Math Question on a Slotplay Promotion

[wwcd]

I wanted to ask about the math behind Westin Casuarina's new member signup promotion. They match slot losses up to $50 within 24 hours of your joining their player's club. The match is via freeplay, and there is no limitation for the match play up to $50. You can always go to their desk and request $20 freeplay for your $20 loss, or $50 freeplay for your $50 loss, but you can only ask for it once.

Just out of curiosity, I want to value this promotion, but I am having a hard time, I think main reason being that I don't know the exact volatility figures for slot games.

From my stock market experience, this promotion seems like a call option, where your downside risk is limited (premium you paid for the call option or house edge for the $50 freeplay in case you end up not winning anything), and upside potential is somewhat unlimited. I think in valuing this promotion, one has to know what that potential upside is, which is driven by the volatility.

The difference is that, for highly volatile stocks, you pay a higher premium on the option, but in this promo, you can play the highest volatility slots, but your premium is fixed (house edge on the $50 freeplay that they give you, when you lose your own $50). So, logic says, one should play the most volatile slots for getting the most out of this promotion.

Another way to approach this question is on your quest to losing $50 to win bigger amounts, what is the win amount that you should stop at? Say on your first spin, you hit $20 payout, should you stop, or should you continue playing until you hit something bigger or lose $50, whichever comes first? And how much is that "something bigger"? $50, $100, $500?

For simplicity, you can assume the following payout values:

- 95% payback on non-volatile slots (these are the ones you will use your $50 freeplay, in case you lost your own $50)
- 90% payback on volatile slots (these are the ones you will use your own $50 in order to win something big, until you lose the $50)

Also once you identify the most volatile slot, is it better to do one spin valued at $50, or 50 spins valued at $1 each? I'm thinking the former, but I'd like to hear your opinions as well. For simplicity, assume there are slot machines available with various denominations, and there are no taxes.

 

[tensplitter]

Use it on a video poker machine

 

[shadroch]

Use it on a video poker machine

Why?

 

[wwcd]

Use it on a video poker machine

OK, fair recommendation, but when do you stop? Say you hit a straight in the first draw, do you stop? How about a flush? a 4-of-a-kind?

 

[sabre]

The higher your target, the higher the EV of the promotion. (within reason, if you set your target too high, then you end up wagering too much and exposing yourself to the house edge ... this is why volatility is good.)

Say hypothetically that you could play the $50 on a roulette game. And you might actually be able to do that if they have electronic roulette there. Also, assume that the rebated $50 is worth exactly $50.

Option 1) Bet on red. Pays 1:1
Option 2) Bet on the first column. Pays 2:1
Option 3) Bet on a single number. Pays 35:1

The EV for each option is

1) $50*(18/38) = $23.6
2) $50*2*(12/38) = $31.6
3) $50*35*(1/38) = $46


Video poker isn't a bad option. I would play until you hit 4oak or better.

 

[wwcd]

The EV for each option is

1) $50*(18/38) = $23.6
2) $50*2*(12/38) = $31.6
3) $50*35*(1/38) = $46

I have hard time following this. Your EV should be the same in each bet.

1) With 18/38 chance you will get back $100, and with 20/38 chance you will get back $0, so it averages to $47.37, hence the EV for your $50 bet is -$2.63.

2) With 12/38 chance you will get back $150, and with 26/38 chance you will get back $0, EV ends up being the same.

Same works for #3 as well.

Your hit frequency will be lower, hence volatility will be higher as you move from #1 to #3, however the EV will always be the same.

 

[shadroch]

I would use the first $50 on a game like Goldfish that has the potential to give a large payout. I'd play 100 play penny poker with the $50 rebate assuming your goal is to recoup your losses.
However, I think I would go for the fences with both the original money and the rebate. It's like getting to play $100 worth of slots with a 2-4-1 coupon.