I mentioned to a colleague that I’d bought two lottery tickets for last weeks Euromillions draw instead of my usual 1 to double my chance at winning. He said “Yeah, that’s not how it works.” I’m sure he is right – but why?
In: 7847
I’d be willing to bet that your colleague is confusing the probability of betting on one event, with the probability of betting on multiple independent events.
Stealing someone elses example from elsewhere in the comments, but let’s imagine you have a wheel split into 5 segments, and you take bets on which segment a marble will land on.
Assuming that it’s truly random, the probability of any one segment being the winner is 20%, so betting on two segments would give you a 40% chance of winning.
But, if you bet on one segment in two independent rounds, your chances are not 40%. Your chances of not winning are 80% (0.8) so your chances of not winning over two rounds is 0.8*0.8 = 0.64 – so you have a 64% chance of not winning and a 36% chance of winning.
If you played the game 5 times, you’d only have a 67% probability of getting a win (probability of the event not occuring is 0.8, so 0.8*0.8*0.8*0.8*0.8 = 0.32768 – round it up to 0.33for simplicity).
Your coworker mixes 2 different types of chance.
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There is the lottery where there is a fixed amount of combinations with a fixed chance. Buying multiple different combinations increase your chances linearly
For example 5 number out of 90 without repetition, means 90*89*88*87*86. Every thicket has a chance of 1 in 5273912160. Two ticket 2 times, 10 ticket, 10 times and so on
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There is a different chance, where the chances don’t increase linearly. When you want something to happen certainly out of a given number of tries. Those are the relations of the same chances over and over.
For example, the chance of you throw 6 with cube dice is 1/6. That is linear, but if you throw it multiple times and you want to be certain that you are going to get a six, then the increasing the number of throws don’t increase your chances linearly.,
I can’t find the equation…. I don’t know how it is called properly in english
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Back to lottery, If you look at a single lottery draw, buying multiple tickets increase your chances linearly with each ticket, to win that lottery
But if you look at multiple lottery draws, buying tickets in each don’t increase your chances linearly to win the lottery anytime.
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maybe it is the binominal distribution
Where the attempts multiply each other.
If you have 1% chance to succeed out of 100 trys, first time you have 1% chance second try 1.99
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Your friend is mistaken. The odds of winning Euromillions are close to 1 in 140,000,000. The 1 is for the 1 set of numbers you get on each ticket. When you buy two tickets, you have 2 sets of numbers that could match the winning the numbers. So, your odds are 2 in 140,000,000.
So long as each ticket has a different set of numbers, you can double your odds simply by doubling the number of tickets you buy.
He is wrong your chances are now two out of however many million possible combinations, instead of just the one chance out of however many millions. You could increase your chances one hundred fold… and still not be likely to win… you still increased your chances.
as others have mentioned, the only way you wouldn’t be doubling your odds is if both tickets have the same number
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He’s not right, you are. A second ticket doubles your odds unless the numbers on both are identical.
Imagine if the numbers were simple, just a single number from 1 to 100 was drawn for the winner. If you have a ticket you have a 1 in 100 chance, if you have a second ticket with a different number then it’s 2 in 100 odds.
Unless you picked the same numbers, your coworker is wrong. Since every combination of numbers has an equal chance of winning, every subsequent entry multiplies the likelihood that you’ll win.
To see this in action, just do some simulations with very small numbers.
If you have a pool of 5 numbers and only need to match 2 of them, you’ll see that every combination has a (1/5)(1/4), or .05, chance of winning. This is true whether you choose 1 and 2, 1 and 3, 1 and 4, 1 and 5, 2 and 3, 2 and 4, and so on.
If you buy two unique entries, your chances become 2(1/5)(1/4) or .1, which is double the odds of one entry. This is true even if one of the numbers on the second ticket is the same as one number on the first ticket because, as mentioned earlier, every combination has an equal chance of winning.
Your coworker is simply wrong. If you buy 10/39/58502 tickets, your chance will increase, still remaining miniscule.
It does double your chances of winning.
It does not however, significantly (realistically) improve your chances of winning.
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