Ask the Slot Expert: Ruin, variance, and video poker

A few weeks ago, I referred to Helping You Understand Bankroll Needs - Volatility on Jean Scott's Frugal Vegas blog that contained an article called "Understanding Variance" by Henry Tamburin.

Variance is a well defined statistical formula. It measures how far a set of numbers is spread out from the set's average value.

Volatility, on the other hand, is not a well defined statistical formula. It can mean whatever you want it to mean. To quote Humpty Dumpty, "It means just what I choose it to mean -- neither more or less."

In the context of the blog post, volatility and variance are used interchangeably. Henry uses the variance of a paytable to determine how volatile it is and to make some Risk of Ruin calculations.

Henry writes, "A game that is volatile means your bankroll will experience some nasty up and down swings, and if you are not properly bankrolled, you can easily tap out."

In the past few months, I've had many instances of running out of bankroll before playing NSU Deuces as long as I wanted. Maybe Henry's article can give me an idea of how underfunded I was.

Henry lists the variances of many paytables in his article. The variance for 9/6 Jacks is 19.51, NSU 25.78, and 10/6 Double Double Bonus 42.16. We'll use those numbers in a minute.

Henry gives an example of using the Bankroll Function in Video Poker for Winners to calculate Risk of Ruin (RofR). Risk of Ruin in this instance is the probability that you will run out of bankroll before achieving a certain goal.

Say you want to play 1000 hands of video poker and you have a $200 bankroll. Henry gives the RofR for these parameters playing 9/6 Jacks as 1.28%. Makes sense. 9/6 Jacks is practically breakeven and, on the face of it, it doesn't seem like too big an ask to get $1250 in action from $200 on a breakeven game.

Henry also gives the RofR for the same parameters playing 10/6 Double Double Bonus. Despite having a higher long-term payback (100.07%) than 9/6 Jacks, the Risk of Ruin for this paytable is 25.12%. That's the effect of the paytable's higher variance. As Henry points out, one-quarter of the time you will run out of money before playing 1000 hands. If you wanted to get your Risk of Ruin down to about 1%, Henry calculates that you would need a bankroll of $337.

Denomination is irrelevant to these calculations, so let's restate the parameters in terms of hands. Henry wanted to play 1000 hands with a bankroll for 160 hands ($200/$1.25). To get a 1% RofR on 10/6 DDB, Henry needed a bankroll for 270 hands ($337/$1.25).

My goal was to play 1200 hands with a bankroll for 100 hands. Although 1000 hands is a little below my goal, which is based on how many points I need to earn each visit to re-qualify for upper-tier status, I wouldn't have been too disappointed if I had tapped out at 1000 hands. Plus, I don't have the data to make a guess for 1200 hands. Nor do I have the data for a bankroll for 100 hands. So let's change my parameters to match Henry's: 1000 hands with a 160-hand bankroll.

Henry didn't do any calculations for NSU, so let's use linear interpolation to make a guess at an RofR using the data we have. After spending 15 minutes struggling before I realized that I didn't remember how to do it, I found a site with an easy-to-understand explanation of the process and I created the following table using Henry's data and an interpolated value for NSU.

Paytable	Variance	Risk of Ruin
9/6 Jacks	19.51	1.28%
NSU	25.78	7.88%
10/6 DDB	42.18	25.12%

The table tells me that if I wanted to play 1000 hands of NSU starting with a bankroll large enough to fund 160 hands, I would go bust about 8 sessions out of 100. I think I was on track to have a bust rate higher than 8%. That makes sense because I was starting with a smaller bankroll than the one used in the calculations.

How large a bankroll do I need to have a 1% chance of ruin before I played 1000 hands? Let's interpolate the bankrolls Henry calculated to find out.

Paytable	Variance	Hands
9/6 Jacks	19.51	160
NSU	25.78	190
10/6 DDB	42.18	270

It looks like a bankroll to fund 190 hands is needed to drop my RofR on NSU down to about 1%. Based on this calculation, I'm considering doubling my bankroll to make going bust really rare.

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