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National Gambling Board

South African Responsible Gambling Foundation

Gambling - Slot Machines

BlackboardBy the end of this Unit you will be able to:-

  • History
  • Statistical principles
  • More on the concepts
  • Differences in no. of playlines


Simulated slots game

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Topic 1: History of Slot machines

Modern Casinos derive the largest part of their revenue from slot machines and in the USA, South Africa and Australia, the Casino business is predominantly a slot-based business. In these countries, table games, primarily Blackjack and Roulette play a secondary role in Casino revenue generation. The United Kingdom and Europe, in contrast, which have had a more regulated Casino environment and do not allow large, slot-based Casinos, have had more exclusive, smaller table-based Casinos. In comparison to table-based games, Slot machines clearly require fewer people to facilitate their operation and per unit of casino outlay have been shown to be considerably more profitable. The largest casino in the world, Foxwoods in Connecticut in the USA has more than 5 000 slot/video-slot machines.

So what is the history of Slot machines? Charles Fey is generally credited with inventing the first mechanical slot machine in the late 1800’s known as “Liberty Bell” in California. This Slot machine, the Liberty Bell used 5 different slot symbols; namely:-

  • Liberty Bell Symbol
  • Diamonds
  • Spades
  • Horseshoes
  • Hearts

Liberty BellThere were three reels and the disc spins on a horizontal axis on a vertical plane. Each of these reels contained all five of the above symbols. Liberty Bell paid out on a single pay line and cost a nickel (5c (US)) per play. The largest payout, known as the “jackpot”, was 10 nickels for three Liberty Bell symbols on the single pay line. The reels were spun by pulling a handle on the side of the machine. Below is a picture of the Liberty Bell machine.

At the same time, machines were developed by Sittman and Pitt of New York. These had playing card symbols on 5 round drums, or reels, each with ten cards on it. Like Liberty Bell, each spin also cost a nickel, and these machines became popular in the bars in New York, but paid out prizes rather than money on winning combinations. It was the responsibility of the bar tender or proprietor to watch the machines and pay prizes to the clients,  these prizes were often cigars or drinks.

Fruit machineIn the wake of the Liberty Bell slot machines, many different types of machines using different symbols and in particular the first fruit Slot machines were introduced with the still popular melon and cherry symbols. In addition Slot machines were introduced by the Bell Fruit Gum company with the Bar symbols that remain on many slot machines today – these machines became known as “fruit machines”.

Bally introduced the first electro-mechanical slot machine in 1964, this was  known as Money-Honey. More recently slot machines became digital and allowed complex bonus games to be won on top of the base game (the conventional reel based game) which involved player interaction and player strategy. Such machines are often called video-slots. Current manufacturers include:

  • Bally Gaming
  • WMS Gaming
  • Konami
  • Atronic
  • Aristocrat  and
  • IGT - International Game Technology

Modern Slot machine play
Slot machineIn a contemporary video-slot machine, the player is faced with a 3x5 video-display which simulates the spinning of 5 vertical reels. Symbols are required in certain line positions on the display, the first line is always the middle horizontal line.  The payouts on a slot machine are given for different sequences (sequences of the same symbol from the left) which can occur on the selected lines in the 3x5 display. This constitutes the base game. Certain sequences of symbols may then lead to one or two bonus features. These are often sophisticated digitally based games requiring player interaction (often touch-screen). Players select the number of lines they want to play and select the bet per line using buttons on the console. Machines come in different denominations, that is, the unit of the play. In South Africa this varies and could be 10c, 50c, R1 or even R5. The machine displays the number of units of play that the machine has remaining as “credits”. There has recently been a move to have digitally-based machines which “remember” a player.; Each machine must be started with a card. This allows one to play games similar to computer games where one reaches different “levels” of play where different prizes or bonuses are available. The trend in video-slots is essentially to take the most exciting features available from computer games and introduce them in Casinos as paid entertainment with monetary rewards. To the right is a picture of a very popular video-slot machine – Lobstermania.

Even today however, Casinos, often still also carry traditional mechanical spinning reel machines operated by handles for spinning, hence the nickname of “one-armed bandits”; these machines are generally low denomination machines (for example, in South Africa they may work on 10 cents).

Activity 1: Be Creative!

In your pairs, design a Slot machine.

  • Think of the theme first
  • Then think of a name for your machine
  • Next think of what icons or symbols you want – you will need around eight (themed icons) plus a bonus icon
  • Draw a sketch of the 3x5 display of your machine showing all nine icons
  • Compare your sketches to those of other pairs and chose a few that you think are most creative to display in class

Topic 2: Statistical principles on which Slot machines are based

A slot machine is in principle a simple device that works according to standard statistical principles. At each play, 5 “reels”, which in most cases constitute digital rather than mechanical reels, spin and come up with a 3x5 display of icons or symbols. The outcome of reel positions is determined by a Random Number Generator (RNG), although the symbol position on each reel is fixed. Each time the reels “spin”, the five reels “spin” completely independently. That is, there is no pattern whatsoever to the various reel positions over time. Each time the reels spin they end up in a position determined by the RNG which is completely independent of past reel positions. Of course, the “spins” are only simulated through a digital display; the reels appear to spin on the digital display. This is to replicate the spinning of mechanical reels in traditional mechanically-based slot machines.

A typical modern Slot machine

Modern slot machine

When the reels have stopped “spinning” the player is faced with the 3x5 display of symbols for that play. The player then receives a payout depending on whether the icons/symbols displayed form winning patterns (working from left to right in most cases) according to a pay table. Sometimes machines have “scatter” payouts on various symbols. This means that the symbols do not have to appear along a line in a sequence from left to right, but simply anywhere on the 3x5 display.

Credits and machine denomination
The unit of currency in Slot machines are so-called credits; the denomination or value of each credit is determined by the machine. Often Casinos put machines with the same credit in the same area of the Casino. The denominations used in SA casinos are usually R1 or 10c. That is, if you play a 10c denomination machine and if you put in a R20 note you will get 200 credits; you can play a game with one credit but as we will see later, players often increase the number of lines played per play, and sometimes the size of the bet per line as well; this in turn increases the number of required credits proportionately to the number of lines and bet per line.

The Paytable
The example below gives the paytable for the FoodFight game. The units of payout in the paytable are credits. If the Casino decides that the denomination of this machine is R1, then we see that if 2 puddings are displayed (on the first and second reel of the middle line) then the machine pays out 10 credits and this equates to R10. If 3 puddings are displayed in the first three reels, working from the left, then 100 credits (R100) is paid out. Similarly, if 4 pies are displayed in the first 4 reels, R75 is paid out. If the casino decides the denomination of the machine is 10c, then each one credit play would cost 10c and the payouts would, similarly, be a factor of 10 less; eg if 4 pies are displayed in the first 4 reels, R7.50 would be paid out rather than R75.

Paytable of FOOD FIGHT



The paytable is constructed to reflect a certain House Advantage, you will remember that the House Advantage is the percentage expected return for the Casino. This is usually around 5% (the so-called win percentage of the player is thus 100% – 5% = 95%) and reflects the return the machine is expected to make. In the long run, with thousands of plays we can expect that the return from the machine will steadily converge to, or move towards, 5% and the win percentage of the player will converge to or move towards 95%. In the short-run the win percentage of the player (and hence the House Advantage) can fluctuate (move up and down) wildly. If, for example, a player starts off with a credit of 10 and has played 10 times (with a bet of 1 credit each time) and has a total (credit) of 4 remaining, the win percentage is 40%. If a player has played 10 times and has doubled his initial credit of 10 to 20 credits, the win percentage is 200%. Either scenario is very likely after 10 plays and indicates the high standard deviation of the win percentage, usually termed volatility in the Casino business, of the win percentage in the short term.

The larger the number of plays, the more the win percentage will converge to 95%. This is a result from the law of large numbers which states that the standard deviation (of the win percentage) declines according to the square root of the number of plays. If we let the volatility of the win percentage after one play be Vol%, the volatility after n plays will be Vol%/sqrt(n), where sqrt stands for square root. So after 10 plays the volatility will be %Vol/sqrt(10); after 100 plays it will be %Vol/sqrt(100) = %Vol/10; after 1 000 000 plays it will be %Vol/1 000.

The volatility of the win percentage after n plays is usually called the standard error of the win percentage and with fairly conservative assumptions we can assume the true win percentage falls within one standard error of the observed win percentage 66% of the time. If we use two standard errors, we can say the true win percentage falls within two standard errors of the observed win percentage 95% of the time. Statisticians call these intervals confidence intervals.
Let us now look at an example.

If a player makes 10000 plays on a machine with a House Advantage of 5% and a volatility (for one play) of 100%. What is the 66% and 95% confidence interval for the player’s Win%?

The standard error (of the Win%) for 10 000 plays is 100%/sqrt(10 000) which equals 1%.
Hence the 66% confidence interval for the player’s Win% is 95%±1%, that is the true Win% lies in the interval (94%, 96%) 66% of the time. We can also say that the 95% confidence interval for the player’s Win% is 95%±2%, that is the true Win% lies in the interval (93%, 97%) 95% of the time.

Topic 3: More on the concepts, Win Percentage; House Advantage ; and Volatility of  player return

Win percentage continued … the expected number of plays

We continue with the example of a machine with a Win% of 95%. This means that each time we play with a credit of one, we will on average lose 5% of the credit and retain 95% of the credit. Of course, we will never actually retain 95% of the credit (if the denomination was R1 this would amount to 95c) because the paytable only pays out whole numbers, but on average we will retain 95c (assuming again a denomination of R1) over a very large number of plays.

So then, how long could we expect to play? Well, this is a bit tricky; let’s assume we start off with 100 credits and that the denomination of the machine is R1 and we make 100 plays. On average, because our Win percentage is 95% we would expect to end up with R95. We then play 95 times with the R95; that is we play 95 times. We will on average then have R0.95*95 = R90.25. Although this isn’t an exact number, let’s assume for the purposes of this demonstration that we can play a fractional number of times.

The total number of plays we can make will be:
100 + 0.95*100 + 0.95*0.95*100 + 0.95*0.95*0.95*100 + …
Where the … (an ellipsis) indicates that the process can continue endlessly (up to infinity)

Well, we know that the geometric progression:
a + ar + ar 2+ ar 3+ ar 4 + ...

Has a sum (n terms) equal to:
a (1 - r n ) / (1 - r )

as n gets large this converges to  a / (1 - r )

In this example a = 1 and r = 0.95 so the sum equals 1 / (1 - 0.95) which equals 20

So the total number of plays when one starts off with R100 and plays R1 bets for a machine with a R1 denomination and a Win% of 95% is 100*20 = 2000. So with a machine with a Win% of 95% and an initial stack of x credits we can expect to play 20x times.

Let us now look at the cost of play

Well, the example we have looked at tells us something about the cost of play on a slot machine with a Win% of 95%. Say we assume each play takes 5 seconds and we start off with R100 (100 credits on the R1 denomination machine). The expected number of plays is 2 000 and the time taken for these 2 000 plays will be 2 000 * 5 seconds = 10 000 seconds = 2 hours and 46 minutes and 40 seconds OR, R1 for 100 seconds = 1 minute and 40 seconds playing time per Rand; which we may well think  doesn’t seem too expensive!

Casinos Winning Formula
As we stated above, in the simple case of a player playing a R1 bet on a slot machine (with a House Advantage of 5% and with one line selected,[we will look at  more on lines below]), then the larger the number of plays, the more the House Advantage will converge to 5% and hence the more the player Win% will converge to 95%. Of course in any given Casino there can be more than a thousand machines being played simultaneously. Since 100 machines being played by 1 person (R1 bets and 1 line selected) is equivalent to one person playing a machine one hundred times, the total number of plays equates to the number of people multiplied by the number of plays made by each person on average.

The graph below shows that the House Advantage is gradually and inevitably forced to the true House Advantage (assumed to be 5%). The House Advantage plus or minus two standard errors (labelled HA + 2*SE and HA – 2*SE) known as the upper and lower confidence limits, gives one an idea of the variation that the Casino can allow for its House Advantage as a function of the number of plays. In fact for any given number of plays the 2*SEs give the 95% confidence limits for House Advantage.


Table of 95% confidence limits for House Advantage for 10 – 200 plays

n HA + 2*SE HA - 2*SE
10 68.2% -58.2%
20 49.7% -39.7%
30 41.5% -31.5%
40 36.6% -26.6%
50 33.3% -23.3%
60 30.8% -20.8%
70 28.9% -18.9%
80 27.4% -17.4%
90 26.1% -16.1%
100 25.0% -15.0%
110 24.1% -14.1%
120 23.3% -13.3%
130 22.5% -12.5%
140 21.9% -11.9%
150 21.3% -11.3%
160 20.8% -10.8%
170 20.3% -10.3%
180 19.9% -9.9%
190 19.5% -9.5%
200 19.1% -9.1%


The table above gives the 95% confidence limits for House Advantage for 10 through to 200 plays. It can be seen that after 100 plays a player has a 95% chance of being between 15% up (the casino is 15% down) and 25% down (the casino is 25% up). Hence the player in the short-term could have significant wins. However, the longer the player plays, the more his return will converge to the Casino House Advantage and the more the player will be forced towards a negative 5% return.

Before we go on to Topic 3, which continues explaining certain key aspects of Slot machines, let us do an Activity that helps us sort out all the new terminology we have been exposed to.

Activity 2: What does it mean?

Below is a list of terms that we have used so far in this Topic. Beneath that list is a group of definitions. Working in your pairs, match the definition with the term. Simply put the number of the definition next to the appropriate term.

List of terms:

House advantage the percentage advantage of the casino (house) over the player
Win percentage the percentage of the stake that the player can expect to be returned
Converge to systematically moves towards
Volatility variability or changeability
Paytable list of prizes for various symbol arrangements
Confidence Interval an interval within which something falls with a particular confidence
Standard Error an error or tolerance around an estimate of Win% (or HA%)
Standard Deviation a particular statistical measure of variability
Playlines  various lines which a player can select
Configuration arrangement

Playing many lines

Modern video-slot machines allow one to play many “lines” simultaneously. Thus, for example, the standard (one credit) play only counts winning configurations of symbols on the middle line. If winning visible configurations of symbols occur on the top line of the 3x5 display or on the bottom line they simply do not count.

However, one can elect to play 3 lines per play  - it costs 3 credits rather than one credit but it means that all 3 horizontal lines are eligible for prizes. In fact in the example given above, namely FoodFight, the machine allows one to play up to 9 lines. The shape of the counting lines is given below for the 3x5 display. So, for example in line 6, if a winning configuration occurs along the indicated blue line (which joins the 1’s) then the player wins that configuration.

Lines on the FoodFight Slot machine

FoodFight lines


We list below all the possible lines (9 in total) for the FoodFight machine given schematically:

FoodFight playlines


The lines are now given as they appear on the FoodFight machine display

3 lines

3 lines


5 lines

5 lines


9 lines

9 lines


Many Lines (just like many machines)
We now show that a player playing many lines amounts to the player playing many slots (of the same type) simultaneously. Let us first consider the 3 horizontal lines on the display, that is, the top, middle and lower horizontal lines. These may be considered independent. That is, the configuration of symbols that occurs on the top line is for all intents and purposes independent of that which occurs on the middle line and independent of that which occurs on the bottom line. So, playing 3 lines on the FoodFight game machine is the same as playing 3 FoodFight machines simultaneously with one line (when one line is selected it is the middle horizontal line).
As we might imagine this does not affect our expected return. Playing the three machines once (with one line) is the same as playing one machine three times (with one line) and our Win% remains 95%.

However, intuitively we know something else is happening. If we play three machines at once the chance of getting something on each play (of three machines) is going to increase. This is called the Hit%. If the chance of getting something in one play (with one line) is say 10%, the chance of getting something when playing 3 machines or one machine with 3 lines is going to be 30%. Players often prefer to play many lines because the Hit% goes up proportionately to the number of lines. [Actually, the relationship between lines and Hit% is not exactly proportionate because the lines are not completely independent when we have a larger number of lines]. Moreover, the volatility of the Win% for playing multi-lines will decline in exactly the same way that it did for many plays. If we, for example play 9 lines on the Food-Fight game we can intuitively see that because of the much higher Hit%, we have a much higher chance of winning something. We are in the same position as playing 9 machines simultaneously, or, in fact, playing one machine 9 times. Hence we can apply the argument applied before using the Law of Large Numbers. The standard error of the %Win equals %Volatility/sqrt(L) where L is the number of lines played.

Let us look at an Example to make sure we understand this clearly.
Imagine that a  player plays 9 lines (once) on the game FoodFight. What is the %Win and the Standard Error (SE) of this %Win?
Assume the Win% is 95% and the %Volatility is 100%.

The answer is:- %Win ± 100/sqrt(9) = %Win ± 100/sqrt(9) = 95% ± 33.3%

Now let us imagine that this same player (playing 9 lines) played 100 times. What is the %Win and the Standard Error (SE) of this %Win?

The answer is:-%Win ± 33.3%/sqrt(100) = 95% ± 3.33%


Fact File: Principles and summary of multi-line play

Players often prefer to play multi-line play because it means they almost always win something on each play; the Hit% is much higher. This makes the game more exciting to play. Playing multi-line play is the same (up to a point) as playing L machines simultaneously or of playing one machine L times (where L is the number of lines played). As such we can apply the Law of Large Numbers to show that the standard error of the Win% decreases according to the square root of L. So players often prefer playing many lines because they tend to win something on just about every play. Casinos don’t mind multi-line play either because it locks in their House Advantage; that is, the Win% converges more rapidly to the true Win% (HA%), and the true HA% is a winning position for the Casino. Playing many lines is classic spreading of risk. In the same way that putting money on {Red} in Roulette gives a much better chance of winning something compared to betting on a single number, playing many lines in slots simply gives you a greater chance of obtaining some payout. Your expected Win% remains the same in each case (one line or many lines) but the Hit% is higher and the risk is lower in the sense that you track the true Win% more closely. A multi-line playing strategy parallels the financial diversification of assets; rather than putting all your eggs into one basket (betting a lot on a single line), spread the risk by playing many lines at the same time.


Does playing multi-line play cost more?
Not necessarily. If, for example, a player plays a 10c denomination machine and selects 10 lines, the cost per play is the same as a machine with a R1 denomination where 1-line per play is selected. The Win% will be the same in each case, but the Hit% is close to a factor of 10 higher for the multi-line play.

Increasing the Bet (per line)
A player can also choose to increase the Bet per line for any machine of some denomination. In the same way you can increase your bet in Roulette (up to a certain maximum), you can increase your slot Bet (up to a certain maximum). This is quite separate from the number of lines selected; for any given number of lines the Bet (per line) applies to each line selected. The effect on risk, however, of an increase in the Bet/line is quite different from increasing the number of lines selected. While selecting many lines means that your convergence to the true Win% is quicker, increasing the Bet/line will tend to increase the volatility (around the true Win%) giving you a good chance of ending up far away from the true Win%. That is, you are most likely to be a very big winner or a very big loser! Why is this?
To explain this, let’s take an extreme case in (European) Roulette. Say you’ve decided to bet 37 chips on each play. One way of betting is to place one chip on each number and one on the {0}. This is the perfectly diversified strategy; in fact it has no risk in the sense that at each play you will win a constant amount – you will get 36 chips back, losing one each time you play. The other extreme type of bet is to bet all 37 chips on a single number, say {8, Black}. If you hit {8, Black}.you will win 36*37 chips. Both these strategies have, in fact, the same expected outcome; that is in the very long-run, if you play for long enough you will lose on average about 3% of the chips every time you play. But the comparative volatilities are very different. The strategy of placing your chips on all numbers has zero volatility and the strategy of placing your chips on one number only has a very high volatility. Placing your chips on {8, Black} each time over an evening will mean you will win big if the number of {8, Black}’s that come up in that evening is more or less than the average – we expect {8, Black} to come up 1 in every 37 spins of the wheel.
The situation in slots parallels this. You can play multi-line play or increase the Bet per line or, in fact, do both. Raising the Bet/line (for a one-line play) simply “gears-up” the strategy – it’s the same as putting a lot of money on any bet. If you win you get proportionately more according to the size of your bet. The Win% still remains the same but the risk (Volatility) is raised proportionately. Machines generally allow one to select a Bet per line of one, two, three, four or five credits. Most players, however, bet multi-line with a one credit bet. A real “high-roller” will play the maximum number of lines AND the Maximum Bet per line.
We may show in fact that the %Volatility (standard error of the Win%) increases according to the sqrt(Bet).

Summary of formulae for %Volatility (standard error of the Win%)

The %Volatility (or standard error) of the Win%

1. Decreases according to the sqrt(number of plays(n)): 
2. Decreases according to the sqrt( number of lines(L)):  
3. Increases according to the sqrt(Bet per line (B)):  


  1. A player plays a R1 denomination machine 100 times (1-line play and a bet of R1 per line) with a Win% of 95% and Volatility% of 100% (for one play). What is the expected Win% with standard error(SE)? What is the total outlay (value of coins passing through the machine) known as the “handle” and what is the expected remaining cash balance and SE of this balance at the end of 100 plays?

    Outlay is R100, remaining cash balance is expected to be  R95±R10

  2. Say the player now plays 10 lines each time holding the Bet/line at R1. What will the total cost of the plays be and what will the expected Win% with standard error now be? What is the total outlay now and what is the expected remaining cash balance and SE of this balance at the end of 100 plays?

    (SE to 2 decimal places)
    Outlay is R1000, remaining cash balance is expected to be R950±R31.60

  3. Say the player now plays 10 lines each time but also increases the Bet/line to R5. What will the total cost of the plays be and what will the expected Win% with standard error now be? What is the total outlay now and what is the expected remaining cash balance and SE of this balance at the end of 100 plays?

    (SE to 2 decimal places)
    Outlay is R5 000, remaining cash balance is expected to be R4750±R353.60

Concluding Technical Principles of slot play
  1. Modern video-slots are determined by a Random number generator. The reels “spin” independently at each play, and there is no pattern in the reel positions over time.
  2. The player selects the number of lines, the Bet per line on a machine with a particular denomination.
  3. The expected return to the player known as the Win% remains fixed whatever the number of Lines selected or Bet per line or the number of plays made.
  4. The player can, however, determine the risk or volatility of the outcome through selection of the number of lines and Bet/line. By increasing the number of lines, the player increases the Hit% and decreases the percentage volatility of the outcome.
  5. For any given Line selection, increasing the Bet/Line does not affect the Hit% and, in fact, increases the volatility of the Win%, but, as always, keeps the expected Win% fixed.


The Psychology of Slot Play

Slots are always configured by casinos so that players can expect to lose in the long run. Patrons play against the House Advantage which is always positive. However the very high volatility of outcomes on slot machines means that in many cases players can win substantial amounts of money in a single gambling session. However, the longer they play the more likely they are to lose as the player “return” will inexorably approach (the negative of) the House Advantage and thus constitute a loss for the player.

A key fact remains that Slot play is very entertaining and exciting for the player. Thus players in general do not object to paying for this disadvantage because they are paying for the excitement and entertainment of playing slot machines in the glitter and razzmatazz of a casino.

What is particularly noteworthy from a psychological perspective is that players can fine-tune their slot machine gambling experience to their gambling requirement. That is, the player can control the form of the “route” that their expected (negative) returns follow by selecting the number of lines and Bet/Line that play. If a player plays a high number of lines he increases the Hit% (chance of a hit of some type) on each play. He may even select the number of lines to be such that his Hit% is greater than 100% - that is, the chance of winning something is more than 100%; of course, many of these winnings (payouts) will be less that the amount bet. In this way the player is following a diversification strategy, tantamount to, for example, betting on all the horses in a race. The %volatility of outcomes is very low and the chance of winning something very high. Such a strategy appeals to a player who wants a high chance of seeing “some action” on every spin. However, such a player realises he is unlikely to ever “win big” with such a strategy.

The player who looks to a big winning payoff will select a large Bet/line which may or may not be selected in combination with a high number of lines. This increases the volatility sharply and ensures that the player will either win a lot in a short space of time or quickly lose all his money. This appeals to a gambler who is looking for a “gambling rush”. Win or bust.

The gambler can fine-tune Line and Bet selection according to psychological preference

The gambler wanting a “gambling rush” when playing slots will select a large Bet/line. This parallels putting a lot of money on a particular horse in a horse race or putting a large amount of money on a bet in Roulette.
The gambler who is more tentative and wants to prolong play and is prepared to accept much lower but more certain returns will play a large number of lines and low bet/line often on a low denomination machine. This parallels the player who plays on {red} or {black} or even both at Roulette or the gambler who plays place-accumulators at the races or bets on several horses for places in the same race.


Activity – Presenting to a class
Small groups

Imagine that that you are part of a group of “experts” that have been asked to present a talk on slot machines to a group of Grade 8’s. Working in your small groups compile a presentation that covers the following topics:

  • How lines work
  • House Advantage
  • How players may vary play to finetune their gambling experience

Use posters to make your points clearer