In general, I support the concept of not telling everyone how to crush casino bonuses. More people that use bonuses correctly means casinos lose money and will likely give less future bonuses for people who can figure this out themselves.

For this reason, I love NewOldGuy's posts. That statement refers to many other threads beyond this one. Not only does he discourage people from trying profitable bonuses, he will attempt to back it up with math. Honestly, if I was trying to discourage people from doing bonuses, I would not be capable of creating the quality of posts NewOldGuy does.

You guys can laugh all you want but even before the rules changed to require 50 bets (or whatever the change was) this was not a profitable offer. The simple EV calculations being shown don't exactly apply because of the restrictions on the offer.

The original rebate offer mentioned in the OP had a maximum of 4 rebates, limited to 1 per week. So let's look at all the possibilities for betting on it, using the single zero roulette wheel as the example again. Wins are 18/37 and losses are 19/37.

First case - we take all 4 rebates. At the simplest case this means 4 bets. I'll use $1000 per bet (or per week, doesn't make any difference). The ways those can come out are:

WWWW - 5.6% of the time we win $4000.
LLLL - 6.95% of the time we lose $4000 and get a $400 rebate, net loss $3600.
WWLL - 37.45% of the time we push.
WWWL - 23.65% of the time we win $2000.
WLLL - 26.35% of the time we lose $2000 and get a $200 rebate, net loss $1800.

Average result: $27.59 loss
(5.6012%*4000)-(6.9536%*3600)+(23.65%*2000)-(26.3504%*1800)

Second case - we take 3 rebates.

WWW - 11.51% of the time we win $3000.
LLL - 13.54% of the time we lose $3000 and get a $300 rebate, net loss $2700.
WWL - 36.46% of the time we win $1000.
LLW - 38.49% of the time we lose $1000 and get a $100 rebate, net loss $900.

Average result: $1.97 loss
(11.5136%*3000)-(13.5412%*2700)+(36.4598%*1000)-(38.4854%*900)

Third case - we take 2 rebates.

23.67% of the time we win $2000.
26.37% of the time we lose $2000 and get a $200 rebate, net loss $1800.
50% of the time we push.

Average result: $1.31 loss
(23.6669%*2000)-(26.3696%*1800)

Fourth case - we take 1 rebate (this is the one in dispute really).

48.65% of the time we win $1000.
51.35% of the time we lose $1000 and get a $100 rebate, net loss $900.

Average result: $24.32 win
(48.6486%*1000)-(51.3514%*900)

The problem here is that you can't average a non-repeatable wager. EV has no practical utility to a single lifetime bet. You are going to either win $1000 or lose $900, period, the end. And the $1000 win happens less than half the time. So more often than not, if you take the single bet option, you will lose $1000. And you have nothing to average it with. And if you decide after a loss that you want to continue, then we're into one of the 3 losing options described above. So you expect to lose even more.

Obviously if every player using this offer placed but a single bet, the casino will come out behind in the long run, so it's -EV for them in that specific (unlikely) case. But over half those players will lose $900 (51.4% of them). And 48.6% of them will win $1000. But YOU, as one player, do not have a real expectation of profit here on a single bet. You will lose money over half the time with no chance to recoup it.

So now go ahead and argue philosophy instead of gambling, and that the apparent +EV applies to a non-repeatable wager. Mathematically that's absolutely true. But then read some of the papers written on how EV isn't useful for decision making on non-repeatable wagers. This has been discussed since the days of Pascal in the 15th century. In the real world, given the restrictions placed on this rebate offer, it is not a profitable wager for any player, single-wager EV notwithstanding.

And obviously for any number of wagers greater than 1 the offer has clear negative expectation. As the number of wagers increases, the expected loss approaches 90% of the house edge (due to 10% rebate).

You have a bright future in casino marketing.

Well, this is wrong.

If I said we could roll a standard dice and if it comes up 1 or 2, then you win and if it comes up 3, 4, 5 or 6, then I win and I said if you win, I'll pay you $10,000 and if I win, you pay me $10. I will only do this once in your entire life. You are either going to win $10,000 or lose $10, period, the end. And the $10,000 win happens happens less than half the time. So more often than not, if you take this bet, you will lose $10. If I were you, I would take this bet.

Yes but now you have dramatically shifted the utility function. I'd argue that a 10% rebate doesn't shift it for anyone. The reason to take your bet is different. That wasn't the argument for the actual offer, and I showed that for all cases other than a single lifetime bet it had negative EV anyway, and that was on a low house edge game perhaps not even actually offered.

I would buy the entire VHS boxed set of your gambling instructional videos.

Change the example to a 5.4% edge game and even the single lifetime bet opportunity goes away, and no case would be +EV.

VHS? I'm waiting for the nationally syndicated radio show. Audience Network right after Dan Patrick Show.

Yes, I made it a much more attractive bet in that example. In the original situation, the player has a smaller edge than in my example, but still has an edge.

The casino is effectively laying odds. The casino is offering the player $1,000 to $900 or 1.11 to 1 (the odds always come out to 1.11 to 1 not matter how much the player bets, assuming that the player doesn't exceed the maximum amount for the 10% rebate). With those odds, if the player wins 47.37% of the time, then it is a breakeven bet and if the player wins more than that, then it is a +EV bet for the player.

1,000 * 47.37% - 900 * 52.63% = X

$473.70 - $473.67 = X

$0.03 = X

X came out to a number slightly off from 0 because I rounded the winning and losing percentages to the nearest hundredth. So, we see here, that the breakeven percentage is around the player winning 47.37% of the time.

In the original example there are 18 possible results where the player wins and 19 possible results where the player loses, so the player has an 18/37 chance to win, which means the player has approximately a 48.65% chance to win. This is greater than the player's breakeven point of slightly less than 47.37%. Therefore, the player has a +EV bet.

I just played around with this Kelly Criterion calculator that I found online:

http://www.winnergambling.com/sports...ly-calculator/

and according to my playing around with that, if we are betting full Kelly, then we need a bankroll of around $37,677 for $900 to be the optimal bet size on this bet.

Just as an example, if a player has a bankroll of $10,000, then his optimal full Kelly bet size on this bet is $238.87.

Yes, but to clarify again, this is only for a one-time lifetime single bet. If the player bets two or more times the EV is always negative (in this roulette example).

So Kelly betting doesn't apply at all. The correct amount is 0.

I don't know how you figure that just because, to our current knowledge, this particular exact bet can only be made once that makes the optimal bet size $0.00 even when the player has an over 2% expected ROI on the bet.

And the player may make hundreds, thousands or more different bets over the course of his life based on the same principals and mathematics even if the exact specifics of every single one of those bets is different.

Why would the specific terms of the bets being different matter?









If everything was exactly the same except that the casino was offering a 75% rebate instead of a 10% rebate thus effectively laying the player 4 to 1 thus requiring the player to win 20% of the time to breakeven, would you say that the "correct amount" to bet is still $0.00?

Kelly betting is only useful for repeated wagering, by definition. If you have a positive EV wager that you can only make once, the correct bet absent any utility concerns is the maximum bet allowed. But this bet has negative EV for more than one wager.

If the rebate were 75% the house edge would not overtake the rebate in just 2 bets like in the roulette example with 10%.

Well for the sake of that question pretend by the terms of the promotion that you are only allowed to make one bet that is eligible for the rebate. Is the optimal bet size $0.00?


Why would it matter that this specific bet can not be repeated?

As a hypothetical, what if the player makes thousands of different low edge bets every year? For simplicity let us just assume that the player has an expected ROI of 2% on every single bet. But the terms of every single bet are different. One of the bets is this roulette example. One is an over/under on a specific basketball game. One is on a bet that is very similar to this roulette example, but has to be played at blackjack. One is a spread bet on a specific NFL game. One is on a specific coin toss. One is on whether a colleague will be late to a meeting. One will be whether or not it rains on a particular day. One is on the winner of a boxing match. Etc.

None of these bets can be repeated. If necessary, then for the sake of this question, just assume that none of these bets can be repeated.

Is the correct bet for all of these thousands of bets $0.00?



This seems to me to indicate that you would say that the optimal bet size here is the maximum allowed wager. But obviously you are not saying that.

Our first wager is a +EV wager. We could just stop after the first wager. I don't see why the fact that additional wagers would be -EV would change the optimal bet size on the first wager from the maximum to $0.00. It would seem to me that the optimal bet size on the first wager would be the maximum and the optimal bet size on all subsequent wagers (on this specific bet under these specific terms) would be $0.00.

Obviously Kelly works if you can make repeated bets with a similar edge. We're a lot outside the realm of the Stars casino offer now, which offers 3 or 4 games and a rebate that can only be claimed 4 times.

It appears you agree that the rebate offer when used on roulette is only good for a single wager and is -EV to repeat it.

I agree. I only said the correct Kelly amount was zero since Kelly only applies to repeating wagers.

Ok. I don't think I really have anything else to say.

RickySteve's position was never all that unreasonable...

What if whoever loses gets a finger chopped off but you get a one knuckle rebate?

Long time, first time. I'll hang up and listen.

Got dealt pocket Aces first hand of the Main Event...

getting deja vu here. the exact same discussion happened with the exact same poster in an earlier thread. first he used math to show it was -ev, then shifted the goalposts later. almost reads word for word like this thread.

given this is a poker forum, and many postflop spots are essentially a "one-off", in that the particular hand against the particular villain in the particular situation will never be repeated in your lifetime, I don't see how you could have 4000+ posts on this forum and come to any of the conclusions you've come to. I'll give you the benefit of the doubt and assume you are a highly recreational gambler.

in summary: the original promotion seemed reasonable and they would probably get some sharp action and some NewOldGuyish action, the new version is a stingy version of what nearly any B&M casino offers. going to hold out for the one where i can earn points to get a stress ball.

Won't happen again. Math says to fold.

Eh?

That's nonsense. You can apply Kelly and EV to one-time bets. That's what sports bettors do. A bet not being repeatable does not make it any more/less attractive from an EV perspective (maybe from a utility perspective).

Actually now that I've typed this I realise you are leveling NoG. GJ.

Corrections in bold. Same for all your other cases.