Mission146
Posted by Mission146
Jun 13, 2015

What is the Expected Value

We are going to take a look at a Promotion that the High Noon Casino offers players making a deposit on Tuesdays that is actually a very valuable and relatively rare promotion.  On Tuesdays, players making a deposit at the High Noon Casino receive a Loss Rebate of 20% on their net loss for the day.

It is important to note that the High Noon Casino is a Wizard of Odds APPROVED casino:

http://wizardofodds.com/advertising/policy/

As such, if a player signs up for this casino through any of the Wizard of Odds links, such as the one on the High Noon Casino Review page:

http://wizardofodds.com/online-gambling/casino-reviews/highnoon/

If the player has a problem with the casino and the casino and the player cannot come to an amicable resolution, then the player can ask the Wizard to intervene on his/her behalf, personally, and the Wizard will do everything he can to make the situation right.  We do ask, of course, that the player at least first make an effort to resolve the situation without the Wizard's intervention and use the guarantee only as a last resort.

The 20% Loss Rebate does exactly what it says on the box.  If a player incurs a net loss playing at the High Noon Casino on a deposit made on a Tuesday, then the player will be awarded 20% of that loss back in the form of a Bonus. 

The good news is that the playthrough requirement for this Bonus is only 2x, so as a result, the player only has to put through twice the amount of the Bonus, depending on the game the player chooses to play. 

The bad news is that this is still a Phantom Bonus, which means that the Bonus amount will be deducted from the player's account in the event that the player wins and decides to make a withdrawal.  However, the player can cash out up to 10x the Bonus amount, which would effectively be double the amount lost.

In order to keep this simple, I'm going to say that the player has $500 that the player will either win or lose, and as a result, the Bonus on a loss would be $100 with a $200 playthrough requirement.  In terms of determining the actual value of this Bonus, simply adjust my final numbers based on your amount lost.  For example, if you lost $1000 and received a $200 bonus, you would simply double my final numbers.

I notice that Craps has a $1000 limit, which is good, because that's where I am going to make my $500 bet.  What I am going to do is try to win $500 by making a $500 bet on the Pass Line.  This isn't necessarily going to be the best way to go about this, but it is certainly going to be one of the easiest.

Okay, now I have a .4929 probability of winning $500 and I have a .5071 probability of losing $500.

If I lose the $500, I am going to get my $100 rebate, which I am going to use to make a bet on the Tie Bet on Baccarat for all $100.  The Tie Bet pays a very generous 9 to 1, so if I win, I will then have a balance of $1000.

The Baccarat bet would constitute $10 of my $200 playthrough requirement, so I would still have $190 in playthrough, which varies, depending on the game. 

Roulette, interestingly enough, works for .4 playthrough, or $0.40 per $1.00 bet, so that would only be $475 left in total bets which represents an expected loss of about $6.42 on the French Roulette.

Okay, so at this point the player would have a balance of $993.58 from which $100 would be removed leaving a new balance of $883.58, or, $383.58 more than that with which the player started.  Awesome!

When it comes to the important bets, there are only really three possibilities.  The player can lose at Craps and lose the Baccarat Tie Bet, lose at Craps and win the Baccarat Tie Bet, or simply, win at Craps.

(500 * .4929) + (383.58 * .5071 * .095156) - (500 * .5071 * .904844) = 35.5359226032

Okay, so as we can see, the Expected Value of this overall play is a profit of $35.54, approximately, on an initial outlay of $500.  In total, then, this represents an overall advantage of 7.108%. 

In my opinion, the best part about this is the probability of winning.  The casino actually has to beat you at two bets and the probability of the casino doing so, under the situation above, is  about 45.88%.  Not only does the player have the advantage, but the player is ALSO more likely to win than lose.

There are other ways to do it, of course.  For instance, the player could begin by making an initial bet of $500 on the Hard Eight or Hard Six bet at Craps and then revert to Baccarat Tie Bet:

(.0909090909 * 4500) + (383.58 * .90909090 * .095156) - (500 * .9090909090 * .904844) = 30.9799437411

The expectation is obviously going to be less due to the higher House Edge on the Hard Eight or Hard Six bet rather than the Pass Line bet.  The probability of winning is also considerably lower, however, this does give a player the opportunity to go for even a HUGE win at an advantage.

In my personal opinion, this is one of the strongest promotions out there because it is one of the few that combine the opportunity for a positive Expected Value with a relatively high probability of winning if a player chooses to do the Pass Line at Craps method.  How often can a player have an advantage of over 7% on a bet that the player is expected to win more often than lose?

The best part of this promotion is that it can be redeemed up to three times, so if it doesn't work out for the player the first time, the player can get another chance.

From the standpoint of an Advantage Player, also, this is going to be nice because of the negligible amount of time it will take to do this.  Depending on the kind of Variance the player wants to deal with grinding the playthrough requirement on Roulette, if it comes to that, this could really be over in as little as six total plays.  Personally, I would tend to bet Roulette at $1 on either Red/Black for the 475 spins to reduce my Variance.

The other thing is that it won't necessarily come to that because the player could always win the initial Craps bet, which itself has a 49.29% chance of happening.  In fact, if the player makes this play 20 times, then the player could expect to lose at Craps and win the Tie Bet, in that order, just under 1 in 20 times, so it's going to be rare for the playthrough thing to even become relevant.

And, if it does become relevant, you've already won, so you can take the amount you expect to walk away with and divide that by your time played for your hourly profit.

This is a strong, strong promotion.  One of the best I've seen.  Enough said.

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