Calculate slot machine game multiplier
I'm developing a slot machine game with 5 slots, each slot has 6 options (pear, lemon, ..., etc.).
Each spin, 5 random values get generated, one for each slot, making the slots spin to the option bound to their random number. When 3 or more consecutive numbers get generated in a spin eg.: (12444 or 42223 or 11111) the player "wins" the spin.
The won amount should be calculated depending on the number of consecutive equal numbers in a won spin, the amount the player bet that spin, and the value of the consecutive numbers (1 should be worth less than 6).
See included image for an example win chart, in short the question would be: how can I calculate the multiplier for each option (eg. 25* 5* in the image) which would result in a +-48% chance of making a profit on the machine?
gambling
asked Jan 3 at 21:24
Bram
1
New contributor
Bram is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
add a comment |
I'm developing a slot machine game with 5 slots, each slot has 6 options (pear, lemon, ..., etc.).
Each spin, 5 random values get generated, one for each slot, making the slots spin to the option bound to their random number. When 3 or more consecutive numbers get generated in a spin eg.: (12444 or 42223 or 11111) the player "wins" the spin.
The won amount should be calculated depending on the number of consecutive equal numbers in a won spin, the amount the player bet that spin, and the value of the consecutive numbers (1 should be worth less than 6).
See included image for an example win chart, in short the question would be: how can I calculate the multiplier for each option (eg. 25* 5* in the image) which would result in a +-48% chance of making a profit on the machine?
gambling
asked Jan 3 at 21:24
Bram
1
New contributor
Bram is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
add a comment |
I'm developing a slot machine game with 5 slots, each slot has 6 options (pear, lemon, ..., etc.).
Each spin, 5 random values get generated, one for each slot, making the slots spin to the option bound to their random number. When 3 or more consecutive numbers get generated in a spin eg.: (12444 or 42223 or 11111) the player "wins" the spin.
The won amount should be calculated depending on the number of consecutive equal numbers in a won spin, the amount the player bet that spin, and the value of the consecutive numbers (1 should be worth less than 6).
See included image for an example win chart, in short the question would be: how can I calculate the multiplier for each option (eg. 25* 5* in the image) which would result in a +-48% chance of making a profit on the machine?
gambling
asked Jan 3 at 21:24
Bram
1
New contributor
Bram is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
I'm developing a slot machine game with 5 slots, each slot has 6 options (pear, lemon, ..., etc.).
Each spin, 5 random values get generated, one for each slot, making the slots spin to the option bound to their random number. When 3 or more consecutive numbers get generated in a spin eg.: (12444 or 42223 or 11111) the player "wins" the spin.
The won amount should be calculated depending on the number of consecutive equal numbers in a won spin, the amount the player bet that spin, and the value of the consecutive numbers (1 should be worth less than 6).
See included image for an example win chart, in short the question would be: how can I calculate the multiplier for each option (eg. 25* 5* in the image) which would result in a +-48% chance of making a profit on the machine?
gambling
gambling
asked Jan 3 at 21:24
Bram
1
New contributor
Bram is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked Jan 3 at 21:24
Bram
1
New contributor
Bram is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked Jan 3 at 21:24
Bram
1
New contributor
Bram is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked Jan 3 at 21:24
Bram
1
asked Jan 3 at 21:24
Bram
1
1
New contributor
Bram is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
New contributor
Bram is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
Bram is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
add a comment |
add a comment |
1 Answer
1
active
oldest
votes
There aren't exactly nice formulas for these things; you just have to use inclusion/exclusion.
If all six symbols are equally likely, the chance of getting all five the same is the chance that the left symbol matches each of the subsequent ones,
$(1/6)^4 = 1/1296$.
The chance of getting exactly four in a row is the chance of getting the first four in a row, plus the chance of getting the last four in a row, minus twice the chance of getting all five in a row (since this is counted twice, once in each case). So that's
$2(1/6)^3 - 2(1/6)^4 = 5/648$
The chance of getting three in a row can be calculated similarly with an uglier expression.
Then you just pick numbers to make the probability come out to what you want; there are lots of potential solutions.
That said, you probably want to optimize the expected value rather than the chance of winning, assuming the payout is higher for four in a row than for three in a row.
answered Jan 3 at 22:04
Daniel McLaury
15.6k32977
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
});
}
});
Bram is a new contributor. Be nice, and check out our Code of Conduct.
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%2f3061016%2fcalculate-slot-machine-game-multiplier%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
There aren't exactly nice formulas for these things; you just have to use inclusion/exclusion.
If all six symbols are equally likely, the chance of getting all five the same is the chance that the left symbol matches each of the subsequent ones,
$(1/6)^4 = 1/1296$.
The chance of getting exactly four in a row is the chance of getting the first four in a row, plus the chance of getting the last four in a row, minus twice the chance of getting all five in a row (since this is counted twice, once in each case). So that's
$2(1/6)^3 - 2(1/6)^4 = 5/648$
The chance of getting three in a row can be calculated similarly with an uglier expression.
Then you just pick numbers to make the probability come out to what you want; there are lots of potential solutions.
That said, you probably want to optimize the expected value rather than the chance of winning, assuming the payout is higher for four in a row than for three in a row.
answered Jan 3 at 22:04
Daniel McLaury
15.6k32977
add a comment |
There aren't exactly nice formulas for these things; you just have to use inclusion/exclusion.
If all six symbols are equally likely, the chance of getting all five the same is the chance that the left symbol matches each of the subsequent ones,
$(1/6)^4 = 1/1296$.
The chance of getting exactly four in a row is the chance of getting the first four in a row, plus the chance of getting the last four in a row, minus twice the chance of getting all five in a row (since this is counted twice, once in each case). So that's
$2(1/6)^3 - 2(1/6)^4 = 5/648$
The chance of getting three in a row can be calculated similarly with an uglier expression.
Then you just pick numbers to make the probability come out to what you want; there are lots of potential solutions.
That said, you probably want to optimize the expected value rather than the chance of winning, assuming the payout is higher for four in a row than for three in a row.
answered Jan 3 at 22:04
Daniel McLaury
15.6k32977
add a comment |
There aren't exactly nice formulas for these things; you just have to use inclusion/exclusion.
If all six symbols are equally likely, the chance of getting all five the same is the chance that the left symbol matches each of the subsequent ones,
$(1/6)^4 = 1/1296$.
The chance of getting exactly four in a row is the chance of getting the first four in a row, plus the chance of getting the last four in a row, minus twice the chance of getting all five in a row (since this is counted twice, once in each case). So that's
$2(1/6)^3 - 2(1/6)^4 = 5/648$
The chance of getting three in a row can be calculated similarly with an uglier expression.
Then you just pick numbers to make the probability come out to what you want; there are lots of potential solutions.
That said, you probably want to optimize the expected value rather than the chance of winning, assuming the payout is higher for four in a row than for three in a row.
answered Jan 3 at 22:04
Daniel McLaury
15.6k32977
There aren't exactly nice formulas for these things; you just have to use inclusion/exclusion.
If all six symbols are equally likely, the chance of getting all five the same is the chance that the left symbol matches each of the subsequent ones,
$(1/6)^4 = 1/1296$.
The chance of getting exactly four in a row is the chance of getting the first four in a row, plus the chance of getting the last four in a row, minus twice the chance of getting all five in a row (since this is counted twice, once in each case). So that's
$2(1/6)^3 - 2(1/6)^4 = 5/648$
The chance of getting three in a row can be calculated similarly with an uglier expression.
Then you just pick numbers to make the probability come out to what you want; there are lots of potential solutions.
That said, you probably want to optimize the expected value rather than the chance of winning, assuming the payout is higher for four in a row than for three in a row.
answered Jan 3 at 22:04
Daniel McLaury
15.6k32977
answered Jan 3 at 22:04
Daniel McLaury
15.6k32977
answered Jan 3 at 22:04
Daniel McLaury
15.6k32977
answered Jan 3 at 22:04
Daniel McLaury
15.6k32977
15.6k32977
add a comment |
add a comment |
Bram is a new contributor. Be nice, and check out our Code of Conduct.
Bram is a new contributor. Be nice, and check out our Code of Conduct.
Bram is a new contributor. Be nice, and check out our Code of Conduct.
Bram is a new contributor. Be nice, and check out our Code of Conduct.
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.
Some of your past answers have not been well-received, and you're in danger of being blocked from answering.
Please pay close attention to the following guidance:
- 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.
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%2f3061016%2fcalculate-slot-machine-game-multiplier%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
