http://gyazo.com/04e1eb7f3c3d407361607e2f56021f7b

Pokerstars is running that promotion there, and haxton tweeted out asking what the most +EV way to use this promotion is. The max bet on stars is $2500. You get 10% back on losses up to $10,000 per week. Off the top of my head I didn't think this would make games +EV but if it does it would definitely be getting up or down $10,000 as quickly as possible because the longer you play the more likely you are to end up a loser. IE betting $2,500 a pop until you hit + or - 10k right? Thoughts? Going to cross post this in casino games forum as well see what they say.

I think this sort of rebate does make these games +EV marginally. And yes, the best way to take advantage is putting on the largest bets possible.

I don't know the EV of Blackjack when played correctly but if you take an example of 00 roulette the margin the casinos take is 2/38, or 5.2%. If you bet 100$ dollars on black, then 47.37% of the time you gain 100$, and 52.63% of the time you lose $90 ($100 plus your 10% rebate back of 10$).

(100)(.4737) + (-90)(.5263) = 0.003

So an extremely marginal profit here. Blackjack operates on a smaller margin that roulette so if you use your offer playing there it will lead to a greater EV.

In theory you could grind it out at the low stakes blackjack tables until you hit 10k in losses for a marginal +EV, but if you factor in opportunity costs and risk aversion, surely the winning move is to pass on the offer.

You must have made a rounding error, because the EV for a single spin of 00 roulette is exactly 0. You are getting 10:9 odds on a 9/19 chance, exactly fair odds (leave your percentages as fractions an it is far clearer).

As blackjack has a lower margin than Roulette, yes it is definitely +EV to make a single max bet. Whether it is worth continuing from +$2500 or -$2500 depends on the exact margin but it is unlikely it is worth betting again (because the result of the second bet cannot put you into or get you out of the negative, you are risking 1:1, and you are relying on the fact that you get to 'play the promotion again' if you get back to exactly $0 to be worth the margin you are giving up... unlikely)

On continuing to bet, I think it depends on how close the game is and the max you can bet. The thing to calculate would be, how close to 50-50 is it that you will either win $10,000 or lose $10,000 (and stop) for the week. If you're in say a - 0.5 % blackjack game then it's only costing you $5 for every $1000 of action. If you can max bet $2500 then I think you're going to fluctuate up or down $10,000 pretty quickly with high probability.

Maybe not though. If you averaged 40 bets to swing 4 you'd put in about $200,000 in action to be up once and down once. That's costing you $1000 for the $1000 rebate the time you're down $10,000.

But if you averaged 20 bets to swing 4 you'd net $500. That would be better than the $250 - $25 you'd make placing just one bet per week for two weeks. EV speaking of course.

So that's the key calculation. What's the average number of bets you'd have to put in to make the swing up or down to $10,000. And how much is the house edge on those bets?

That's how I see it anyway.


PairTheBoard

http://forumserver.twoplustwo.com/31...ze-ev-1524297/

An early post in that thread points out that this has been solved with the solution available somewhere. I know there are "Bonus Whores" forums where these things are regularly worked out.

It's clear that if you could play a 0 EV casino game then you would only stop betting if you got down $10,000 for the week. Therefore, as the house edge approaches 0 your optimum strategy would approach that one. So if the house edge is small enough it must become better to make more than one $2500 bet.

So I think that for whatever size bet, B, you make based on Kelly considerations, and depending on the house edge, e, there are functions U(B,e) and D(B,e) such that your optimum play is to continue making bets of size B until you are either up U(B,e) or down D(B,e) for the week. Where D(B,e) ---> $10,000 as e ---> 0. I expect someone has worked this out on a good Bonus Whores forum.

The rest of the linked thread above looks pretty sidetracked except for this rather important update of information:

Post 18 from that thread:
Ans: Depends on how close to 0 EV a game you can get to play.



A good friend of mine who I'm afraid is no longer with us was the resident expert on these things on one of the Bonus Whores forums. I actually invested funds 50-50 with him to operate Bonus Whoring on my computer with him doing the work and me splitting the profits with him. He needed to branch out to other computers because he'd exhausted the Bonus opportunities on his.


PairTheBoard

The bet sizing mostly only factors in to your risk aversion and risk of ruin. Like, if you have a legit EV edge at a casino game, your most +EV play is to keep playing for as much money as you can. Think about it when the roles are reversed: normally the house has a tiny EV edge, and they want players betting big all the time. Of course, the house has a ginormous bankroll such that they can ride the variance roller coaster all day long.

So, like, if you've got a 1% edge at a casino game, your most +EV move is to play big all day long. But the risk of ruin means that's probably not a smart play. Basically, there's more to think about here than raw EV.