Highest EV on this promotion

[Erdnase]

Hi all,

I just ran across this promotion:

A betting site online offers a 25 % rebate on my next wager. Meaning, if I opt to wager 100 on a given bet, I get 25 back.

Now, here is my question: do I go for a long shot or an even money bet if I want to maximize my expectation?

Greets, Erd.

[Bozeman]

Highest EV, independent of longshot-ness.

[M.B.E.]

[ QUOTE ]
Hi all,

I just ran across this promotion:

A betting site online offers a 25 % rebate on my next wager. Meaning, if I opt to wager 100 on a given bet, I get 25 back.

Now, here is my question: do I go for a long shot or an even money bet if I want to maximize my expectation?


[/ QUOTE ]
Not sure if I understand this. Will you get the rebate regardless of the success of the underlying bet?

If the promotion is that you get 25% back on your next bet if it loses, then you'd want to go for the longshot.

[Paul2432]

I believe that given two bets with the same house edge without the rebate, the wager that is the bigger long shot will benefit most from the rebate.

This is because you only collect the rebate when you lose which is much more likely with a longshot.

Paul

[lunchmeat]

If you only get the rebate if you lose, then the bigger the longshot the higher the Expected Value if the house edge for all bets is the same. BUT the house edge for the biggest longshot prop bets is usually enormous, so you'll have to figure out what the house advantage is for the bets you're considering putting down for this promo.

[jgraeffe]

After spending way too much time doodling equations on paper, I found that Paul and Boozeman are both correct.

I) Given that the rebate applies regardless of the outcome of the wager, simply go with the higher EV bet. The EV of this promotion can be expressed mathematically by:

EV PromotionI(n) = (.25-Rake)*n
where Rake is the house edge and n is the amount of the wager. This will make any bet have a positive EV if the house rake is less than 25%.

II) If the rebate applies only if the wager is lost (though I doubt this is the case), the EV of the rebate is:

EV PromotionII(n) = [.25-Rake-.25(Pw)]*n
Where Pw is the probability of winning the bet, the "longshot-ness" so you should go for the long shot if EV is your only motive. That said, you probably won't because even if a lottery ticket for $1,000 had a postive EV most people wouldn't buy it (diminishing marginal returns on the utility of money).


Where in Bryn Mawr you from Paul? I'm from Bryn Mawr also.

-Alex

[Paul2432]

Alex,

I sent you a PM with my location information.

I guess we are thinking of different things. With slot machine rebates, I agree, the rebate comes no matter if you win or lose.

On the other hand with "match play" type promotions, you really only collect if you lose. For example, suppose you have 10 coupons that let you bet $100 in the form of $75 of your own money plus the coupon worth $25. After 10 50/50 wagers you have an expected profit of $125 or $25 for each of the five times you lose (500-5*75=125). On the other hand on a 9:1 payout your expected profit after 10 bets is $225 (assuming fair odds).

Paul