Mises on buying more then one lottery ticket

Economics Economics Questions
1

Mises in Human action:
"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. If he were to buy all the tickets, he would certainly lose a part of his outlay. Yet every lottery customer is firmly convinced that it is better to buy more tickets than less. The habitués of the casinos and slot machines never stop. They do not give a thought to the fact that, because the ruling odds favor the banker over the player, the outcome will the more certainly result in a loss for them the longer they continue to play. The lure of gambling consists precisely in its unpredictability and its adventurous vicissitudes. " #######

I find it hard to grasp why buying more then one ticket does not improve your chances of winning. I do understand his reasoning about buying all the tickets and surely loosing, yet it still doesn’t seem correct about buying 2 tickets instead of 1 for example. Is this statement by Mises correct? and is there a way to statistically validate it? because I can’t think on one.

2

Your chances of winning do increase, however, the increase in the probability of winning is more than offset by a reduction in the return that comes from holding a winning lottery ticket.

Look at it this way, if you hold every lottery ticket, you’re assured to win, however, the return is negative. So the worst possible option is to buy all the tickets. As you decrease the amount of tickets bought, you increase the return more than you decrease the probability of winning (this is because the total amount to be won is smaller than the combined value of all the tickets - if they were the same it would not matter how many you bought, you’d have the same chance regardless).

3

Also interesting is that the odds of winning power ball are like 1 in 180,000,000. Sometimes, the jackpot can be bigger than this (without taxes) in which case the lottery differs from the one Mises describes.