permutations vs combinations on slot machines with repeating elements on each reel
$begingroup$
For a slot machine with 5 reels where there are repeated elements on each of the reel.
Example:
Reel 1 [ 1, 1, 2, 1, 3, 5, 6 ]
Reel 2 [ 1, 2, 3, 4, 5, 5 ]
Reel 3 [ 2, 2, 3, 2, 4 ]
Reel 4 [ 1, 2, 3, 4, 5 ]
Reel 5 [ 1, 2, 3, 4, 5 ]
Are all possibilities (7 x 6 x 5 x 5 x 5) called permutations?
Given, that only one element comes from each of the reels to make a combination. In normal mathematics, is 1-4-2-5-5 the same permutation as 1-4-2-5-5 IF the only difference is the first 1 are on different positions on the first reel?
Please note that a different 1 could effect the other "paylines" such as a diagonal payline vs the main horizontal one. Personally, I believe they are different. I just want to verify my assumptions.
"Pay lines are lines on which the right combination of icons has to appear for a player to win rewards. A pay line can be defined as the line that runs through the reels, intersecting with a symbol on each reel. Different games have different numbers of pay lines – when a particular slots game is described, one of the first things mentioned is how many pay lines it has. Pay lines can vary in number from one onwards – most have less than ten, some less than fifty, and a few less than hundred. Early slot machines all had horizontal pay lines but modern slot games can have pay lines that are zig-zag or diagonal as well as horizontal. Some games even have combinations of different types of pay lines, such as those with three horizontal pay lines and two diagonal ones. The number of pay lines in a particular slot machine game is related to the number of coins that are accepted."
probability combinatorics
asked Jul 5 '15 at 23:33
Rick ApichairukRick Apichairuk
12
$endgroup$
add a comment |
$begingroup$
For a slot machine with 5 reels where there are repeated elements on each of the reel.
Example:
Reel 1 [ 1, 1, 2, 1, 3, 5, 6 ]
Reel 2 [ 1, 2, 3, 4, 5, 5 ]
Reel 3 [ 2, 2, 3, 2, 4 ]
Reel 4 [ 1, 2, 3, 4, 5 ]
Reel 5 [ 1, 2, 3, 4, 5 ]
Are all possibilities (7 x 6 x 5 x 5 x 5) called permutations?
Given, that only one element comes from each of the reels to make a combination. In normal mathematics, is 1-4-2-5-5 the same permutation as 1-4-2-5-5 IF the only difference is the first 1 are on different positions on the first reel?
Please note that a different 1 could effect the other "paylines" such as a diagonal payline vs the main horizontal one. Personally, I believe they are different. I just want to verify my assumptions.
"Pay lines are lines on which the right combination of icons has to appear for a player to win rewards. A pay line can be defined as the line that runs through the reels, intersecting with a symbol on each reel. Different games have different numbers of pay lines – when a particular slots game is described, one of the first things mentioned is how many pay lines it has. Pay lines can vary in number from one onwards – most have less than ten, some less than fifty, and a few less than hundred. Early slot machines all had horizontal pay lines but modern slot games can have pay lines that are zig-zag or diagonal as well as horizontal. Some games even have combinations of different types of pay lines, such as those with three horizontal pay lines and two diagonal ones. The number of pay lines in a particular slot machine game is related to the number of coins that are accepted."
probability combinatorics
asked Jul 5 '15 at 23:33
Rick ApichairukRick Apichairuk
12
$endgroup$
$begingroup$
You said getting different ones from the same reel could affect the paylines. Will it always affect the paylines?
$endgroup$
– Amy B
Jul 5 '15 at 23:51
$begingroup$
Yes, because position matters.
$endgroup$
– Rick Apichairuk
Jul 5 '15 at 23:54
add a comment |
$begingroup$
For a slot machine with 5 reels where there are repeated elements on each of the reel.
Example:
Reel 1 [ 1, 1, 2, 1, 3, 5, 6 ]
Reel 2 [ 1, 2, 3, 4, 5, 5 ]
Reel 3 [ 2, 2, 3, 2, 4 ]
Reel 4 [ 1, 2, 3, 4, 5 ]
Reel 5 [ 1, 2, 3, 4, 5 ]
Are all possibilities (7 x 6 x 5 x 5 x 5) called permutations?
Given, that only one element comes from each of the reels to make a combination. In normal mathematics, is 1-4-2-5-5 the same permutation as 1-4-2-5-5 IF the only difference is the first 1 are on different positions on the first reel?
Please note that a different 1 could effect the other "paylines" such as a diagonal payline vs the main horizontal one. Personally, I believe they are different. I just want to verify my assumptions.
"Pay lines are lines on which the right combination of icons has to appear for a player to win rewards. A pay line can be defined as the line that runs through the reels, intersecting with a symbol on each reel. Different games have different numbers of pay lines – when a particular slots game is described, one of the first things mentioned is how many pay lines it has. Pay lines can vary in number from one onwards – most have less than ten, some less than fifty, and a few less than hundred. Early slot machines all had horizontal pay lines but modern slot games can have pay lines that are zig-zag or diagonal as well as horizontal. Some games even have combinations of different types of pay lines, such as those with three horizontal pay lines and two diagonal ones. The number of pay lines in a particular slot machine game is related to the number of coins that are accepted."
probability combinatorics
asked Jul 5 '15 at 23:33
Rick ApichairukRick Apichairuk
12
$endgroup$
For a slot machine with 5 reels where there are repeated elements on each of the reel.
Example:
Reel 1 [ 1, 1, 2, 1, 3, 5, 6 ]
Reel 2 [ 1, 2, 3, 4, 5, 5 ]
Reel 3 [ 2, 2, 3, 2, 4 ]
Reel 4 [ 1, 2, 3, 4, 5 ]
Reel 5 [ 1, 2, 3, 4, 5 ]
Are all possibilities (7 x 6 x 5 x 5 x 5) called permutations?
Given, that only one element comes from each of the reels to make a combination. In normal mathematics, is 1-4-2-5-5 the same permutation as 1-4-2-5-5 IF the only difference is the first 1 are on different positions on the first reel?
Please note that a different 1 could effect the other "paylines" such as a diagonal payline vs the main horizontal one. Personally, I believe they are different. I just want to verify my assumptions.
"Pay lines are lines on which the right combination of icons has to appear for a player to win rewards. A pay line can be defined as the line that runs through the reels, intersecting with a symbol on each reel. Different games have different numbers of pay lines – when a particular slots game is described, one of the first things mentioned is how many pay lines it has. Pay lines can vary in number from one onwards – most have less than ten, some less than fifty, and a few less than hundred. Early slot machines all had horizontal pay lines but modern slot games can have pay lines that are zig-zag or diagonal as well as horizontal. Some games even have combinations of different types of pay lines, such as those with three horizontal pay lines and two diagonal ones. The number of pay lines in a particular slot machine game is related to the number of coins that are accepted."
probability combinatorics
probability combinatorics
asked Jul 5 '15 at 23:33
Rick ApichairukRick Apichairuk
12
asked Jul 5 '15 at 23:33
Rick ApichairukRick Apichairuk
12
edited Jul 5 '15 at 23:58
Rick Apichairuk
asked Jul 5 '15 at 23:33
Rick ApichairukRick Apichairuk
12
asked Jul 5 '15 at 23:33
Rick ApichairukRick Apichairuk
12
asked Jul 5 '15 at 23:33
Rick ApichairukRick Apichairuk
12
12
$begingroup$
You said getting different ones from the same reel could affect the paylines. Will it always affect the paylines?
$endgroup$
– Amy B
Jul 5 '15 at 23:51
$begingroup$
Yes, because position matters.
$endgroup$
– Rick Apichairuk
Jul 5 '15 at 23:54
add a comment |
$begingroup$
You said getting different ones from the same reel could affect the paylines. Will it always affect the paylines?
$endgroup$
– Amy B
Jul 5 '15 at 23:51
$begingroup$
Yes, because position matters.
$endgroup$
– Rick Apichairuk
Jul 5 '15 at 23:54
$begingroup$
You said getting different ones from the same reel could affect the paylines. Will it always affect the paylines?
$endgroup$
– Amy B
Jul 5 '15 at 23:51
$begingroup$
You said getting different ones from the same reel could affect the paylines. Will it always affect the paylines?
$endgroup$
– Amy B
Jul 5 '15 at 23:51
$begingroup$
Yes, because position matters.
$endgroup$
– Rick Apichairuk
Jul 5 '15 at 23:54
$begingroup$
Yes, because position matters.
$endgroup$
– Rick Apichairuk
Jul 5 '15 at 23:54
add a comment |
1 Answer
1
active
oldest
votes
$begingroup$
Since each 1 is distinct on the first reel, you should probably label them 1a, 1b,1c. Once you label everything distinctly, it is easier to see that you are correct.
It is confusing to say 1-4-2-5-5 is different than 1-4-2-5-5.
It is clear that 1a-4-2-5-5 is different than 1b-4-2-5-5
answered Jul 5 '15 at 23:58
Amy BAmy B
43649
$endgroup$
$begingroup$
Are 1-4-2-5-5 and 5-5-1-4-2 considered to be the same combination?
$endgroup$
– Rick Apichairuk
Jul 6 '15 at 2:18
$begingroup$
Normally yes, but if the 1 means something different in different positions than you aren't working with combinations. If I pick out 5 numbers from a bag the order doesn't matter then those could be the same combination of numbers.
$endgroup$
– Amy B
Jul 6 '15 at 19:27
add a comment |
Your Answer
StackExchange.ifUsing("editor", function () {
return StackExchange.using("mathjaxEditing", function () {
StackExchange.MarkdownEditor.creationCallbacks.add(function (editor, postfix) {
StackExchange.mathjaxEditing.prepareWmdForMathJax(editor, postfix, [["$", "$"], ["\\(","\\)"]]);
});
});
}, "mathjax-editing");
StackExchange.ready(function() {
var channelOptions = {
tags: "".split(" "),
id: "69"
};
initTagRenderer("".split(" "), "".split(" "), channelOptions);
StackExchange.using("externalEditor", function() {
// Have to fire editor after snippets, if snippets enabled
if (StackExchange.settings.snippets.snippetsEnabled) {
StackExchange.using("snippets", function() {
createEditor();
});
}
else {
createEditor();
}
});
function createEditor() {
StackExchange.prepareEditor({
heartbeatType: 'answer',
autoActivateHeartbeat: false,
convertImagesToLinks: true,
noModals: true,
showLowRepImageUploadWarning: true,
reputationToPostImages: 10,
bindNavPrevention: true,
postfix: "",
imageUploader: {
brandingHtml: "Powered by u003ca class="icon-imgur-white" href="https://imgur.com/"u003eu003c/au003e",
contentPolicyHtml: "User contributions licensed under u003ca href="https://creativecommons.org/licenses/by-sa/3.0/"u003ecc by-sa 3.0 with attribution requiredu003c/au003e u003ca href="https://stackoverflow.com/legal/content-policy"u003e(content policy)u003c/au003e",
allowUrls: true
},
noCode: true, onDemand: true,
discardSelector: ".discard-answer"
,immediatelyShowMarkdownHelp:true
});
}
});
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f1350721%2fpermutations-vs-combinations-on-slot-machines-with-repeating-elements-on-each-re%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
Since each 1 is distinct on the first reel, you should probably label them 1a, 1b,1c. Once you label everything distinctly, it is easier to see that you are correct.
It is confusing to say 1-4-2-5-5 is different than 1-4-2-5-5.
It is clear that 1a-4-2-5-5 is different than 1b-4-2-5-5
answered Jul 5 '15 at 23:58
Amy BAmy B
43649
$endgroup$
$begingroup$
Are 1-4-2-5-5 and 5-5-1-4-2 considered to be the same combination?
$endgroup$
– Rick Apichairuk
Jul 6 '15 at 2:18
$begingroup$
Normally yes, but if the 1 means something different in different positions than you aren't working with combinations. If I pick out 5 numbers from a bag the order doesn't matter then those could be the same combination of numbers.
$endgroup$
– Amy B
Jul 6 '15 at 19:27
add a comment |
$begingroup$
Since each 1 is distinct on the first reel, you should probably label them 1a, 1b,1c. Once you label everything distinctly, it is easier to see that you are correct.
It is confusing to say 1-4-2-5-5 is different than 1-4-2-5-5.
It is clear that 1a-4-2-5-5 is different than 1b-4-2-5-5
answered Jul 5 '15 at 23:58
Amy BAmy B
43649
$endgroup$
$begingroup$
Are 1-4-2-5-5 and 5-5-1-4-2 considered to be the same combination?
$endgroup$
– Rick Apichairuk
Jul 6 '15 at 2:18
$begingroup$
Normally yes, but if the 1 means something different in different positions than you aren't working with combinations. If I pick out 5 numbers from a bag the order doesn't matter then those could be the same combination of numbers.
$endgroup$
– Amy B
Jul 6 '15 at 19:27
add a comment |
$begingroup$
Since each 1 is distinct on the first reel, you should probably label them 1a, 1b,1c. Once you label everything distinctly, it is easier to see that you are correct.
It is confusing to say 1-4-2-5-5 is different than 1-4-2-5-5.
It is clear that 1a-4-2-5-5 is different than 1b-4-2-5-5
answered Jul 5 '15 at 23:58
Amy BAmy B
43649
$endgroup$
Since each 1 is distinct on the first reel, you should probably label them 1a, 1b,1c. Once you label everything distinctly, it is easier to see that you are correct.
It is confusing to say 1-4-2-5-5 is different than 1-4-2-5-5.
It is clear that 1a-4-2-5-5 is different than 1b-4-2-5-5
answered Jul 5 '15 at 23:58
Amy BAmy B
43649
answered Jul 5 '15 at 23:58
Amy BAmy B
43649
answered Jul 5 '15 at 23:58
Amy BAmy B
43649
answered Jul 5 '15 at 23:58
Amy BAmy B
43649
43649
$begingroup$
Are 1-4-2-5-5 and 5-5-1-4-2 considered to be the same combination?
$endgroup$
– Rick Apichairuk
Jul 6 '15 at 2:18
$begingroup$
Normally yes, but if the 1 means something different in different positions than you aren't working with combinations. If I pick out 5 numbers from a bag the order doesn't matter then those could be the same combination of numbers.
$endgroup$
– Amy B
Jul 6 '15 at 19:27
add a comment |
$begingroup$
Are 1-4-2-5-5 and 5-5-1-4-2 considered to be the same combination?
$endgroup$
– Rick Apichairuk
Jul 6 '15 at 2:18
$begingroup$
Normally yes, but if the 1 means something different in different positions than you aren't working with combinations. If I pick out 5 numbers from a bag the order doesn't matter then those could be the same combination of numbers.
$endgroup$
– Amy B
Jul 6 '15 at 19:27
$begingroup$
Are 1-4-2-5-5 and 5-5-1-4-2 considered to be the same combination?
$endgroup$
– Rick Apichairuk
Jul 6 '15 at 2:18
$begingroup$
Are 1-4-2-5-5 and 5-5-1-4-2 considered to be the same combination?
$endgroup$
– Rick Apichairuk
Jul 6 '15 at 2:18
$begingroup$
Normally yes, but if the 1 means something different in different positions than you aren't working with combinations. If I pick out 5 numbers from a bag the order doesn't matter then those could be the same combination of numbers.
$endgroup$
– Amy B
Jul 6 '15 at 19:27
$begingroup$
Normally yes, but if the 1 means something different in different positions than you aren't working with combinations. If I pick out 5 numbers from a bag the order doesn't matter then those could be the same combination of numbers.
$endgroup$
– Amy B
Jul 6 '15 at 19:27
add a comment |
Thanks for contributing an answer to Mathematics Stack Exchange!
- Please be sure to answer the question. Provide details and share your research!
But avoid …
- Asking for help, clarification, or responding to other answers.
- Making statements based on opinion; back them up with references or personal experience.
Use MathJax to format equations. MathJax reference.
To learn more, see our tips on writing great answers.
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f1350721%2fpermutations-vs-combinations-on-slot-machines-with-repeating-elements-on-each-re%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
$begingroup$
You said getting different ones from the same reel could affect the paylines. Will it always affect the paylines?
$endgroup$
– Amy B
Jul 5 '15 at 23:51
$begingroup$
Yes, because position matters.
$endgroup$
– Rick Apichairuk
Jul 5 '15 at 23:54