Slot Machine Design

This question is based on a real slot machine design. The only information on the machine are the following payouts.

$2	$40
$4	$60
$10	$80
$20	$120

On the assumption that you are feeding this slot at ten dollar coins per minute, look at the two following pay tables based on the average time between payouts. Both are designed to payback 92%.

H:M:S	Artificial	True Design
0:01:55	$2	$2
0:02:09	$2	$10
0:11:16	$12	$20
0:36:46	$40	$40
0:45:58	$50	$4
5:08:28	$300	$80
5:45:36	$360	$60
17:16:48	$2,039	$120

The artificial system of payouts is designed to pay out $1 fairly close to the average number of minutes between when this "event" will occur. It has a kind of fairness, but it would be exceedingly dull since you would be getting a lot of $2 payouts roughly every minute, and you would have to wait for the big payouts for a long time. It is closer to the payout system in craps or roulette, where the payout usually gets bigger the harder it is to achieve a combination. What you are primarily aware of is that you are feeding in $10/minute, and most of your payouts are coming at the rate of $2/minute.

The second system of payouts is the real design. It does two things: (1) it moves the relatively small payout of $4 way out of sequence, (2) It increased the second payout that occurs every 2 minutes, and 9 seconds to $10. In order to do that it is necessary to decrease radically the rare payouts. They are still large, but not nearly in proportion to their rarity.

This design is much more reinforcing, as the constant $10 payouts on average every 2:09 and a $2 payout every 1:55. At the same time you are feeding in $10 a minute. But the average time between the $2 and the $10 payout is 60.75 seconds. Plus you may get one of the higher payouts. Your money is slowly grinding away.

Remember the payouts were chosen so that both designs, but a player is far more apt to keep playing the second design. Even the displacement of the $4 might convince someone that he is getting lucky because he always goes straight to the $10 and skips the $4. The player may be unaware of how much more difficult it is to hit anything above $40. He is apt to think that the $80 strike is twice as difficult as the $40 hit.

The question is not does the designer have the right to do whatever he wants, but does the patron have the right to know how the machine works? With normal financial transactions you have truth in lending laws that try to protect customers from arbitrary rules. Even in the supermarket things are always posted with prices on a per ounce or per pound basis so comparisons can be made.

Quote: video poker

The payouts in video poker do not correspond to their true odds, but at least you can look them up and be aware of the difference

True odds per 100,000 hands dealt
Full House 144.0
Flush 196.5
Straight 392.5

Data should be available?

I guess its a question of who the player is. A drunk? A semi-sloshed tourist? A retiree who spends all day in the casino?
I recall reading a recent review of that Rockin' Olives slot machine: the discussion was on the graphics and the enjoyment. There was very little mention of payouts other than a brief mention of dribbling a small payout every third spin or so. No discussion of house edge or effective return or anything.

Consider the famed and now probably obsolete survey of slots. The Rio sure got publicity mileage out of it, but I didn't see everyone walking out of the casinos at the bottom of the list and treking towards the Rio for its Loosest Slots in Town. The Venetian is at the bottom of the list (other than the airport) yet people still play at the airport and at the Venetian. Do these people want any information?

Under the dead horse category, we can drag in things such as a single zero roulette wheel lying fallow while a double zero wheel a few steps away gets modest action. We can also drag in that 6:5 stuff being in foot high letters on the marquee and people flocking to the place.

So yes, I'm a great believer in the availability of information and do not think that fine print or ask at the cashier's window and get a dumb look and a delay constitute adequate disclosure but lets face it. If the drunk doesn't know or care about the information, what is the worry about disclosing it?

I think the payout % breakdown should be available in the casino IF it is advertised. In other word's to make a claim of 100.05% return, the figures behind it should be readily available (and open to independent verification). Other than that, I don't think casinos need to supply information on how they meet the state mandated minimum payout percentage (but I would be amused to the see the breakdown for Megabucks.)

Quote: FleaStiff

I guess its a question of who the player is. A drunk? A semi-sloshed tourist? A retiree who spends all day in the casino?

Consider the famed and now probably obsolete survey of slots. The Rio sure got publicity mileage out of it, but I didn't see everyone walking out of the casinos at the bottom of the list and treking towards the Rio for its Loosest Slots in Town. The Venetian is at the bottom of the list (other than the airport) yet people still play at the airport and at the Venetian. Do these people want any information?

So yes, I'm a great believer in the availability of information and do not think that fine print or ask at the cashier's window and get a dumb look and a delay constitute adequate disclosure but lets face it. If the drunk doesn't know or care about the information, what is the worry about disclosing it?

Actually the Wizard's survey done in 2002 picked the Palms (which opened 15 Nov 2001). The Rio was near the bottom.

Part of the point of the post was that both designs return 91.96%, but the money comes back in very different ways. So just disclosing the return is not all the information.

Also if you disclose information (perhaps on a website), you don't make value decisions on whether people will do anything with the information. Some people would be interested, and people who evaluate slots for a living will make value judgements.

Quote: pacomartin

The question is not does the designer have the right to do whatever he wants, but does the patron have the right to know how the machine works? With normal financial transactions you have truth in lending laws that try to protect customers from arbitrary rules. Even in the supermarket things are always posted with prices on a per ounce or per pound basis so comparisons can be made.

I would say that no, a patron doesn't have a right to know. Customers learn pretty quickly whether the payout structure is one they like. High volatility games seem to have a much longer lifespan than low volatility games.

Mark

Its similar to that Rockin' Olives machine that pays out often ... just about every third spin.
It does this of course by lowering the Jackpot payouts.

However, the reason people play slots is to get the Jackpot, not the dribble of reinforcing quarters.

So its perhaps possible to think of it as an inherently deceptive machine but that might be an extreme view.

Perhaps the player only has to know its a one armed bandit and not just how strong that one arm is? With all the rumors and myths about slot machines, I don't know if any formal disclosure is going to get any believers anyway.

Payout is primary disclosure.
Value for each coin is secondary.
Value of prizes is probably the tertiary consideration.

Quote: FleaStiff

However, the reason people play slots is to get the Jackpot, not the dribble of reinforcing quarters.

Payout is primary disclosure.
Value for each coin is secondary.
Value of prizes is probably the tertiary consideration.

On this old version of Blazing 7's machine , the following is true.
91.96% one coin (average 8.83 plays per payout)
92.52% two coins (average 8.80 plays per payout)
92.70% three coins (average 8.80 plays per payout)

People know that the payout is best for maximum coins, they just don't know how little the improvement actually is.
But the rate of return shows you very little about how the payouts will happen.

The bottom line is the manufacturers produce the PAR sheets for every machine anyway. It's just a question if they should be made available without a court order (as was done in Canada where the psychologist sued under the Freedom of Information Act).

(as was done in Canada where the psychologist sued under the Freedom of Information Act).

I read years ago about a woman in Detroit suing a casino because The Wheel of Fortune atop the machine was not random.
There were 12 possible payoffs ( I think ) and she thought she should have had a 1 in 12 chance of the biggest payout.
Not sure how it ended up. But she sort of had a point ? They arrest carnie operators for such offenses, it is bent pegs or a
magnet instead of a RNG. Where was Matthew Brady when this came was in court ?

Carney operators?
Well, the fraud and deception in the carney world is a bit different.
An air rifle with mis-aligned sights so that even the National Junior Rifle Champion was unable to hit the target is a carney scam as is the throwing a ball into a pail routine wherein the carney operator places a ball in the pail and then throws another one in to show that it can be done, but without that initial ball already there, the one he tosses in would bounce out. These are rigging of the games to make them different that what is displayed to the consumer.

A slot machine is known to payoff randomly. Its probably known that there will be "teaser" payoffs of a few dribbles, but the lure of a slot machine is the huge payoff. Otherwise everyone would be over at the craps table or something. Slot players know they get better booze service than craps players but the deciding factor is probably not the comped booze but the dream of the huge payoff.

I believe the probabilities should be posted right on the machine, in the paytables. For example:

Play $1

Symbols - Pays - Probability
AAA - $1 - 15%
BBB - $5 - 5%
CCC - $10 - 2%
DDD - $25 - 1%
EEE - $50 - 0.25%
FFF - $100 - 0.001%
XXX - $1,000 - 0.0001%

No win - 76.74899%

Return - 97.70%

That's what I want to see!

Quote: cardshark

I believe the probabilities should be posted right on the machine, in the paytables. For example:

Play $1

Symbols - Pays - Probability
AAA - $1 - 15%
BBB - $5 - 5%
CCC - $10 - 2%
DDD - $25 - 1%
EEE - $50 - 0.25%
FFF - $100 - 0.001%
XXX - $1,000 - 0.0001%

No win - 76.74899%

Return - 97.70%

That's what I want to see!

Unfortunately, it would be very difficult to implement, since the paytables on some of the multiline video slots span 10 pages of images. Would your slot choices be changed by this info if it was available?

Quote: cardshark

I believe the probabilities should be posted right on the machine, in the paytables. For example:

Play $1

Symbols - Pays - Probability
AAA - $1 - 15%
BBB - $5 - 5%
CCC - $10 - 2%
DDD - $25 - 1%
EEE - $50 - 0.25%
FFF - $100 - 0.001%
XXX - $1,000 - 0.0001%

No win - 76.74899%

Return - 97.70%

That's what I want to see!

On a PAR sheet they don't traditionally print out the actual percentages since they are too small.

three coins	actual	% hits	% payout
$2	5.221%	43.34%	3.75%
$4	0.029%	1.81%	0.31%
$10	0.218%	38.64%	16.74%
$20	4.655%	7.36%	6.38%
$40	0.272%	2.26%	3.91%
$60	0.585%	0.24%	0.62%
$80	0.010%	0.27%	0.93%
$120	0.015%	0.08%	0.42%
$200	0.887%	4.85%	42.04%
$300	0.032%	0.75%	9.71%
$400	0.025%	0.07%	1.16%
$600	0.008%	0.12%	3.24%
$1,000	0.090%	0.20%	8.86%
$5,000	0.001%	0.01%	1.93%
Nothing	87.953%	0.00%	0.00%
	100.00%	100.00%	100.00%
Casino			7.30%
Player			92.70%

The ACTUAL % like you asked can be confusing since there is usually a big percentage of times you win nothing.
The alternatives are to print the % of hits, or the % of payout.

On the side they usually show 100%-87.953%=11.047% as the percentage of times you hit.


Finally they show the dollar return.

Casino 7.30%

Player 92.70%