ODDS

Lotto Odds:

• 3 numbers – 1 : 55.65593
• 4 numbers – 1 : 1,031.397
• 5 numbers – 1 : 55,490.33
• 5 numbers + Bonus ball – 1 : 2,330,365
• 6 numbers – 1 : 13,983,815

Source

Alternative Lotto odds and potential winnings:

• The Jackpot - 6 Numbers (Typical prize: £2 million)
  6 numbers are drawn at random from the set of integers between 1 and 49, which means there are 49!/(6!*(49-6)!) combinations of numbers - this means that the jackpot chance is 1 in 13,983,816 or approximately 1 in 14 million.
  

• 5 Numbers + Bonus Number (Typical prize: £100,000)
  You are still matching 6 numbers from the 1 to 49 set as above, but you can now do it in 6 different ways (by dropping each of the main numbers in turn), therefore the chance is 1 in 13,983,816/6, which works out as 1 in 2,330,636.
  

• 5 Numbers (Typical prize: £1,500)
  This is 42 times more likely than getting 5 numbers + the bonus number - the chance is 1 in 2,330,636/42, which evaluates to 1 in 55,491.33333.
  

• 4 Numbers (Typical prize: £65)
  Firstly, let's take the case of the first 4 of your numbers matching and the last 2 not matching.
  In this single case (where each set of chances relies on the previous event occurring):

  Chance that your 1st number matches a winning lottery number is 1 in 49/6.
  Chance that your 2nd number matches a winning lottery number is 1 in 48/5.
  Chance that your 3rd number matches a winning lottery number is 1 in 47/4.
  Chance that your 4th number matches a winning lottery number is 1 in 46/3.
  Chance that your 5th number doesn't match a winning number is 1 in 45/(45-2) [because there are still 2 unmatched winning numbers].
  Chance that your 6th number doesn't match a winning number is 1 in 44/(44-2) [yes, still 2 unmatched winning numbers].

  Source

  
  

  
  

  Thomas