Using Return to Player and

Variance to increase your winning

chances
This article deals with the strategies you can follow in nearly every game of
chance. But firstly we need to understand how casinos work - once you change
your money into chips its worth noting that all of your money is now at the
casinos disposal. Essentially, they keep the money you wager on games of
chance and skill - slot machines, roulette, blackjack and baccarat to name a few
- and they payout your possible winnings . You surely already suspect that all of
these games are somehow manipulated into providing advantage for the casino.
And all of that makes perfect sense casinos have to earn money somehow,
dont they? Now well learn more about how they do it.
Casinos make money because every game they offer has a built-in statistical
advantage for the casino called the house edge - the edge might be very
small, but over time and the millions of bets placed by those people patronising
a casino, that edge earns the casino money.
The long-term statistics put you, as a player at a disadvantage, although its
quite common to play a game or two in a casino and leave with more money
than you wagered at the beginning. The effects of house edge on the game
youre playing are rarely noticed even during a long-lasting game because its
value is often negligible. But at the same time its high enough to earn the casino
money in the long run. (i.e. the odds of you losing a round due to the house edge
are insignificant). And here is where fortune comes into play (or luck, if you will).
Fortune is what enables lucky winners to walk away with huge sums of money
and beat the casino at its own game. So as to maximize the potential fortune, its
vital to understand the two basic concepts of every game of chance:RTP
(Return to Player) and Variance.
In the next paragraphs, youll find out more on how to take full advantage of RTP
and variance so that you dont inadvertently decrease your chances of winning
money back from the casino.

What is Return to Player?

The term Return to Player (RTP) is defined as the long-term ratio of the winnings
from a game and the bets placed. Its typically expressed as a percentage, (e.g.
95 %), which would mean that out of every 100 bet, the player may expect to
receive 95 back in winnings. You can also think of RTP as the flip side of the
House Edge which can be calculated by subtracting the RTP value from 100%.
For instance, if the RTP is 95%, then the House Edge will be (100% - 95%) which
is 5%.

The RTP of roulette

Lets start with the game of roulette when placing a bet on black colour the
odds of you winning can be calculated as follows: there are 18 black numbers in
the roulettes layout and 37 numbers in total (37 since we cant omit the 0).The
payout is 2:1, thus the odds at winning are 2 * 18/37 = 0.937 = 97.3 %, hence
the House Edge is (100% - 97.3%) = 2.7%.
The RTP of blackjack
Should you employ the generic recommended strategy in online blackjack you
can expect the RTP of around 99.5%. In other cases the blackjacks RTP depends
on the specific set of rules, the betting system used by the player and the
number of packs of cards used. When following the basic blackjack strategy (link
na blackjack clanok), the RTP can fall anywhere within the range of 95% to 102%
(the exact number depends on the cards remaining in the pack at a given
moment). In theory, were the player to count the cards theres a very good
chance the RTP would raise above 100% which could be exploited and used to
ones advantage. Sadly enough, casinos have devised special methods aimed at
preventing the aforementioned from taking place.
The RTP of slot machines
The RTP of online slot machines falls within the 92% to 97% range and is
determined by the placement of the symbols on the reels, the payout ratio when
you match a certain winning combination and other specific rules typical of the
given slot machine.
The RTP in a game of chance and the long-term RTP in a betting
strategy
First and foremost, its crucial to realize the RTP is exactly the same for every
single round/hand you play but if you want to calculate the long-term RTP you
might be surprised at the fact that it can actually decrease if you utilize an
ineffective betting strategy. Say you bet 100 and win back your bet twelvefold
(1200). But then you bet the winnings again. So you bet 100 12 times
(12*100) on a certain combination of numbers. Supposing youre playing
a game of roulette you would statistically lose (100 + 12 * 100) * (100% 97.3%) = 1 300 * 2.7% = 35.1 (97.3% is the RTP of roulette, for your
reference). So if you bet your winnings from one round in a different round, the
amount of money the casino pays back to you slowly, but surely decreases. Keep
in mind however, that people who bet their winnings again far outnumber the
ones who stop gambling after a fluke.
Its essential to be able to distinguish between the RTP of a game itself and the
RTP of the betting strategy you use. The RTP of the strategy could be
defined as the ratio of the players winnings and their bets. Beware of some
websites however which deliberately swop the terms RTP of the game and RTP
of the betting strategy. By doing this they give the wrong impression that the
odds of losing are notably lower than in reality. And as long as you use the
wrong betting strategy, your RTP can even plunge below 50%.

On the other hand, if your aim is to win back as much money as possible you
shouldnt bet your winnings again. The easiest way to achieve this (in theory)
would be to bet all of the money youre willing to lose in one round. Say you can
handle losing 100 and youd be satisfied with winning 900. You could place
a corner bet of 100. In this case the odds are very much in your favour however
the main drawback to this betting strategy is the length of your game you cant
play for a longer period of time.
What is a betting strategy?
A Betting strategy is a structured long-term approach to gambling which a player
uses in the attempt to produce profit. The RTP of any betting strategy hinges on
the games RTP, the height of the bets, the games variance (will be
explained in the next chapter) and under what circumstances you stop
playing and walk away with the money youve won. If the rules of your strategy
which you follow are clear and unambiguous, its fairly easy to determine its RTP
either by calculating it or by running a computer simulation. Its also worth
noting that the betting strategys RTP is often lower than the games RTP
(although in an ideal case they can be equal).
What is the Variance of a game (of chance)?
In a nutshell, variance is a measurement of the change in your bank account
while playing the game. In the games whose variance is low youre likely to win
or lose smaller amounts of money hence the balance of your bank account will
change evenly (unfortunately, were we to a draw a line on a graph it would slope
gently down). In the games whose variance is high however, you win nothing
back for several rounds, but when you finally win, its usually a substantial sum
of money. So in this instance the prevailing downward slope would sometimes be
interrupted by the line shooting up dramatically.
To be precise, variance is a measurement of the spread between the numbers in
the set of players winnings. Since the amount of money which can be won is
directly proportional to how much money a player bets, the winnings are often
expressed as multiples of the bet. For instance, roulette players placing an
outside bet on the pocket colour might win twice the initial bet and roulette
players placing an inside bet selecting the exact number of the pocket the ball
will land in might win 36 times the initial bet.
Alas, establishing variance on slot machines is not so straightforward because
its possible to win various multiples of the initial bet by matching different
winning combinations. As a result, producing companies often label the variance
on a slot machine using vague terms such as low average and high.
However what we discovered is that variance could be described more
accurately by way of a graph, which would show the occurrence of winning
combinations in percentage terms. Thus, weve decided to devote an entire
article to this issue which can be accessed by simply clicking on this sentence.
(pozn. Cela veta bude link na ten clanok)
Variance has a strong influence on your odds of leaving a casino inpocket. So if
you want to maximize your chance of success you need to keep in mind that the

higher the variance, the better. Firstly, when playing a game with a high
variance, the likelihood is that you could get lucky and win a large enough sum
of money for you to feel satisfied with. Or you could win so much money in one
round that you wouldnt manage to lose all of it before leaving the casino.
Secondly, more rounds end with players losing and so people are less likely to
bet again(which negatively effects the RTP of your strategy in the long run).
Now suppose the exact opposite an imaginary game with the variance equal to
0 and the RTP of 99%. For each 1 you bet, you get back precisely 99 cents. In
this case the outcome of every single round would be the same and noone could
win in such a game which would make the game incredibly dull and boring.
Long-term betting strategys RTP and how it links to the games
variance
A simple and effective betting strategy can be demonstrated on a game of
roulette. Notice how the variance of the game chosen affects the betting
strategys RTP in the long run. Suppose there are two players both of which
entered the casino with one hundred . Player X places his bets inside on the
number whereas player Y places his bets outside on the colour. Each one of them
leaves the casino as soon as they amass more than 500 or if they lose
everything. We ran both of these scenarios in a computer simulation (using a
simple programme and a random number generator ), repeated the simulation a
million times and the results were as follows:
In 14.8% of the cases, player Xs averaged on leaving the casino with 648 after
playing 16 rounds. From this we can calculate the RTP which in this case was
equal to (648/100)*14,8% = 95.90%
On the other hand, player Ys averaged on leaving the casino with 500 after
playing 274 rounds only in 5.15% of the cases. Thus, the RTP of his strategy was
only (500/100)*5.15% = 25.75%.
From the cases explored above, we can easily conclude that greater variance
singnificantly improves your chances of leaving the casinos with a large sum of
money. Just for your reference, the RTP of player Xs betting strategy was 3.7
times higher than the one of player Y.
Long-term betting strategys RTP and how its connected to how much
you bet
Your winnings in a game of chance derive from how much you bet. So that also
comes into play in determining the RTP of a betting strategy. Fortunately, we
have an easy rule to help us : the higher the bets, the higher the betting
strategys RTP assuming well settle for the same sum of money as previously.
Well again use the game of roulette in our example well use our players X
and Y who entered the casino with 100 and will leave when they get to 500.
Player X bets 20 on the colour black and player Y bets 5 on the colour black .
Using a computer simulation in the same way as previously we get that player X
managed to win 500 in 10.9% of the cases (on average after 84 rounds and

with the RTP of 54.5%). Player Y left the casino with 500 in JUST 0.88% of the
cases(on average after 706 rounds and with the RTP of 4.41%). The reason for
this is that winning sequences of bets on the black colour are very rare (the
number of wins has to be 80 units greater than the number of losses - we need
to win 80 times in order to reach 500 - 80 * 5 = 400).
Weve established that when the bets you place and the variance are small you
can play longer, nevertheless your odds at gaining a satisfactory amount of
money plummet.
At the opposite end of the spectrum are high bets and high variance. Player
Z entered the casino with 100 and decided to bet it all on the number 1 in
roulette. From 1 million players in a computer simulation 2.71% of them left the
casino with 3 600 (RTP 97,67%) and every one of them played just one round.

Whats the perfect betting strategy then?

An appropriate AND working betting strategy is really just striking a balance
between odds at winning back a satisfactory sum of cash and the length of your
play. The question remains however, what should you do if youd like to play for
a while with a fairly acceptable odds at winning? In the table below you can find
the results from numerous roulette simulations with various bets on
either number or colour. The players start out with 100 and end either after
losing all of their money or after reaching 500 or more:
Bets on:
Number

2
16,15% avg.
522
RTP 84,40%
292 rounds
0,0015% avg.
500
RTP 0,013%
1850 rounds

5
16,7% avg.
555
RTP 92,8%
52 rounds
0,88% avg.
500
RTP 4.4%
706 rounds

10
20
50
14,8% avg.
12,8% avg.
5,33% avg.
648
760
1 825
RTP 95,96%
RTP 97,38%
RTP 97,65%
15,9 rounds
4,73 rounds
1,97 rounds
COlour
5,13% avg.
10,85% avg.
15,94% avg.
500
500
500
RTP 25,7%
RTP 54%
RTP 79,7%
274 rounds
84 rounds
15 rounds
Avg. = average winnings in case of reaching/surpassing 500

100
2,71% avg.
3 600
RTP 97,67%
1 round
17,9% avg.
500
RTP 89,6%
3 rounds

Colour

Bets on:
Number

0,5
9,55% avg.
505
RTP 48%
3832 rounds
0%
RTP 0%
7399 rounds

1
13,9% avg.
511
RTP 70,9 %
1083 rounds
0%
RTP 0%
3698 rounds

As you can see from the table the high variance you have when betting
on number easily beats even the 10-times higher bets on colour at the RTP
value, plus you can play for much longer. The table also shows that bets under

2 are completely unreasonable because the odds of you leaving the casino with
500 are zero in that case.
So if youre visiting a casino or are playing a game for your own enjoyment but at
the same time want to have a good shot at winning something, your best bet is
to play the games with high variance and place generally low bets.

Conclusion
The RTP presented by the game-makers only applies to 1 round. Your longterm RTP might be (and usually will be) lower due to repeated betting of
partial winnings.
Statistically, you lose no matter what bet you place. Lesser bets result in
a smaller house edge for the casino.
Long-term RTP of your betting strategy depends on the games RTP, its
variance, the amount of money you wager and under what circumstances
you decide to leave the casino/continue gambling to win more money.
Variance is directly proportional to the payout ratio. The higher the payout
ratio, the higher the variance.
Games with a high variance are in most cases favourable since the
advatange of higher variance far outweighs the one of slightly greater RTP.
The higher the variance, the higher the chance of turning small sums of
money into huge ones.
The higher the bets in one round, the higher the long-term RTP of your
strategy (it effectively minimizes the house advatange).
In case of playing just for the sake of it, you should look for games with
high variance, place smaller bets and settle for a few strokes of luck. In
essence, you need to strike a balance between the time you want to play
and your strategys RTP.