Quote: CrystalMath

This is where slot designers add anticipation sounds. It trains the player very quickly what will and will not trigger a bonus.

Exactly

Quote: tringlomane

To the casual player, I feel this would be confusing.

Not to a player that can be bothered to look at rules/paytable etc

These type of feature triggers are nothing new.

Quote: Loveslots20

Not to a player that can be bothered to look at rules/paytable etc

These type of feature triggers are nothing new.

I don't think I have ever witnessed another player view a rules/paytable screen. Of course I have stared at many since I'm a math dork. If you make a slot machine that is easy to understand, those screens should rarely be examined.

Also, I can't think of a slot machine that triggers a bonus in this fashion offhand.

Quote: CrystalMath

This is where slot designers add anticipation sounds. It trains the player very quickly what will and will not trigger a bonus.

Yeah, totally agree with this.

Quote: teliot

There are 3 ways to trigger a bonus with bonus symbols that I have worked with. You can have them as a scatter (3+ anywhere in the 15 locations), as a line-scatter (3+ anywhere on a line), or as a line-pay (3+ from left-to-right). These are all okay. It's just a matter of what the company wants for their slot.

Ah, a "line-scatter"! I didn't know what to call it, thanks!

So does it sound right for calculating returns that balance out no matter how many lines are played:

Scatter: multiply by total bet (line bet x # of lines played)
Line-Scatter: if only one line-scatter win is granted but more than one occur concurrently, add together the payouts for all matches and multiply by the line bet?
Line-Pay: simply multiply by line bet

Quote: tringlomane

Also, I can't think of a slot machine that triggers a bonus in this fashion offhand.

I sure hope that it's possible to figure out how to properly calculate the return for this kind of bonus trigger ... are people not using line-scatter bonus triggers because it's impossible to balance the single-line return with multiple-line play? <--that is my big fear.

Quote: Shannon

I sure hope that it's possible to figure out how to properly calculate the return for this kind of bonus trigger ... are people not using line-scatter bonus triggers because it's impossible to balance the single-line return with multiple-line play? <--that is my big fear.

That depends on the form of your "Bonus Round". If it's a free-spin type mechanism, then adding the bonus spins awarded for each bonus trigger would keep the return balanced. With other mechanisms it's more tricky.

Example: 3 Bonus Symbols award 5 Free Spins, 4 Bonus Symbols award 10 Free Spins, 5 Bonus Symbols award 25 Free Spins.

You hit 3 Bonus Symbols on Lines 12 and 17 and 4 Bonus Symbols on Line 8. Then you would give a Bonus Game of 10+2*5 = 20 Free Spins

I'm using regular Scatters to initiate Free Spins. The Bonus Symbols trigger a bonus game.

Quote: Shannon

So yeah, the way we have it set up is that you can get match-3 on one line and a match-4 on another line, but only the highest match "counts". So if you are playing nine lines per spin, and match both 3 symbols on one line and match 4 symbols on another line, only the match-4 gets counted. These are being used to initiate a bonus game, so match-3 gives you a 1x multiplier to the bonus game payout, but a match-4 would give you a 2x multiplier (the difference in payouts for each match are in the spreadsheet).

So if you played 9 lines, and won both a match-4 and a match-3, you'd award the match-4 with a 3x multiplier (1x+2x) to the bonus game payout in addition to the line bet? But if you played 9 lines and only won a single match-3 of bonus symbols, you'd simply award the 1x multiplier times the line bet towards the bonus game payout?


Thanks, tringlomane!

Yep, summing the multipliers is the same principle since the base values of the bonus game will remain constant. Generally speaking, to keep payouts balanced for any number of lines chosen, any bonus trigger on a line must be fully awarded. So with your example above, you can play either 2 bonus games one at 2x and one at 1x, or more simply 1 bonus game at 3x. The latter is the method that is typically used.

Quote: tringlomane

Yep, summing the multipliers is the same principle since the base values of the bonus game will remain constant. Generally speaking, to keep payouts balanced for any number of lines chosen, any bonus trigger on a line must be fully awarded. So with your example above, you can play either 2 bonus games one at 2x and one at 1x, or more simply 1 bonus game at 3x. The latter is the method that is typically used.

Thanks so much for confirming that! My friend kept saying that bonus symbol wins should be multiplied by total bet, which was doing my head in.

I owe all of you guys drinks. Since we're here, please accept my gratitude as a stand-in.