Hello GM. long-time reader, first-time writer. I'm writing to let you know of my first experience with Video Poker and to ask you a couple of questions. Here's the story:

I just got back from a trip to Vegas and played a lot of Jacks or Better Video Poker. I found "Full Pay" machines at the Luxor for $1-$5. I was using the "Simple Strategy" I printed from The Wizard of Odds (http://www.thewizardofodds.com/game/jacksorbetter_simp.html). Anyways, the Comp Card provided an easy mechanism to keep track of my play. At $5 per hand, 3 hands were required to receive 2 points. By the end of the trip I had 3000 points, which meant I had played 4500 hands. I spent other time at the BJ table, but never presented my Comp Card, because they don't "rate" you at the cheap tables, so I know all points were accumulated on the Video Poker machines. My sessions were always done with $100. I would stop if I reached $0 OR, if I cleared any $100 interval, I would stop as soon as the money made it back down to a rounded $100 interval. This would make keeping track of the money won/lost easier.

Total Money Bet: 4500 hands * $5/hand = $22500
Expected Return Rate: 99.46% (as per the Simple Strategy)
Expected Loss: $22500 - ($22500 * 99.46%) = $121.50
Actual Loss: $1000
Actual Return Rate: 95.56%

Here's the Major Hand Breakdown I received:
0 Royal Flush
0 Straight Flush
3 Four of a Kind

Here's a table of Probabilites for the different hands (http://www.thewizardofodds.com/game/vidpoktables.html#jacksorbetter). If I'm reading that right, here's how many hands (on average) you can expect to play between each "hit" of a hand, how many I "should have" had, and the payout that I am "owed":

Royal Flush: 1 every 38,462; 0.117 total hands expect; (0.117 - 0 received) * $4000 = $468
Straight Flush: 1 every 9000; 0.5 total hands expected; (0.5 - 0 received) * $250 = $125
Four of a Kind: 1 every 424; 10.61 total hands expected; (10.61 - 3 received) * $125 = $951

Obviously, I made up for all these hands with other lower paying hands, or I'd be down close to $1700. I understand there's no such thing as 0.117 Royal or 0.5 Straight Flush, and I'm not really concerned with their "expected payout". I was kind of shocked at how far "behind" I was in the Four of a Kind. Is this a major anomaly? Also, in case you're wondering, I practiced using the following Java game that would correct you if you made a mistake (http://www.thewizardofodds.com/java/vidpok2/vidpok.html). I played it enough that I can say I never made a mistake for the last 2-3 hours I played it. Also, I know 4500 hands is hardly the "long run" and I haven't lost hope. I just feel like I'm "owed". :)

I did want to let you know I'm a big fan of the mathematical/logical approach you take to gambling. I'm sick of hearing about "betting strategies" such as "Increase after win/loss", "Cards run hot and cold", etc. without mathematical/simulation evidence to back it up. I usually play BJ, but wasn't willing to bet $25/hand just to be Comped (although I might start). I was turned on to Card Counting by your advice and practiced it a lot and am fairly proficient. Of course, the tables at both Vegas and AC have become tougher and tougher (more decks, little penetration, house favored rules), making it difficult even for the Counter. What pains me is that I've now gone to Vegas twice and AC half a dozen times (4 hours away by car) and I've NEVER come out ahead. Prior to this last trip, I always played BJ and counted. I know, I know... I hardly have enough play for it to be considered the "long run". But still, you would have thought ONE time I'd come out ahead. Meanwhile, my buddies don't play perfect or go to "less than favorable" games and they will win. Oh well, now I'm just ranting...

I did enjoy the Video Poker, and if my real loss had been my expected loss of $121.50, I would have been thrilled. I received approximately $200 in Comps. If that continues, I'll be playing for free. :)

Thanks for taking the time to read this and for all the great information you provide!

Jeff

Hello, Jeff.

Thanks for taking the time to write. I appreciate your compliments.

Receiving only three 4Ks in 4500 hands of play is unusual, but not impossible and, since I think the casino's games are probably honest, it's just a case of "bad luck", which was amplified by a relatively small sample size. The 99.5% expected return is, as you undoubtedly know, a figure that will be realized only in "the long run", so to have lost at a rate of 4.5% isn't a surprise. In fact, it's very typical and, if you are going to pursue Video Poker more seriously, my advice is simple: get used to it. It's just the nature of the beast, I'm afraid. For some background on what to expect, check out my article, "Is This Game Rigged? -Part 2", which is in the archives of the GameMaster's Secrets page of my site. But I'm glad to see that you're keeping accurate and detailed records of your play, because that's very important so you'll always know where you stand. The culprit here is "variance" which is just a fancy way of saying that you spend a lot of time losing, then, Boom!, along comes a Royal and you're back to even or ahead. The tough part is that we never know when those elusive rascals are going to show up. Also bear in mind that full-pay Jacks returns less than 100%, so you're destined to lose in the long run, but you obviously have a good handle on how comps and cash rebates can get that return over 100%. You have learned well, grasshopper. It's probably the same story with your Blackjack play. You just haven't gotten to the "long term" yet, but it will come, although you probably don't have a very big edge over the games they deal in AC. But be patient, because although your friends are winning now, in time the odds will get them and you'll be on a huge winning streak that they'll talk about for years. You're exactly correct when you say you are "owed". That's the joy of relying upon math to play these games, rather than relying upon luck.

Yours for winning,
The GameMaster
10/17/02