My wife and I are trying to figure out the EV difference (if there is any) between these 3 scenarios:

1) Depositing $100 and playing Keno online, $1 per spin, on a machine that pays out at 92%.
2) Same as #1, but before you play you redeem a 200% casino code that puts $300 into play for your $100 deposit. There's a $7500 playthrough however, and you can't withdraw any amount until the playthrough conditions have been met.
3) Same as #2, but you can withdraw any amount you want above the bonus amount of $200.

I think that covers everything. If more info is needed, I can provide it. We're coming up with 2 completely different sets of answers for some reason. Intuitively it feels like risk of ruin should come into play pretty heavily for #2, and not nearly as much in #1 and #3. Unfortunately, I can't express my intuition mathematically. Is it important here?

Also, with bonus money, comps, rakeback, and other offers, can this ever get to over 100% payout?

You haven't really defined what your intentions are with #1 and #3. If you play for a long enough period of time, you're going to lose money in all situations, so you're playing for something more like a cash-out strategy when you reach a certain threshold. For example, if your goal is to make $1, I would think that 1 and 3 basically the same, but 2 is much worse. (3 should have a slightly higher chance of "winning" since you have a small number of miracle comebacks that you couldn't have with only $100.)

So I think you need to define an "exit strategy" for this scheme.

Maybe we should redefine the parameters of the OP to come up with the optimal exit strategy instead?

EDIT: I guess we could set it to the playthrough amount for #s 2 & 3, but that might not be the best strategy. Perhaps there's an "optimal" way of minimizing losses (or even cracking 100%) that involves abandoning the bonus money?

What do you mean by "abandoning the bonus money"?

Also, I think knowing the payout structure that leads to 92% return matters. Are you playing an even money bet?

Nope, not at all. Probably as far from even money as possible. Keno is all about small odds paid on common hits and mucho odds paid on rare hits.

I know it's around 92% using the Keno calculator here (GREAT site btw):
http://wizardofodds.com/games/keno/

By abandoning the bonus money, I mean some sites let you keep it after the playthrough is complete and others don't. I just found out that #3 doesn't let you keep the bonus (which, unlike a poker bonus, is fronted to you in a casino). But, issuing a revision here will only serve to divide the thread, so let's just assume for purposes of this example that both #2 and #3 let you keep the bonus money.

Can you bet more than 1$ at a time? (need also paytable and rules of game).The best strategy here is almost always to bet it all in one step and then the amount won again all and then one more until you have satisfied requirement(300+600+1200+2400+3000). You easily create a profit that way but of course you lose most of the time (so only on avg you make that profit i mean).

If forced to bet 7500 in steps of 1 at a time you will have less than 1 in 1000 chance to see a profit by the end unless keno has great sd. If its sd is near 1 then its terrible to go 1 by 1 , its a sure loss >99.9% of the time.

This is a nice one time offer (i imagine your casino account is dead if you play and lose and still have requirements left from that offer on a future one though, unless you can clear req. playing poker or bj with counting partially).

Casino offers are worthless if you play like they want you to play ie a little bit at a time. Its no different than roulette. If you bet 1$ at a time in red after 7500 bets you will be typically down a lot (but here its much more terrible at 92%). So if they wipe out the requirements when you bust and they do not add up to future offers then try the all in approach. If they carry on then try the all in 1 time and if you win then play with much less steps after that to try to clear the req. before you lose it all.


This version here;
http://casino.bovada.lv/lobby/12192/FUN (please note i got that from your own link above i am not advertizing on SMP the least of them casinos lol, Zeno can edit if this is a violation sorry)

implies Keno is a game of picking 10 numbers out of 80 and then having 20 randomly selected by the computer that then pays you according to how many of your picks hit. So payouts in that link looked like 0 for less than 5 hits and then for 5,6,7,8,9,10 hits are respectively x2,x25,x150,x1200,x10000,x25000.

Based on that example one can estimate EV and SD and produce a best strategy. I think it will still be close to betting each round as much as legally allowed trying to get lucky.

If you do get lucky we can arrange afterwards what to do depending how lucky you got and your objective here. But playing a negative EV game like that you want to use volatility to your benefit when they give you bonus and its absolutely possible if they allow you to bet all of it to produce a profit but most people dont know how to do it right. Find out the maximum they let you bet each round and report back for more analysis.

So then you would need to say precisely what bet you're making (so that you can know the SD and all that stuff). Knowing that it pays 92% doesn't mean the same thing as playing in a way as to earn a 92% return.

I'm not sure that I follow. Letting you keep the bonus money would mean that #3 is an instant EV=200 by just cashing out right away. That makes for a very boring question.

What is coming to mind is something like a casino voucher where you can sit down at a blackjack table and the voucher plays like a $10 chip or whatever, and then if you win the hand you get an actual $10 chip as your winnings. Is this what you mean regarding #3?

Also, #2 sounds like a poker bonus, so that when you wager $7500 (akin to playing X hands), they will then give you $200 cash and you can walk away with it at that point (plus whatever cash you might have left in your bankroll).

Is this corect?

It seems Keno has a huge SD of about 30 (in some example used in the links above) . And sd is your firiend in games that loss is capped and you have a big bonus too. So it may be possible to see a profit often enough at any limit even at 1$ at a time (way different than say roulette in that sense because of the huge sd). Of course its still going to be true that the best EV strategy is to bet as much as possible at once but in terms of utility theory it may be interesting to play 1 at a time with such huge SD.

Very roughly (the central limit theorem application here is very very rough) your distribution may look like (-600,(7500/size)^(1/2)*size*30) only of course adjusted for the barrier at 0 so its going to be somewhat different. Since you have so much possible gains but only 100 loss it will be possible to design a winning strategy it seems with 7500 fulfilled.

The probability Forum would have been a better place for the OP - so thread moved.

Thanks for the advice so far guys. It's been helping a lot.



(casino name photoshopped out for privacy)

So in your version you have the paytable above and the choice is for 14 numbers and the computer then chooses 20 randomly out of 80. Correct? Also what is the maximum $ amount they let you bet per trial (out of the 300$ you start with)?

That changes a bit the things. After you verify that i understand it correctly (plus submit maximum and minimum unit of wagering allowed 5-10-20$? 1c?) i can give you an idea how to play both to win maximally and to also sacrifice EV in order to win more often and not have the feeling you didnt get anything.

Which by the way is the key problem with the bold (bet it all at once) theory (other than that they dont have such limits anyway) for such kind of game. Because a big payoff is rare playing bold may maximize the EV (when there is bonus involved even make it positive) but the gains come so rarely that the vast majority of the time you bust and it takes so many trials to actually recognize that the method works nice leaving you unsatisfied in general.

It looks like the $250,000 max payout might complicate things if it means $10 bets don't get the full 50,000-1 payoff on 13 and 14 matches.


PairTheBoard

It's already capped on that screenshot, which is why I don't normally play more than x numbers for y amount bet. Plus, I normally don't play higher than 25c or $1 per spin. Still getting used to proper bonus play.

If the bet was $10 rather than 5 for that game, I'd have won $80,000 instead (yay) but the EV would have been worse. The $250,000 max win is already adjusted for in the payouts. The payouts for 12 and 13 spots should really be $50,000 and $100,000 but unfortunately the cap makes the payout only $50,000 for 13.

Sorry but its not clear from what you said, if you play only $1 or 2$ for 10 rounds what is the paytable like? Is 250k a maximum across any choice? If so we do need to know what is the paytable for a level at least below 5 shown here to get the clean picture of the maximum EV choice.

By the way if you have already won 40k as the balance shows (congrats indeed if real and not an ad ! thats amazing) all from $300 then do yourself a favor and play until you finish the requirement (and then some to show some gratitude i suppose lol to avoid any potential banning or profits locked as serial promotions abuser accusation ) in the most ideal EV way possible depending on the question's above response. Your objective is to protect the profits and volatility is no longer your friend because clearly you can still lose a few thousands if you play big limits (till you exceed 7500 req. i mean) . If you play small limits you will tend to lose only 8%of the remaining requirement plus or minus something less than 50% of that. You want to reduce volatility as much as possible now that you won. But at the same time you need to protect your reputation as a player too. So you see after winning the problem is very different. So make clear if you have won or this was an example pic. If a winner your key problem now is to cash out! This is what you need to protect by raising absolutely no flags and at the same time playing also responsibly.

The paytable you see in that pic is correct, except for the 14th spot. That should be 100,000 instead of the 50,000 you see there. The only reason it's 50,000 that game is because I was betting $5 a spin, and 50,000:1 is the most the game can pay with a $250,000 cap.

Thanks. The screenshot was both a joke and a brag post. Being a degenerate and playing -EV games pays off big sometimes (especially in an odds game like Keno)

My wife and I already hit the playthrough requirement of $55,000 in bets, and were able to escape with a withdrawalable $32,500. That was Thursday and we haven't played since. Are you suggesting we give them some more action before cashing out?

Thanks for the help btw.