Discounts on sports tickets & risk/house edge

Hi everyone,

I have a question regarding risk and house edge.

Consider if someone is playing sports lottery tickets in a state-run system. The state gives retailers a certain commission on the number of tickets that they sell. If one player is purchasing tickets in bulk and a retailer gives them a discount on the total price of tickets, does that effect house edge/risk?

So instead of a $100 ticket that has a potential payout of $150, the person may have a $97 ticket that has a potential payout of $150. So two people with the same ticket could win $150, but one paid $97 and $100 (the $97 ticket is $97 due to the discount given by the retailer, which is possible due to the commission the retailer receives).

Quote: zero216

Hi everyone,

I have a question regarding risk and house edge.

Consider if someone is playing sports lottery tickets in a state-run system. The state gives retailers a certain commission on the number of tickets that they sell. If one player is purchasing tickets in bulk and a retailer gives them a discount on the total price of tickets, does that effect house edge/risk?

So instead of a $100 ticket that has a potential payout of $150, the person may have a $97 ticket that has a potential payout of $150. So two people with the same ticket could win $150, but one paid $97 and $100 (the $97 ticket is $97 due to the discount given by the retailer, which is possible due to the commission the retailer receives).

Of course, if you pay $3 less for your ticket, you are expected to win $3 more compared to the regular prized ticket. If the nominal prize is $100, you gain 3% in less house edge.

Does it help you win the game ? Of course, but probably not enough.

Quote: MangoJ

Of course, if you pay $3 less for your ticket, you are expected to win $3 more compared to the regular prized ticket. If the nominal prize is $100, you gain 3% in less house edge.

Does it help you win the game ? Of course, but probably not enough.

Thanks so much for your reply. I think I understand you conceptually why it works this way, but can you explain to a non-math guy how this formula actually works? Also, when you say it helps you win (albeit slightly), does this mean that on the aggregate you have a better probability of winning?

Sorry if I'm not making much sense here, I'm finding this quite complex!

If your ticket seller rebates you $3 for every ticket you buy from him, you have 3 dollars more in your pocket, so you actually just paid $97.

If the normal prize for a ticket is $100, you save $3/$100 = 3%. It cannot get much simpler than that.

Quote: zero216

Hi everyone,

I have a question regarding risk and house edge.

Consider if someone is playing sports lottery tickets in a state-run system. The state gives retailers a certain commission on the number of tickets that they sell. If one player is purchasing tickets in bulk and a retailer gives them a discount on the total price of tickets, does that effect house edge/risk?

So instead of a $100 ticket that has a potential payout of $150, the person may have a $97 ticket that has a potential payout of $150. So two people with the same ticket could win $150, but one paid $97 and $100 (the $97 ticket is $97 due to the discount given by the retailer, which is possible due to the commission the retailer receives).

The short answer is that you don't have enough information to solve the problem.

We need to solve for the EV of the ticket, and there are too many unknown variables. The first thing you have to solve for is the "EQUITY" or the amount of profit per ticket. You need to know the entire prize pool, not just the potential prize. You then divide the entire prize pool by the total number of tickets involved. Then, and only then would the $3 discount come in, i.e. is the $3 discount sufficient to create positive EQUITY per ticket?

The short answer is $3 less per ticket helps reduce the house edge, but the $3 discount is still too small to create a positive EQUITY per ticket.

In the state of CA, the prize pool is about 50% of each dollar generated for scratchers. That means even if you got a $3 or 3% discount, that means you paid $0.97 to win an expected $0.50. You can see the house edge is reduced, but you still don't have positive EQUITY.