FIRSTLY - DO NOT LOTTO. That is the best advice I can give. However, if you'd like to read into the maths, please continue. I am currently studying business at university, however, I do have some experience in Mathematical Methods and Probability. I may have made some mistakes so please correct me if I am wrong. Lottery Information The lottery is a vicious place for builders and residents (or higher!) to loose thousands and thousands of Ecodollars. If I were to write a personal guide, it would be to avoid lotto completely because in the long run you always loose out (Statistically). 1 Ticket costs $1,000 1 Ticket adds $850 to the pot 10 Tickets cost $10,000 10 Tickets add $8,500 You get the idea, for every ticket purchased, $150 is swallowed up by the lotto monster's void-like stomach. That's not much right? But what if 100 tickets are purchased, $15,000 has literally vanished. Buying 1 ticket out of these 100 costs you $1,000 and gives you a 1% chance of winning $85,000. That's not bad right? If you bought 10 tickets, that costs you $10,000 but gives a 10% chance of winning $85,000. You may think it's better to buy more tickets? Actually no, read on. Statistics and Mathematics (That boring stuff!) Lets start with profit ratios (Assuming you're the only one playing): - I buy 1 ticket, this adds $850 to the pot, and gives me a 100% chance of winning $150 Loss (0.85 ratio) - I buy 10 tickets, this adds $8,500 to the pot, and still have 100% chance of winning because of solo-lotto. $1,500 Loss (Still 0.85 ratio but greater loss, due to tax) So that's playing alone, obviously you're going to win. Yet with a 100% win chance, you only have an 85% return. Lets add a few more players. Situation 1 - Player A buys one ticket, and I buy one ticket. This adds $1700 to the pot. - I have a 50% chance of winning $1,700. Yet I spent $1,000 to enter. This gives me a 50% chance of a 170% return. If you did this 100 times, statistically you would spend $100,000 and win $85,000. Loosing a total of $15,000. Again statistically speaking, RNG does take affect! Situation 2 - Player A buys 9 tickets, and I buy one ticket. This adds $8,500 to the pot. - I have a 10% chance of winning $8,500. Yet I spent $1,000 to enter. This gives me a 10% chance of a 850% return ($7,500 profit). Again, if you did this 100 times, statistically you would spend $100,000 yet win $85,000. Loosing a total of $15,000. The statistics are exactly the same, assuming you stick to 1 ticket. Situation 3 - Player A buys 20 tickets, Player B buys 9 tickets, and I buy one ticket. This adds $25,500 to the pot. - I have a 1/30 chance of winning (3.33% recurring, lets stick to fractions here). I spent $1,000 to enter. This gives me a 1/30 chance of a whopping 2550% return (25.5x your investment). If this happened 100 times, statistically you would spend $100,000 yet win $85,000. Again loosing a total of $15,000. Do you see the pattern? So all these situations involve X total tickets, with you holding 1. In the long run, you loose 15% for buying 1 ticket. If there's 1000 tickets, or 10 tickets, your return/profit ratio is the same. But if I buy more tickets, am I better off? Lets find out: Situation 1 - Player A buys 10 tickets, I decide to buy 20 tickets to snipe! This adds $25,500 to the pot. - But this time, I have a 2/3 chance of wining (66.66% recurring, again fractions are preferred). So great, I'm going to win more times in the long run! - Yet... $17,000 of the jackpot is your own money (After tax), and you spent $20,000 on tickets. So you're actually only profiting $5,500 per win. Spending $20,000 for a 2/3 chance of winning $5,500? Not worth it. - If this happened 100 times, I'd be spending $2,000,000, but statistically only winning $1,700,000. That's a grand total loss of $300,000, compared to the 1 ticket - $15,000 loss over 100 games. Still an 85% loss. Situation 2 - Many players buy tickets, 200 tickets actually. I buy 100 tickets to snipe the lotto, a risky move. This results in a total of $255,000 in the pot. A big jackpot. - I now have a 1/3 chance of winning (33.33% recurring, you get the percentages now). It's risky, but a decent chance. - I've spent $100,000 for tickets in this lotto. Winning would give me $255,000 but the profit itself would only be $155,000 because of the money I spent. $100,000 for a 1/3 chance of $155,000? Not worth it! - If this again happened 100 times, I'd be spending a huge $10,000,000 but statistically only winning $8,500,000. That's a $1,500,000 loss. 85% return. Situation 3 - Many players buy tickets again, this time 90 tickets. I buy 10 tickets to give myself a decent chance. This results in $85,000 in the pot. - I have a 10% chance of winning - I spent $10,000. Winning gives me $85,000, yet $75,000 profit. - If this happens 100 times. Statistically I'd spend $1,000,000. and gain $850,000. A loss of $150,000 (85% return). Now that we have gone through a tedious amount of calculations and statistics, it's quite obvious that with each lotto, the return is 85% (Tax is reduced to 85% of investment also!) Because no ticket has a greater probability than another, tax is the only contributor to profit, or rather loss. Without tax, your profit ratio over an infinite amount of games would hit 100% (Neither loss nor win). So when I buy 1 ticket, no matter how many tickets are already in the pot, I will only loose $15,000 (Statistically) per 100 games. If I were to buy 100 tickets, no matter how many tickets are already in the pot, I will loose $1,500,000 (Statistically) per 100 games. I would suggest, to minimize loosing, that you purchase 1 ticket per lotto (If you must play!). As this reduces the amount of money you will loose in the long term. As the statistics show, you will eventually loose out. But that does not mean you cannot be extremely lucky and win $1,000,000 with a single ticket. Or snipe 10 lotto's in a row successfully. That is all possible, but the lotto gods will eventually catch up to you, and you will eventually loose, whether that is in your next game, or in a thousand games. The most profitable option is to not play, the second best option is to only invest 1 ticket per lotto, this way you lose LESS of your money, but still have the same returns as dropping 100 tickets. Here are some photos: The longer you play, the more likely you will hit that 15% loss. Lotto is in ECC to reduce inflation, hence the tax. Yet overall you'll lose out. "Sniping" and buying at the "right time" really has no affect on your own returns, it DOES have affect on other players though, they may want to add more tickets if you add some, etc. But if you have 1000 tickets or 1 ticket, at the end of the day you'll get 85% back (Over many, many repeat trials). Thanks for reading
Although I give you props for your hard work/number crunching @obblebobble, there is one method that beats all others: Spoiler Don't Play.
"If I were to write a personal guide, it would be to avoid lotto completely because in the long run you always loose out (Statistically)." I stated that early on, of course that's the best method yes.
You see, statistically this is correct, but, lotto isn't run on statistics. Some people are positive by a lot, while others are negative. It all depends on your timing, luck, and how many ticks you buy. Some of it is down to statistics, but most times, something unpredictable happens.
To quote jamie... Source: http://www.ecocitycraft.com/forum/threads/suggestion-lotto.116195/#post-624828 Math is wonderful. Math is useful. Even if lotto isn't, math is. Math will never disappoint you nor make you incredibly happy lotto addict. :x3:
Thank-you for your posts. No there is no real skill involved as it is all luck basically, what I am saying is that in the long run (According to statistics) you will be out of pocket, everyone will (Eventually). Yes Exilenela, this was based on statistics only, of course RNG plays a major part and can cause you to profit millions. There's always something unpredictable happening, but as I said, due to the 15% tax per ticket, everyone in the long term is out of pocket. The more games you play, the more likely your results are to match statistics. Playing 1 game alone can have crazy results, yet if you play 100,000 games, your stats are likely to be near the 15% loss margin. Thanks for your post though
Um, one question. You give plenty of examples to simply make the point that the return is always 85%. Then you say the best method is to put one ticket in per round. I don't agree, as there is no best method to lotto. You even state it with your math: there is no best method, on average you lose 15% of what you put in.
I stated the best method is to not play. The second best method would be to invest only 1 ticket, because yes, in all situations it's a 15% loss. But 15% of $1,000 is lesser than any higher amount of tickets. 1 ticket, and 100 tickets are equally profitable percentage wise, numbers wise the 1 ticket reduces your loosing.
Yup Lotto is a dangerous place, one of it's major reasons is to take away half a million ECD in tax per day.
I'd like to point out that most players only lotto to win a game, not in the long run. So this may not be important to the average lottoer
Yes that is true, I'm just writing this to inform others that there is an eventual decline in profit.
What your statistics missed I believe is that the only winner in the lotto is the server - it is designed that way. It is a great way for some to donate to the server - I personally prefer to do it thru donating for every rank I can. The big winners that have actually contributed to the well being of the server have been few and far between in my time here - @Riggs316 is one such player that won big and has proven to be a huge asset to the community. Unfortunately, a high percentage of big winners tend to get hooked and then turn to scamming or hacking to keep up the addiction. I of course will not mention any names for these examples If you can't afford to lose - Don't play lotto (and may I recommend everyone stop loaning money or expensive tools to lotto addicts as well?)
Thanks for your post. That is true yes, unfortunately it is a form of gambling, which does tend to be very addictive. Similar to players loosing thousands on in-game casinos. Thanks for your words of advice!
Since this thread is about the fun math behind lotto, this might actually fit. When others are bored and think about lotto, they buy tickets. When 314 is bored and thinks about lotto, he creates a Delphi program to give nice statistics about lotto. Spoiler: Calculation examples The program calculates how many tickets you can buy at max to still profit from the lotto in case you win. ("Own tickets") Next goal: I want to add the percentage of winning with buying the maximum profitable amount. So, I guess that goes in hand with your primary suggestion to not lotto at all. I agree to that but still think about the math. The best way IMO. EDIT: Mh, apparently there is another part where we see the 85% chance. Simply because of the fact that you can only own a maximum of 85% of the tickets if you still want to make profit. (Or no profit at all at 85%).
Very interesting program, thanks for your post Yeah 85% is the magic number in ECC Lotto. Your program calculates the amount you can buy without loosing, however the number is unrealistic. Spending $192,000 for an 84.956% chance of winning $100. Not worth the risk, although I haven't calculated what is the "best" or "least worst" method of sniping, if there even is one. This program would be great during crazy lotto's when there is a prize greater than money at the end, such as spawn eggs or being the SG boss.
