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Lotto Probability

tsg said:
The intermediate prizes, including the one you mention, and the jackpot have a negative expected value. Over the long run you will spend more money than you will win.
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This is obvious, as most 649 type lottery return approx. 50 cents per dollar.

I was making the point that your 1 dollar wager is not facing a 1:14,000,000 odd but a 1:5 odd.

nimzo
 
tsg said:
I've seen it before. I always thought it was pretty offensive. But that's just my opinion.
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Oh well, I've never been very "PC" and Southpark makes me laugh....

Different senses of humor I suppose...
 
nimzov said:
This is obvious, as most 649 type lottery return approx. 50 cents per dollar.

I was making the point that your 1 dollar wager is not facing a 1:14,000,000 odd but a 1:5 odd.

nimzo
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I think tsg is suggesting that any risk is irrational. Unless there are varying degrees of irrationality?

Is it any more irrational to put one dollar on 1 in 13,000,000 odds to win several million dollars or 1 in 5 odds to win back your dollar?
 
So is buying insurance also irrational? After all, in both cases, you're losing a small amount now against an huge but unlikely benefit. Unless you're willing to argue that avoiding loss and gaining benefit are qualitatively different. But if you argue that, you must accept the premise that utility is not linearly and symmetrically related to cash, and from that premise it flows that playing the lottery *can be* (I wouldn't go as far as to argue that it *necessarily* is) rational in terms of expected utility payoff, even if it is clearly a losing proposition in terms of dollars and cents.
 
rudar said:
So is buying insurance also irrational? After all, in both cases, you're losing a small amount now against an huge but unlikely benefit. Unless you're willing to argue that avoiding loss and gaining benefit are qualitatively different. But if you argue that, you must accept the premise that utility is not linearly and symmetrically related to cash, and from that premise it flows that playing the lottery *can be* (I wouldn't go as far as to argue that it *necessarily* is) rational in terms of expected utility payoff, even if it is clearly a losing proposition in terms of dollars and cents.
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Good point about insurance. I would argue that tsg's logic would state that insurance IS irrational. And I guess I would agree.

Call me irrational.
 
macgyver said:
Good point about insurance. I would argue that tsg's logic would state that insurance IS irrational. And I guess I would agree.

Call me irrational.
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However, perhaps there is a difference here, especially depending on the type of insurance.

Life Insurance: Odds of collecting it are 0, because you'd be dead. So what is your risk/benefit ratio here?

However, odds of your beneficiaries collecting it are 100% because you will, in fact, die...at some point.

Car insurance: odds of collecting it depend on a whole host of factors, but there is a random component. If over the course of paying for it you spend as much as your vehicle cost...then I don't see much of a difference between this and the lotto. For the liability component this seems even more lotto like, because it assumes that you will kill or seriously injure somebody with your car.
 
macgyver said:
I think tsg is suggesting that any risk is irrational.
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No, just that the reward (an extremely unlikely chance to win millions of dollars on a bet that has a very negative EV) doesn't justify the risk (one dollar). If it was a positive EV, it's completely rational assuming, of course, that you aren't betting more than you can afford to lose.

rudar said:
So is buying insurance also irrational? After all, in both cases, you're losing a small amount now against an huge but unlikely benefit. Unless you're willing to argue that avoiding loss and gaining benefit are qualitatively different.
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The risk of not having insurance can be very detrimental. The risk of not playing the lottery is zero. But even so, I would argue against insuring against an event that had such a low probability of happening and a cost if it did happen that was significantly less than the premiums paid by the time it did. Of course there are other factors that affect whether or not the policy is justified, but they generally don't apply to playing the lottery. For instance, you aren't going to find yourself owing several million dollars that you don't have because you didn't buy a lottery ticket.

But if you argue that, you must accept the premise that utility is not linearly and symmetrically related to cash, and from that premise it flows that playing the lottery *can be* (I wouldn't go as far as to argue that it *necessarily* is) rational in terms of expected utility payoff, even if it is clearly a losing proposition in terms of dollars and cents.
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I never said it can't be. If the pleasure you derive from playing is worth more to you than the cost of the ticket, go for it. But if that pleasure is at all derived from the possibility of winning, I suggest that your understanding of how really unlikely it is may not be as much as you believe it is.
 
Taking the definition of "irrational" to mean "lacking reason or understanding", this is where I get hung up on labeling certain actions that involve risk as irrational or not.

tsg has stated that it is irrational to bet one dollar on a 6/49 lottery, but later states that it is rational to buy insurance at a much higher cost, because there is an associated greater risk to not having the insurance.

However, there is essentially no risk to playing the lotto, assuming that you do not require the $1 to survive.

So is it more rational to hedge one high cost risk against a potentially higher cost one? I think this is a common dilemma for those in the US that can't afford health insurance.
 
tkingdoll said:
Say wha? I do believe that Rasmus credited my post with giving him perspective.
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Yes, very sorry, swap places with macgyver. I appreciated your point and will try it on my brother-in-law seeing as it was pivotal for Rasmus. :)
 
macgyver said:
tsg has stated that it is irrational to bet one dollar on a 6/49 lottery....However, there is essentially no risk to playing the lotto, assuming that you do not require the $1 to survive.....
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The irrationality in playing lotto is that, considering the odds, you are essentially throwing money away; and to play lotto because of "the thrill of possibly winning" is irrational because you have to deny that above fact.
 
macgyver said:
I think it IS completely irrational to buy more than one entry on any of these lotteries. That would definitely mean you have no concept of the odds that you are playing. While there is a difference between 0 and 1, there is essentially no difference between 1 in 13,000,000 and 2 in 13,000,000
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Down here, very few lotto players buy just one ticket. I think the average is eight. The "rationale" is that they have all numbers covered :)
 
macgyver said:
Taking the definition of "irrational" to mean "lacking reason or understanding", this is where I get hung up on labeling certain actions that involve risk as irrational or not.

tsg has stated that it is irrational to bet one dollar on a 6/49 lottery, but later states that it is rational to buy insurance at a much higher cost, because there is an associated greater risk to not having the insurance.

However, there is essentially no risk to playing the lotto, assuming that you do not require the $1 to survive.
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The risk of playing the lottery is $1. I have made no statements that depend on the loss of that $1 being detrimental in any way. From an expected value point of view, the reward for playing the lottery isn't worth $1. The arguments that say the utility of the jackpot prize outweigh the negative expected value generally lack understanding of how remote the possibility of winning it really is. The risk of not playing the lottery is zero. In order to rationally decide that playing is better than not playing, there has to be a benefit to playing that justifies spending the dollar on it. I have yet to see one.

The risk of not having insurance can be quite detrimental. The benefit of having insurance generally outweighs the risk of not having it. This benefit is worth the cost of the policy. If it isn't, then the decision to buy the policy isn't rational.

So is it more rational to hedge one high cost risk against a potentially higher cost one?
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Depending on the circumstances, yes.

I think this is a common dilemma for those in the US that can't afford health insurance.
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A $100 policy that will insure you against a 1 in 1000 chance of needing a $500,000 medical procedure is certainly worth the expense, especially if you don't have $500,000 tucked away for an emergency and the cost of not getting the treatment is your ability to work or possibly your life. If you can't afford the $100 policy, however, the decision has been made for you. We have been assuming all along that the person buying the tickets is not spending more than they can afford, so the cost of an insurance policy being too high doesn't really apply to the argument.
 
tsg said:
The risk of playing the lottery is $1. I have made no statements that depend on the loss of that $1 being detrimental in any way.
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If we argue insurance vs. lotto then I would think how detrimental the loss is becomes relevant in both cases. However, I agree that the risk of NOT playing the lotto is the salient point, and certainly is a significant difference between lotto and insurance.

tsg said:
A $100 policy that will insure you against a 1 in 1000 chance of needing a $500,000 medical procedure is certainly worth the expense, especially if you don't have $500,000 tucked away for an emergency and the cost of not getting the treatment is your ability to work or possibly your life.
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Agreed, however are these really the odds? I would also suggest that many people's choices to buy insurance of this type (myself included) is not the result of rational analysis of the odds of needing to claim it, but rather for the "comfort" of knowing it's there should "something" happen. In many ways this would be no more rational a choice than playing the lottery.

My point here is that while you are arguing the logic of a rational vs. irrational choices I don't think we can exclude the indivual's motivation for the choice. What seems a rational choice to you, could have been made irrationally by somebody else.

I honestly don't know if I'm getting value for my health insurance dollar (I'm in Canada, so the costs are somewhat shrouded in mystery for us) but I'm certainly glad to have the insurance. Am I being rational in that case? I can't say that I fully understand or have reasoned through the cost/reward benefits of my situation.
 
tkingdoll said:
Ha! Eat that macgyver! neener! :p
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Hey, I did start this thread...and it's been pretty enlightening for me. I've definitely benefitted from the various views on both sides.

Not to mention that it's ended up far from where it started off.

So you can have your little victory....it's still my sandbox :boxedin:
 
macgyver said:
Hey, I did start this thread...and it's been pretty enlightening for me. I've definitely benefitted from the various views on both sides.

Not to mention that it's ended up far from where it started off.

So you can have your little victory....it's still my sandbox :boxedin:
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Aw, is there room in there for two? :hug1:
 
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