Lottery with free tickets to another lottery. Calculate EV?

[AA Suited]

Scenario 1:

Lottery A:
Chances of winning are 1:550k
Price: $1/ticket
Current prize $400k
Promo- But 5 Lottery A tix, get 1 free lottery B tix

Lottery B:
Chances of winning are 1:150k
Price: $1/ticket
Current prize: $150k


Scenario 2:

Lottery A:
Chances of winning are 1:550k
Price: $1/ticket
Current prize $550k
Promo- But 5 Lottery A tix, get 1 free lottery B tix

Lottery B:
Chances of winning are 1:150k
Price: $1/ticket
Current prize: $300k


In both scenarios, I think Lottery B is more +EV, but i cant do the math to prove it.

Am i right? If so, how do you do the math to figure it out?

[sixhigh]

1. Lottery B has an EV of 0. A has an EV of 400/550 + 1/5*(0) - 1 = -0.27

2. B: EV = 1. A = 1 + 1/5*(1) - 1 = 1/5.

Thus B > A in both cases.

[Freyalise]

[ QUOTE ]
1. Lottery B has an EV of 0. A has an EV of 400/550 + 1/5*(0) - 1 = -0.27

2. B: EV = 1. A = 1 + 1/5*(1) - 1 = 1/5.

Thus B > A in both cases.

[/ QUOTE ]

Why are you adding 1/5*(0) when calculating A's equity in the first scenario. You get a free lottery B ticket. Your calculation would be correct if you had to buy the lottery B ticket.

Correct answer should be 400/550 + 1/5*(1) -1 = -0.07

Your calculation for scenario 2 is wrong as well, although the answer that B is better is correct for both.

[sixhigh]

Whop! My mistake.

[AA Suited]

[ QUOTE ]
[ QUOTE ]
1. Lottery B has an EV of 0. A has an EV of 400/550 + 1/5*(0) - 1 = -0.27

2. B: EV = 1. A = 1 + 1/5*(1) - 1 = 1/5.

Thus B > A in both cases.

[/ QUOTE ]

Why are you adding 1/5*(0) when calculating A's equity in the first scenario. You get a free lottery B ticket. Your calculation would be correct if you had to buy the lottery B ticket.

Correct answer should be 400/550 + 1/5*(1) -1 = -0.07

Your calculation for scenario 2 is wrong as well, although the answer that B is better is correct for both.

[/ QUOTE ]

so the answer to scenario 2 is:

B: Ev =1
A: 1+ 1/5(2) -1 = .4

Thus B > A

RIGHT?! [img]/images/graemlins/confused.gif[/img]

So the general formula for my scenanrios is:
prize A/odds A + 1/5(EV Lottery B +1) -1??

Why (Lottery B +1)? and why -1 at the end?

[sixhigh]

[ QUOTE ]

so the answer to scenario 2 is:

B: Ev =1
A: 1+ 1/5(2) -1 = .4

Thus B > A

RIGHT?! [img]/images/graemlins/confused.gif[/img]

So the general formula for my scenanrios is:
prize A/odds A + 1/5(EV Lottery B +1) -1??

Why (Lottery B +1)? and why -1 at the end?

[/ QUOTE ]

Right. You subtract 1 because you have to pay 1 for a ticket and in the calculation for lottery A you add 1 to the EV of b, because you don't have to pay for this ticket (whereas in the previous calculation of EV(b) we included the entryfree ... and now we have to remove it).