How Do I Figure? – Gambling With An Edge

I received the following email. It requires more analysis than I normally do without charge for strangers, but since I can get a column out of it, why not?

Upcoming video poker excursion commencing Friday, leaving Saturday evening.  

 Playing exclusively $1 9/6 JOB 99.54%.  

 My Offers for this Trip:

 1 night comp’d in the best tower on a Friday night, no taxes or resort fees.  

  1. $50 Walmart Gift Card to pick-up (Friday)
  2. $50 Bonus Slot Play (not sure if this can be played on VP since I’m fairly new to the casino) – Saturday only
  3. 4x Tier Credits all day Saturday 7a-midnight – likely all of my play will be Saturday

 How do I calculate whether I have an advantage or not, or is it even mathematically possible? 

Okay. I wasn’t given enough information to completely analyze this, but let’s give it a shot. The following are things to consider in no particular order:

9/6 Jacks or Better does indeed return 99.544% — if you play it accurately. Many players do not play it accurately. You don’t automatically receive that return by showing up. So, how well do you play this game?

A free room is nice, and a nicer room is better than a standard room, but I don’t include this in my calculation as to whether or not I have an advantage. I have a place to stay at home that I’m paying for whether I’m there or not. Just because other people might be charged $200 to stay in that room doesn’t mean that me not paying for it adds $200 to my equity.

On the other hand, how much is it costing me to get to this casino? If it’s 15 miles away, I’m not taking that into consideration (other than for tax reasons.) If it’s 1,500 miles away and I have significant expenses to get there which are not being reimbursed by the casino, then that definitely should count as negative Expected Value.

If you view playing video poker as a hobby, and hobbies cost money, then it can be easy to justify an airfare expenditure as part of the cost of enjoying your hobby. But this does not mean that you’re gambling with an edge. It means you are, maybe, paying less than retail to enjoy your hobby.

I include the gift card and free play at face value. To be sure, I’d rather have $100 in cash than a $50 gift card and $50 free play, but it’s “close enough.” If it were a $50 Chevron card, however, that’s not worth so much to me. Nothing against Chevron. It’s just that I drive an electric car and don’t buy gas.   

This letter stipulates that he picks up the gift card on Friday but isn’t going to play until Saturday. Are you going to spend the rest of Friday costlessly? 

Picking up a gift but not playing on a particular day may or may not sit well with the casino. Doing this occasionally is no big deal. Making a practice out of it may well cause the casino to stop giving you these gifts. Remember, even though players generally see these gifts as a reward for past play, casinos generally see these rewards as an incentive to get you to come in and play more. If you collect the gift but do not play more, and do this regularly, some casinos will punish you by not giving you these rewards in the future. 

Playing 9/6 Jacks or Better costs you, on average, $45.60 per $10,000 coin-in. It isn’t specified how much is going to be played. If you only play $1,000 that weekend, it’ll cost you $4.56 on average, but you’re not likely going to get these offers in the future. If you play $100,000 that weekend (not likely on a $1 single line game), your expected loss is $456, which swamps the offers you are scheduled to received.

The $50 in free play and the $50 gift card are “one time stock amounts.” The losing of $45.60 per $10,000 coin-in is a “recurring flow amount.” You can’t really add up stock amounts and flow amounts. If you say, I’m going to play $xxxx amount of coin-in, and that is going to cost me 0.00456 * $xxxx, then the Expected Value of what you’re going to play becomes a specific stock amount which can be offset by the other stock amounts. But so long as it’s a nebulous amount of play, the amounts are not addable.

You mention that you’ll receive 4x tier credits. That’s nice. That’s clearly better than 2x tier credits. But I have no idea what tier credits are worth at this casino to you. (I don’t know which casino or even in which state this casino is located.) Are you planning on playing enough to reach a particular tier level in the requisite time. (Usually, tiers are recalculated annually or semi-annually. January 1 through December 31 is perhaps the most typical time interval to calculate tiers, but it can be April 1 – September 30, or any other interval.)

If a free (actually “highly discounted”) cruise is part of your tier benefits, is this something of value to you? Some people like cruising. Some don’t. Some have a cruising partner. Others don’t and may not like taking a cruise unaccompanied. If a daily free buffet is a tier benefit, and you’re only going to be at this casino for four days the entire year, then this isn’t such a big deal. Even if you plan to be at this casino fifty or more times, eating at the same place so frequently gets to be rather tiresome. If free internet is a benefit but you’re wary of using free internet and always travel with your own secure hot spot, then this benefit isn’t worth anything to you. You get the idea. A list of benefits in a brochure is not the same as the value to you – which may very well be different than the value of the same tier level to me.

You mention tier credits. Do you earn other credits and how much are they worth? The Caesars system, for example, gives you Reward Credits as well as Tier Credits. You can spend these RCs for food, merchandise, and other things. You can even turn them into free play — discounted 50%. Is there anything similar to this at this particular casino?

Are there other benefits you didn’t mention? Perhaps drawing tickets for a new car at the end of the month? You’re not likely to earn enough tickets playing one day of single-line dollars to give you a meaningful shot at this, but if you’re going to be at this casino anyway when the drawing is going on, surely this drawing is worth something.

Finally, unless this is your last time at this casino ever (in which case your tier level is irrelevant), you’ll be earning benefits down the road for your play this time. You might get free play in the mail. You might get future offers similar to the current one. You can’t take this one weekend in isolation. It’s part of the overall package.

I go through this kind of calculation for every offer I get. I play at enough casinos that I frequently have choices of offers at more than one place. I use the process described here to rank these offers. Sometimes I can take advantage of two or more offers in the same time period, but usually they are mutually exclusive.

And whatever answer I come up with this weekend, next weekend I’ll go through the same process again to decide what to do then.