Home
Forums
New posts
What's new
New posts
Latest activity
Log in
Register
What's new
New posts
Menu
Log in
Register
Install the app
Install
Home
Forums
Other Topics
Off topic discussion
Aunt sues nephew over a conjoined lottery ticket
JavaScript is disabled. For a better experience, please enable JavaScript in your browser before proceeding.
You are using an out of date browser. It may not display this or other websites correctly.
You should upgrade or use an
alternative browser
.
Reply to thread
Message
<blockquote data-quote="Built to Fade" data-source="post: 1211361" data-attributes="member: 9905"><p><strong>Calculating Lottery Odds & Their Expected Value (Datasheet)</strong></p><p></p><p></p><p></p><p></p><p></p><p></p><p><span style="font-size: 18px"><strong>[NOTE: This post shows some math. It'll take some time to read. If there's enough interest, I may do the mathematics of loans in a future post.]</strong></span></p><p></p><p><span style="font-size: 22px">I only buy lottery tickets when the expected value of return is zero or positive.</span></p><p>The formula for expected return in lotteries is <a href="https://ibb.co/hT2jPe" target="_blank"><img src="https://preview.ibb.co/iN2UqK/EXPECTED_RETURN_OF_LOTTERY_JACKPOT_WIN.gif" alt="" class="fr-fic fr-dii fr-draggable " style="" /></a></p><p></p><p>To calculate the required jackpot for zero or positive expected value, use the below formula: </p><p></p><p><a href="https://ibb.co/ixM0xz" target="_blank"><img src="https://preview.ibb.co/hRU9qK/EXPECTED_RETURN_MINIMUM_LOTTERY_JACKPOT_WIN_FOR_POSITIVE_RETURN_1.gif" alt="" class="fr-fic fr-dii fr-draggable " style="" /></a>, then rearrange to get <a href="https://ibb.co/frPaVK" target="_blank"><img src="https://preview.ibb.co/dRW0xz/EXPECTED_RETURN_MINIMUM_LOTTERY_JACKPOT_WIN_FOR_POSITIVE_RETURN_2.gif" alt="" class="fr-fic fr-dii fr-draggable " style="" /></a></p><p></p><p>Therefore, the formula is <a href="https://ibb.co/iigNAK" target="_blank"><img src="https://preview.ibb.co/kH1dje/EXPECTED_RETURN_MINIMUM_LOTTERY_JACKPOT_WIN_FOR_POSITIVE_RETURN.gif" alt="" class="fr-fic fr-dii fr-draggable " style="" /></a></p><p></p><p>These are maths of a majority of lottery draws (combinations):</p><p><img src="https://blog.udemy.com/wp-content/uploads/2014/03/Capture2.png" alt="" class="fr-fic fr-dii fr-draggable " style="" /></p><p>Where:</p><p><strong>n</strong> <em>represents the amount of numbers in the barrel</em> &</p><p><strong>r</strong> <em>represents the amount of numbers drawn from the barrel</em></p><p></p><p><strong><u>Example of a lottery using 45 numbers & drawing 7 numbers:</u></strong></p><p>45<strong>C</strong>7</p><p>= (45!)/(7!x38!)</p><p>= (45x44x43x42x41x40x39)/(7x6x5x4x3x2x1)</p><p>= 3x44x43x41x5x39 [42/(7x6) cancels out, 45/(5x3) = 3 & 40/(4x2) = 5]</p><p>= 45379620</p><p>Therefore, in a 45 number lottery, <strong>the total amount of 7 number combinations is <u>45 379 620</u>.</strong></p><p><strong>To have positive expected value at</strong>, let's say, <strong>$1.30</strong> (one game), <strong><u>the jackpot must be $58 993 504.71 or greater.</u></strong></p><p>1.3 x 45379619 = 58993504.7 </p><p></p><p><span style="font-size: 22px">Lottery jackpots only become massive when the amount is significantly higher than the total number of combinations. From the previous example, a >$90 million jackpot is massive. Lotteries with jackpots reaching $200 to >$500 million would probably have it set up to have over 100s of millions of drawn number combinations.</span></p><p></p><p><strong><u>Combinations of Powerball (US), a lottery utilising the "extra number":</u></strong></p><p>69<strong>C</strong>5 x 26 (the 26 are the "extra number" segment)</p><p>= (69!)/(5!x64!) x 26</p><p>= (69x68x67x66x65)/(5x4x3x2x1) x 26</p><p>= (69x17x67x11x13) x 26 [68/4 = 17, 66/(3x2) = 11, 65/5 = 13]</p><p>= 11238513 x 26</p><p>= 292201338</p><p>Therefore, from 69 regular numbers & 26 "Powerballs", <strong>the total amount of 7 number+Powerball combinations is <u>292 201 338</u>.</strong> There are <u>11 238 513 seven number combinations when the "Powerball" is not included</u>.</p><p>When calculating the lottery odds, calculate the combination component first, then multiply that number of combinations by the "extra number" if the lottery uses one.</p><p><strong>To have positive expected value at</strong>, let's say, <strong>$2</strong> (one game), <strong><u>the <span style="color: #FF0000">pre-tax jackpot</span> must be $584 402 674.01 or greater.</u></strong></p><p>2 x 292201337 = 584402674</p><p></p><p><span style="font-size: 22px"><span style="color: #0000FF"><strong>If you follow the maths of your local lotteries <a href="https://www.random.org/quick-pick/" target="_blank">by substituting the relevant numbers in the formula</a> you'll know when to buy a ticket, which would either be 3-5 times a year or never again since lotteries have an inherent negative expected value.</strong></span></span></p><p><span style="font-size: 22px"></span></p><p><span style="font-size: 22px">PS: The principles of expected value apply to all gambling & investments & is linked to various types of returns.</span></p></blockquote><p></p>
[QUOTE="Built to Fade, post: 1211361, member: 9905"] [b]Calculating Lottery Odds & Their Expected Value (Datasheet)[/b] [SIZE=5][b][NOTE: This post shows some math. It'll take some time to read. If there's enough interest, I may do the mathematics of loans in a future post.][/b][/SIZE] [SIZE=6]I only buy lottery tickets when the expected value of return is zero or positive.[/SIZE] The formula for expected return in lotteries is [url=https://ibb.co/hT2jPe][img]https://preview.ibb.co/iN2UqK/EXPECTED_RETURN_OF_LOTTERY_JACKPOT_WIN.gif[/img][/url] To calculate the required jackpot for zero or positive expected value, use the below formula: [url=https://ibb.co/ixM0xz][img]https://preview.ibb.co/hRU9qK/EXPECTED_RETURN_MINIMUM_LOTTERY_JACKPOT_WIN_FOR_POSITIVE_RETURN_1.gif[/img][/url], then rearrange to get [url=https://ibb.co/frPaVK][img]https://preview.ibb.co/dRW0xz/EXPECTED_RETURN_MINIMUM_LOTTERY_JACKPOT_WIN_FOR_POSITIVE_RETURN_2.gif[/img][/url] Therefore, the formula is [url=https://ibb.co/iigNAK][img]https://preview.ibb.co/kH1dje/EXPECTED_RETURN_MINIMUM_LOTTERY_JACKPOT_WIN_FOR_POSITIVE_RETURN.gif[/img][/url] These are maths of a majority of lottery draws (combinations): [img]https://blog.udemy.com/wp-content/uploads/2014/03/Capture2.png[/img] Where: [b]n[/b] [i]represents the amount of numbers in the barrel[/i] & [b]r[/b] [i]represents the amount of numbers drawn from the barrel[/i] [b][u]Example of a lottery using 45 numbers & drawing 7 numbers:[/u][/b] 45[b]C[/b]7 = (45!)/(7!x38!) = (45x44x43x42x41x40x39)/(7x6x5x4x3x2x1) = 3x44x43x41x5x39 [42/(7x6) cancels out, 45/(5x3) = 3 & 40/(4x2) = 5] = 45379620 Therefore, in a 45 number lottery, [b]the total amount of 7 number combinations is [u]45 379 620[/u].[/b] [b]To have positive expected value at[/b], let's say, [b]$1.30[/b] (one game), [b][u]the jackpot must be $58 993 504.71 or greater.[/u][/b] 1.3 x 45379619 = 58993504.7 [SIZE=6]Lottery jackpots only become massive when the amount is significantly higher than the total number of combinations. From the previous example, a >$90 million jackpot is massive. Lotteries with jackpots reaching $200 to >$500 million would probably have it set up to have over 100s of millions of drawn number combinations.[/SIZE] [b][u]Combinations of Powerball (US), a lottery utilising the "extra number":[/u][/b] 69[b]C[/b]5 x 26 (the 26 are the "extra number" segment) = (69!)/(5!x64!) x 26 = (69x68x67x66x65)/(5x4x3x2x1) x 26 = (69x17x67x11x13) x 26 [68/4 = 17, 66/(3x2) = 11, 65/5 = 13] = 11238513 x 26 = 292201338 Therefore, from 69 regular numbers & 26 "Powerballs", [b]the total amount of 7 number+Powerball combinations is [u]292 201 338[/u].[/b] There are [u]11 238 513 seven number combinations when the "Powerball" is not included[/u]. When calculating the lottery odds, calculate the combination component first, then multiply that number of combinations by the "extra number" if the lottery uses one. [b]To have positive expected value at[/b], let's say, [b]$2[/b] (one game), [b][u]the [color=#FF0000]pre-tax jackpot[/color] must be $584 402 674.01 or greater.[/u][/b] 2 x 292201337 = 584402674 [SIZE=6][color=#0000FF][b]If you follow the maths of your local lotteries [url=https://www.random.org/quick-pick/]by substituting the relevant numbers in the formula[/url] you'll know when to buy a ticket, which would either be 3-5 times a year or never again since lotteries have an inherent negative expected value.[/b][/color] PS: The principles of expected value apply to all gambling & investments & is linked to various types of returns.[/SIZE] [/QUOTE]
Insert quotes…
Verification
Post reply
Home
Forums
Other Topics
Off topic discussion
Aunt sues nephew over a conjoined lottery ticket
Top
