How reel EGMs work
In Victoria, Australia, almost all electronic gaming machines are multi-line video slot machines (known in the USA as "nickel"machines. In Victoria, these machines account for the great majority of problem gamblers.
84% of problem gamblers cited electronic gaming machines as their favourite form of play (Department of Justice, Victoria 2005 (Loved Ones) p 84)
78.14% of men and 96.2% of women who attended Gamblers Help played EGMs.
Let us now look at the design of games on Australian machines.
The game on a modern standard Australian machine is the virtual reel, five-line, multi-line video slot game. These games have gained in popularity around the world.
Conceptually, the Australian machine works like this.
Imagine five reels each with, say, 35 symbols. The computer notionally spins each of the reels independently and, using a random number generator, chooses the centre-line symbol.
The reel is then displayed on the screen with the selected symbol in the centre and its neighbouring symbols above and below. The content and order of symbols on each reel is fixed.
Traditionally, reel gambling machines pay out on the centre line reading the symbols from left to right.
Modern machines allow multiple pay lines, not only horizontal but also diagonal with combinations of over 20 paylines.
In the case of Australian machine standards and machine standards in any regulated jurisdiction, there is one
feature which players must understand.
There is no standard requiring balanced (symmetrical) reels.
Put another way, there is no requirement that each type of symbol appear at the same frequency on each reel.
The Australian gaming industry player information booklet published by the Australian Gaming Machine Manufacturers Association states EGMs use unbalanced reels
(AGMMA, pp. 15 & 16):
In this example, then, there are 6 King symbols placed on the first reel in the positions mentioned. Other symbols are assigned to other positions on the reel so that all 35 stopping positions have a symbol assigned.
In almost all instances, the symbols will be assigned differently to the first reel.
For example, there may be only two Kings on reel 2 on stopping positions 15 and 19.
It is clear the machines described are unbalanced (or asymmetric) reel machines.
Devilishly Clever
Professor Philip G. Fox, a teacher of statistics at
"I'm told the three dials clicking to a series of stops build up suspense far more effectively that the simultaneous halting of all dials.
A glance at the arrangement of the symbols, given above, reveals the devilish cleverness of the setup.
There are three bars on the second dial to raise hopes of a jack pot, but only one bar on the last dial.
On the second dial there are no lemons which ruin a player; but four lemons on the third dial lower the boom on him."
Fox's analysis was cited with approval by Dr. Warren Weaver, former Vice President, Alfred P. Sloan Foundation and former mathematics teacher [Weaver (1964, pp. 157 - 160)].
The first diagram shows just how critical symbol distribution can be.
This machine is full of high paying symbols, only five types of symbol and each reel full of them.
And it would not pay a cent. The machine on the left would not be legal in Australia though because all machines have to have a minimum theoretical payout.
However, a subtler version, for example, starving each of the three left hand reels of one type of winning symbol which is more plentiful on the others, would give somebody playing the machine in the expectation the reels were identical the impression that their chances were much better than they really were. Look at the right-hand diagram.
The player gets nines on reels 1 and 3
He says, "I just missed three nines!"
But did he really?
The player assumes that the chance of getting a Nine on reel 2, is the same as getting a Nine on reels 1 and 3.
Let us suppose this machine is a thirty-five stop machine with six Nines on reel 1 and six on reel 3.
There is no rule in Australia to say that reel 2 might not have only two Nines.
If that were the case the player did not have an equal chance of getting the third Nine, the player only had one-third of the chance.
Let us consider a theoretical machine which we can call the Cat God of Sidi Barani machine.
Reel design of Cat God machine
Its reels look like this.
Numbers of each type of symbol on each reel
The first column shows the symbols. The next five columns represent the reels and show the numbers of each symbol on each reel. The "Total" column shows the total number of each symbol by totalling the number of that symbol on the five reels.
For our purposes say the payout is:
· Nine pays on 2 and above
· All others pay on 3 and above
·
Pyramid and
We need to introduce some terms:
· Starving severely limiting the number of symbols on a reel, particularly reels 1, 2and 3
· Puffing associated with starving, putting large numbers of symbols next to starved reels
· Dithering mixing up the pattern of starving; fuzzing it to make it less obvious
The analysis of the Cat God machine is as follows.
Nine and Ten are both puffed on reels 2 and 3 but are both covered by starved reel 1.
Jack is pufffed on reels 1 and 3 but covered by starved reel 2.
The Queen is puffed on reels 1 and 2 but is covered by starved reel 3.
The King is puffed on reel 1 but is covered by starved reel 2.
Just as all Nine, Ten, Jack, Queen and King are starved on one of the first three reels so it follows that none is puffed on all of the first three reels.
Scarab and Pyramid are puffed on reel 2 and Pyramid on reel 4.
The starving is dithered: two on reel 1, two on reel 2 and one on reel 3. Queens, not the lower cards are the most frequent reels 1+2 symbol (but require 1+2+3 for a payout). Pyramid is puffed on line 4.
Making starved reels less discoverable
Starving of reels is masked by a number of factors:
· Expectation - the player does not expect it and so does not look for it - the expectancy of the player that the equipment is regular has been discussed above,
· Concealment - just as a dice player cannot see the numbers on the opposite side of a dice, the EGM player cannot see the concealed symbols on the reel,
· Bias - even the starved reels do generate the starved character, just less often. Reels are never completely starved of a particular symbol. This resembles loaded dice which are designed to favour one number but not so much as to make other players suspicious,
· Dithering - the starving is dithered; different reels are starved of different characters - the pattern is obfuscated, like in camoflaging where part of the technique involves breaking up the outline, and
· Diversion - the player's attention is continually being diverted from one symbol to another - in the gaffed milk bottle or cat rack game, the operator keeps moving the weighted bottles or cats around so the customer will not twig to the difference  – this is similar to the gaffed milk bottles and gaffed cats.
Notwithstanding these factors, it would make sense to switch the starved reels around as much as possible to avoid the player either consciously or unconsciously discerning the pattern.
There is nothing to stop the different versions of this machine having a different allocation of starved reels which would enable switching starved reels between individual machines which have the same external appearance. If permitted by the gambling regulator, it would be possible for switching to occur where different reel design/payout tables were activated depending on the number of coins or lines chosen by the player. This in a physical reel machine would be akin to a mechanic coming in and swapping reels on the machine between button pushes without the player being aware of it.
If technology is installed to enable reconfiguration of machines by remote instruction over the lines, starved reels could be rearranged at will. This would be known as remote switching or hot switching. It would be only a small step to program each machine to automatically switch reels between plays or every few plays (dynamic switching) without the need for any external instruction; this would enable even higher levels of reel starving without any pattern becoming apparent.
Greatest asymmetry on left-hand reels
The figures in yellow in the table above show the sums of the absolute differences between the reels. For example, with reels 1 and 2 we have one Nine and four Nines giving an absolute difference of three. For tens, we have one ten and five tens giving an absolute difference of four. With Jacks there is an absolute difference of five, Queens, one, Kings, five etc. If we add up these differences down reels 1 and 2 we get a total of 22. This is a measure of the asymmetry of or difference between the two reels. The greater the total, the more the difference.
We can see from the totals in yellow that as we move towards the left of the machine, from which the counting is started, the totals, the asymmetry, is higher.
Asymmetry Naturally Limiting Combinations
Not only does starving left-hand reels drastically restrict winning combinations but unbalanced (asymmetric) design has another effect, quite fascinating in its simplicity.
Asymmetric design automatically limits combinations of characters by the operation of simple arithmetic.
To take an example from the machine, symbol Nine is distributed 1, 4 and 7 on reels 1 to 3 respectively. This gives 28 combinations - ways of winning.
If symbol Nine were distributed evenly, as 4, 4, 4 instead of 1, 4, 7 there would be 64 ways of getting three instead of only 28 and 16 ways of getting two instead of 4.
It is little wonder that players who unconsciously assume the reels are identical feel they should be winning. If the numbers of symbols were symmetrically distributed the machines would be paying out heavily in favour of the player. This effect is in addition to misplaced excitement at the "vertical near misses" caused by starved reels.
Effect of unbalanced design on Jack payout
In the table above, the column headed "Combinations" shows the number of combinations possible for each symbol. With the Jack, there are 6x1x5x4x4 = 480 ways of getting five symbols.
The column headed "Perceived combin." (short for Perceived combinations) shows in each cell a calculation of the number of combinations possible where the symbols are distributed amongst the reels equally. Â This is done by taking the number of each symbol, dividing by five and raising to the power five. Once again, to take the Jack, with twenty symbols that would be 20 divided by 5 equals four and thus 4x4x4x4x4 = 1024 ways of getting five symbols. (Decimals are used where the number of symbols is not a multiple of five.)
Unbalanced design affects large prizes too
Even with the Pyramid, if the four Pyramids on reel 4 were redistributed to even up reels 3, 4 and 5 and one of the Pyramids on reel 2 was given to reel 1, the ways of getting a Pyramid would increase from 1x3x1x4x1 = 12 to 2x2x2x2x2 = 32. Given this is a large prize, even puffing/starving reels on the right hand side can have a significant effect on the larger payouts.
Perceived combinations - higher left-hand imbalance
If the reels were balanced these machines would, looking at the example above, be paying out double the money put in - instead of taking 10% to 13%. That is, for every $100 put in the player would get back about $200. Put another way, the machines would be returning about 200% instead of about 90%. This is calculated by comparing the actual numbers of winning combinations with the numbers of winning combinations which would occur if the symbols were evenly distributed over the reels - as shown in the "Combinations" and "Perceived combinations" columns. To this would be added the additional effect of the placement of starved reels in the left hand column.
Obviously, a person who assumes the reels are balanced could well believe from observing the wealth of symbols on the reels and the number of appearent near misses that he or she could not lose. And the gambler would be quite correct - if the reels were balanced.
Physical reel machines
Although the machines in Australia are all video machines, in other parts of the world there are machines which have solid reels. These are called, rather confusingly, "virtual reel" machines. They are called virtual reel machines because the solid reels are controlled by a computer which has a virtual, imaginary, reel.
Computer weighted symbols
Without going into the technicalities, the virtual reel machines can have unbalanced reel design similar to the Australian machines. In addition, these machines can weight different symbols on a reel with different values.
How unbalanced reels/symbols affect outcome
This diagram shows the difference in the operation of unbalanced reels and unbalanced symbols. Unbalanced symbols are not allowed in Australia though they are in some other parts of the world. There is no physical reason why a machine cannot incorporate both unbalanced reels and unbalanced symbols.
Further details may be obtained from Know the Odds Inc
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Created: 7 August 2006
Last Modified: 7 January 2008
Author/Maintainer: Know the Odds Inc- e-mail address: knowodds@knowodds.org
Internet address: http://www.knowodds.org