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# help me understand this statement in human action pls.

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Renboy Posted: Sat, Dec 18 2010 11:33 AM
I just started on this fantastic book but I cant help but think this statement is wrong. I know that maybe he is just not saying what he means in a way that is accurate, or I'm just wrong. Both are possible. I'm inclined to believe that I'm wrong but I just cant see how. So I'm hoping someone can explain it to me better. here goes.... "Cool reasoning must show the gambler that he does not improve his chances by buying two tickets instead of one of a lottery in which the total amount of the winnings is smaller than the proceeds from the sale of all tickets." Now I agree that buying more tickets does not increase the winnings necessarily, but buying more tickets DOES increase the CHANCES of winning. Lets boil it right down and say that there is a lottery with only two tickets.. Right? If you buy one you have a 50% chance of the ticket you buy being the winning ticket. If you buy both the CHANCE of you buying the winning ticket is a 100%. Now if it is a lottery with a hundred or a million tickets the CHANCE of buying the winning ticket will increase with the number bought. No one can argue that if you buy them all you have 100% chance of having the winning ticket. You would of made a massive loss, but you would of won the lottery. Maybe I'm just missing the point he is trying to make, (probably) but it really bugging me. :-) P.S I think the lottery is for people that are bad at math, so I'm not looking to convince myself its a good idea to throw my money away. Thanks
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Jonathan M. F. Catalán replied on Sat, Dec 18 2010 11:47 AM
The lottery works by choosing random numbers, and so there's a chance that no tickets will be the winning ticket. The chances, therefore, of winning the lottery, even if you buy two tickets, remain the same. But, statistics is not my strong point, and so I can't really judge Mises's beliefs on statistics (which he borrows heavily from his brother, Richard von Mises). I know they have been critiqued before.
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Renboy replied on Sat, Dec 18 2010 12:46 PM
ok I get that, but the way he speaks about the lottery is not like the lotto today. he speaks of it as a fixed number of tickets of which one will be drawn. later on he says that if not all of the tickets are sold then the lotto owner takes the place of the gamblers in relation to the unsold tickets. But now that I think about it, even in the lotto today there is only a fixed number of options that the result can be. Yes there can be billions (?) of permutations but there is a finite number. ie if you bought one ticket for everyone of the billion sequences that it could be you would have a 100% chance of owning a winning ticket. No? Obviously you would lose much more then you gain but you would have a "winning" ticket.
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sami replied on Sat, Dec 18 2010 1:13 PM
Ren, the case where buying two tickets gives you 100% chance of winning may be a different kind of lottery say scratch games unless the lottery agency does not want to play fair. I personally believe Mises is talking about lotteries like 6/49 and the like. No matter how many tickets you buy, even thousands, there is still a chance that none of your tickets will be winner. Since all depends on chances, you pray that the new set of numbers should be different from your original ticket. If it is different, I strongly believe your chance boosts up. However this depends on chance too. The probability that your second ticket would be different from the first needs to be considered. Now lets assume the second ticket is indeed different from the first; our gambler, just like any other ticket holder, can win with one and only one ticket with one set of random numbers. So even if the gambler holds a lot of tickets, the probability that a single ticket will win is the same for the one holding a single ticket and the one holding thousands of tickets. I strongly believe Mises is talking about the probability of a ticket winning not necessarily the ticket holder.....................Just what I personally think of that. I believe it is not about Mises being right or wrong. It is about reasoning from what he wrote and that is really hard. Just like Hazlitt said, it is hard to read the thoughts behind other peoples' statements. Only the writer can defend him/herself.
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Renboy replied on Mon, Dec 20 2010 12:41 AM
Thanks sami I'm not sure how a 6/49 lotteries work, (I'm in south africa) but here you can let the machine pick your numbers for you or you can pick them for yourself. Obviously if you get two tickets with the same number there is no change in your chances of them winning, but I just can not see how having two different sets of numbers doesn't increase your chances. you said.. "I strongly believe Mises is talking about the probability of a ticket winning not necessarily the ticket holder.....................Just what I personally think of that." This is the only way I can see the meaning I THINK he is trying to put across. It's the only thing that makes sense to me, but the statement defiantly does not read that way. "Cool reasoning must show the gambler that he does not improve his chances by buying two tickets instead of one of a lottery " I dont know.. Its something to puzzle over for a bit at least.
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