question: How are my odds of winning the lottery impacted if I buy 10 tickets as opposed to 1 ticket?
comment: You're odds go up by a factor of 10, but it's such a minuscule amount to begin with it's still effectively 0. You go from a 0.0000003% chance of winning to a 0.000003%. For comparison your odds of being struck by lightning at some point in your life is about 0.03%. In other words you'd need to buy about 100,000 tickets before you have a better chance of winning the lottery than being stuck by lightning in your lifetime.
passages: The additive nature of this measure also comes in handy when weighing alternatives. For example, imagine that the surprisal of harm from a vaccination is 20 bits. If the surprisal of catching a disease without it is 16 bits, but the surprisal of harm from the disease if you catch it is 2 bits, then the surprisal of harm from NOT getting the vaccination is only 16+2=18 bits. Whether or not you decide to get the vaccination (e.g. the monetary cost of paying for it is not included in this discussion), you can in that way at least take responsibility for a decision informed to the fact that not getting the vaccination involves more than one bit of additional risk.
   This example can be used to illustrate the main guarantee of the chosen system (a 4-win if four of the 10 player’s numbers are drawn): Suppose the numbers 7,12,29, and 40 are drawn (these are shaded in the player's tickets), then the system guarantees at least one 4-win, by design. Indeed, it is easy to check that this is so. In fact, in this particular case, the system gives two 4-wins (in tickets 13 and 16), and it also gives seven 3-wins (these can be found in tickets 1,2,3,6,10,14, and 15).
   "Example: Participants are indifferent between receiving a lottery ticket offering a 1% chance at $200 and receiving $10 for sure. Additionally, people are indifferent between receiving a lottery ticket offering a 99% chance at $200 and receiving $188 for sure." 
  
  In line with diminishing sensitivity, the first hundredth of probability is worth $10, and the last hundredth is worth $12, but the 98 intermediate hundredths are worth only $178, or about $1.80 per hundredth. PT captures this pattern of differentially weighting (objective) probabilities subjectively with an S-shaped weighting function.
  
  Section::::Framing effects.
   The odds of winning can also be reduced by increasing the group from which numbers are drawn. In the SuperEnalotto of Italy, players must match 6 numbers out of 90. The chance of winning the jackpot is 1 in 622,614,630.
  
  Most lotteries give lesser prizes for matching just some of the winning numbers, with a lesser prize for fewer matches. Although none of these additional prizes affect the chances of winning the jackpot, they do improve the odds of winning something and therefore add a little to the value of the ticket.
  
  Section::::Scams and frauds.
   Actual payouts after a draw will vary to what payouts are advertised before a draw, depending on whether the jackpot is hit or not. Typically jackpot amounts that are not hit or paid out are then rolled over to the next draw. In this sense, typical RTP or returns to player percentages will vary with the size of the jackpot. It can happen that after several rollovers, a jackpot becomes that large that there is real 'positive RTP; with a lottery ticket, i.e. if you were to buy every single ticket you would make a profit after your ticket costs. This will of course also depend on your chances of sharing or not sharing the jackpot with another player, any taxes payable plus whether you are taking the cash or annuity option or not (as available).
   Many lotteries have a Powerball (or "bonus ball"). If the powerball is drawn from a pool of numbers different from the main lottery, the odds are multiplied by the number of powerballs. For example, in the 6 from 49 lottery, given 10 powerball numbers, then the odds of getting a score of 3 and the powerball would be 1 in 56.66 × 10, or 566.6 (the "probability" would be divided by 10, to give an exact value of formula_15). Another example of such a game is Mega Millions, albeit with different jackpot odds.
   In 2016, Rolf Dobelli presented a choice between two games of chance. In one, you have a one in 100 million chance of winning $10 million; in the other, you have a one in 10,000 chance of winning $10,000. It is more reasonable to choose the second game; but most people would choose the first. For this reason, jackpots in lotteries are growing.
   Prizes are awarded to players who match at least three of the six drawn numbers, with prizes increasing for matching more of the drawn numbers. All players who match all six drawn numbers win equal shares of the jackpot; the chance of doing so is 1 in 20,358,520. If four, five, or six balls are matched, the relevant prize is divided equally between all who match that many balls. If no player matches all six numbers, the jackpot is added to that of the next Lotto draw—a "Rollover".
   The solution is to buy a total of 14 tickets, in two sets of seven. One set of seven is every line of a Fano plane with the numbers 1-7, the other with 8-14, i.e.:
  
  1-2-5, 1-3-6, 1-4-7, 2-3-7, 2-4-6, 3-4-5, 5-6-7, 8-9-12, 8-10-13, 8-11-14, 9-10-14, 9-11-13, 10-11-12, 12-13-14.
   Mega Millions tickets bought with the Megaplier option, beginning September 12, 2010, automatically won $1 million (instead of $250,000) if the five white balls – but excluding the Mega Ball – are matched.
   Section::::Prizes and chance of winning.
  
  Overall odds of winning a prize are about 1 in 6.6, though the great majority of prizes consist of a free ticket for the next draw (a break-even scenario at best, not a win in the strictest sense).
  
  From the 2004 price change until September 18, 2013, this table was distributed thus:
  
  Before July 2010, if there was no winning ticket for a jackpot of $30 million or higher, the following prize structure was applied to all subsequent draws until the jackpot was won. This did not apply to bonus jackpots.
   BULLET::::- The odds of getting none of the 50 main balls but getting both lucky stars is approximately 1 in 115. This means that it is less likely than getting 2 main balls and one lucky star (1 in 49). However, there is no prize for only getting 2 lucky stars.
  
  BULLET::::- The figures for the estimated prize are just a guide, and the actual amount varies according to the total in the prize fund and the number of winners for each prize. (Estimated prizes as per reverse of UK payslip)
   In bonusball lotteries where the bonus ball is compulsory, the odds are often even lower. In the Mega Millions multi-state lottery in the United States, 5 numbers are drawn from a group of 75 and 1 number is drawn from a group of 15, and a player must match all 6 balls to win the jackpot prize. The chance of winning the jackpot is 1 in 258,890,850.
   where formula_11 is the number of balls in lottery, formula_12 is the number of balls in a single ticket, and formula_13 is the number of matching balls for a winning ticket.
  
  The generalisation of this formula is called the hypergeometric distribution.
  
  This gives the following results:
  
  When a bonus number is included, the adjusted odds are:
  
  Section::::Pick8-32 odds and calculations.
   High-probability condition: The median price paid to avoid a 99% chance of shock, $10, was substantially lower than the median price paid to avoid a 99% chance of cash penalty, $18.
  
  Results: Taken together, for the affect-rich electric shock, the size of the right-hand jump in the weighting function is about $10 ($19.86 - $10), but for the affect-poor cash penalty, the size of this jump is much smaller at $2 ($20 - $18). Again, we see that the weight of the 99% is smaller for the affect-rich shock than for the affect-poor cash."
   Of the 258 combinations that match 5 of the main 6 balls, in 42/43 of them the remaining number will not match the powerball, giving odds of formula_18 for obtaining a score of 5 without matching the powerball.
   In the US, large lottery winnings generally are advertised as an annuity amount, paid in 20 or more installments; in most cases, a cash option is available. The cash option in the US can be 40-60% of the advertised annuity amount.
  
  Legislation varies by US jurisdiction; many statutes specify a minimum payout percentage. To make lotteries competitive, some jurisdictions increase payout percentages versus those of a neighboring lottery. The percentage changes are likely due to competition from illegal numbers on daily numbers games.
  
  Section::::See also.
  
  BULLET::::- Lottery
  
  BULLET::::- Lump sum
  
  BULLET::::- Structured settlement
  
  BULLET::::- Annuity (finance theory)
   For example, let there be three states of nature, "beautiful and eventful trip by car", "staying home", and "death by car accident". Their consequences and utility values for a particular individual are:
  
  BULLET::::- Beautiful and eventful trip by car: 16 utils
  
  BULLET::::- Staying home: 9 utils
  
  BULLET::::- Death by car accident: 4 utils
   Using the same principle, the odds of getting a score of 2 and the powerball are formula_19 for the score of 2 multiplied by the probability of one of the remaining four numbers matching the bonus ball, which is . Since formula_20, the probability of obtaining the score of 2 and the bonus ball is formula_21, approximate decimal odds of 1 in 81.2.
  
  The general formula for formula_13 matching balls in a formula_11 choose formula_12 lottery with one bonus ball from the formula_11 pool of balls is: 
  
  formula_26
   Rolldown: A rolldown occurs when a top prize pool is not won, and that money is redistributed to be shared with those that win a smaller prize. In Lucky Money, when a $2 million jackpot is not won, any funds in excess of $2 million are rolled down and added to the pools for all other winners, except players who only matched the "Numbers" (they still get a free ticket). In Fantasy 5, whenever no player matches all five numbers, the top prize pool is added to the second prize pool (correctly matching four numbers.) On September 15, 2008, the Fantasy 5 rolldown was modified; the top prize pool now is added to second prize. However, matching four numbers is capped at $555 per occurrence; in such cases, the third prize (three numbers matched) pool receives the remainder of rolldown funds.
   The probability and odds can be taken into a mathematical perspective: The probability of winning the jackpot (through October 27, 2017) was 1:(C) x (15); that is: 75 ways for the first white ball times 74 ways for the second times 73 for the third times 72 for the fourth times 71 for the last white ball divided by 5 x 4 x 3 x 2 x 1, or 5!, and this number is then multiplied by 15 (15 possible numbers for the "Megaball"). Therefore, (75 x 74 x 73 x 72 x 71)/ (5 x 4 x 3 x 2 x 1) x 15 = 258,890,850, which means any combination of five white balls plus the Megaball has a 1:258,890,850 chance of winning the jackpot. Similarly, the odds for second prize were 1:(C) x (15/14) = 1: 18,492,204 chance of winning. The overall probability of winning any prize was 1 in 14.7. If there are no jackpot winners for a specific drawing, the jackpot will keep increasing; however, the odds will still remain the same.
   If the powerball is drawn from the "same" pool of numbers as the main lottery, then, for a given target score, the number of winning combinations includes the powerball. For games based on the Canadian lottery (such as the lottery of the United Kingdom), after the 6 main balls are drawn, an extra ball is drawn from the same pool of balls, and this becomes the powerball (or "bonus ball"). An extra prize is given for matching 5 balls and the bonus ball. As described in the "other scores" section above, the number of ways one can obtain a score of 5 from a single ticket is formula_16. Since the number of remaining balls is 43, and the ticket has 1 unmatched number remaining, of these 258 combinations will match the next ball drawn (the powerball), leaving ways of achieving it. Therefore, the odds of getting a score of 5 and the powerball are formula_17.
   According to the Euromillions website, the chances of winning the UK Millionaire Maker game on a Tuesday can be estimated as 1 in 1,900,000. This can shrink to 1 in 2,250,000 in the events of rollovers. On a Friday, it can be calculated as 1 in 2,950,000 but again the odds can fall to 1 in 3,400,000 in the events of a 4 times rollover. Winning in this game depends entirely on the number of the payslips sold so the odds fluctuate. The odds may also fluctuate during a super draw or a special event in the UK Millionaire Raffle.
   The chance of winning can be demonstrated as follows: The first number drawn has a 1 in 49 chance of matching. When the draw comes to the second number, there are now only 48 balls left in the bag, because the balls are drawn without replacement. So there is now a 1 in 48 chance of predicting this number.
   "Experiment 2: In a subsequent, and more realistic study, two similar and financially equivalent prizes - a $500 coupon redeemable toward payments associated with a European vacation (affect-rich) and a $500 coupon redeemable toward payment of tuition (affect-poor) were presented. For each prize, some participants were told they had a 1% chance of winning, and others a 99% chance of winning. Participants then had to indicate how much money they would have to be offered for them to be indifferent between receiving that dollar amount for sure and having the specified chance of winning the prize."
  