Chat wih Rob Singer
Earlier this summer, a reader asked my opinion about a June 24, 2009 interview of controversial video poker writer Rob Singer conducted by John Brokopp. For those unfamiliar with Rob Singer, he is former writer for Gaming Today, and he has two books published about his strategy for playing video poker. Briefly, Singer ridicules the mathematically based strategies that skilled players like me employ. Instead, he follows a progressive betting system, setting a small winning goal each day and ramping up the denomination of his bets until he hits his winning goal. He does not detail a holding strategy but advocates playing more conservatively than skilled strategies in some situations. It should go without saying that my position on video poker is 180 degrees away from Singer's. I had always filed Rob Singer with John Patrick in my folder of people who do not merit serious discussion.
However, I also consider one of my niches to be exposing casino cheating wherever I can find and prove it. According to the Brokopp article, Singer claimed to have conducted an extensive test of video poker games in Las Vegas and Laughlin to prove the draw is not random. Singer's hypothesis is that when the player keeps a two pair, four to a flush, or four to an outside straight, the card he gets on the draw will be the same rank as the one he discarded a disproportionately high number of times. To test his hypothesis, he claims to have played 40,000 hands of video poker on a single-line game. Of these 40,000 hands, 4,685 were one of the three situations above. Of those 4,685 hands, he claims he received the same rank as the discarded card 2,211 times.
The probability of drawing the same rank as the discarded card is 3/47 (three suits remaining of the discarded rank divided by 47 cards left in the deck). In 4,685 opportunities, you would expect to get the same rank on the draw 4,685 * (3/47) = 299 times. The 2,211 Singer claims he saw the same rank is 7.4 times expectations. That is 114 standard deviations too high. That is truly off the charts. Excel can't handle numbers that close to zero, without calling them zero, but if the probability were 1 in x, then x would be a number with thousands of digits.
With all due skepticism, I felt I would be remiss in my duties if I didn't at least give Singer a chance to make his case. So I approached him, I think through his web site vptruth.com. He quickly responded, and he knew who I was. So I asked him about his evidence. I think proper documentation would include dates, casinos, and machine numbers of when and where his experiment was carried out. That was not given to me. I imagine he kept a simple running tally. He did mention that after the Brokopp interview another skeptic contacted him, leading him to play at the M casino with this skeptic through 180 qualifying opportunities. Of those 180, he observed the repeating rank 11 times. The expected number is 180 * 3/47 = 11.5, so nothing there. Although he did not make a convincing case via e-mail, we decided to meet anyway to do our own test, and to get to know each other a little better. I'm sure many gambling writers and advantage players will be disgusted that I even gave Singer an audience. However, I'm of the opinion that the world would be a better place if disagreements were approached with face-to-face communication, as opposed to personal insults, or worse.
Singer and I met on August 30, 2009 at the Red Rock casino for about an hour. I found him to be pleasant and soft spoken. I did not know that he has an impressive resume. He has a BS degree in electrical engineering from Northeastern and an MBA from Boston College. Before devoting himself to video poker, he worked for the government in the Middle East and for Motorola and Northrop-Grumman throughout the world. Today he is a grandfather, living in Arizona, making occasional trips to Las Vegas and Laughlin. From 1990 to 1996, he gave video poker advantage play the old college try and lost about $250,000. Then he cast aside everything sacred to skilled play and developed his own betting system and strategy. He claims he has nearly accomplished his goal of winning a million dollars following his strategy, and has the tax returns and bank statements to prove it. I did not ask to see them. His strategies cannot be put to a computer simulation, because Singer doesn't buy the assumption that video poker machines play fairly. He says he doesn't know exactly how they work, but his strategies allegedly exploit patterns he has observed through the years.
Before I go further, let me make it perfectly clear that I absolutely believe that every video poker machine made by a major manufacturer is completely fair and random. A Nevada Gaming Control Board regulation states the following:
"For gaming devices that are representative of live gambling games, the mathematical probability of a symbol or other element appearing in a game outcome must be equal to the mathematical probability of that symbol or element occurring in the live gambling game. For other gaming devices, the mathematical probability of a symbol appearing in a position in any game outcome must be constant." Source: Regulation 14.020.2b (PDF, 87K)
Having known many people that work for the slot machine makers, I feel strongly that this regulation is followed. Thus, I feel every video poker machine in Nevada is fair. That opinion does not necessarily extend to other states where a video poker game may just be an illusion, fronting for an electronic pull-tab game.
For our last half hour, I suggested we play a 50-play video poker game to get a bigger sample size. Singer remarked that multi-play video poker may not play the same way as single-play but he would give it a try. We observed 10 hands that met his criteria for the fifth card test. With 50 hands on the draw, you would expect a duplicate rank on the 5th card 10*50*(3/47)=31.9 times. We observed it 29 times. So that test was close to expectations, much like the aforementioned test at the M. I told him that I would be willing to play any video poker machine in Vegas or Laughlin if he could give me results indicating a non-random game specific to that machine. He said he is semi-retired from video poker and could not promise anything.
So I remain very unconvinced of his assertion. I did not try to debate him on the overall merits of his unorthodox video poker strategy. Without an agreement that the games are fair to begin with, there is no common ground to have a discussion about it. I will say that he was very friendly and respectful toward me, despite the fact that I'm sure he vehemently disagrees with me about video poker. He also had a good sense of humor. His pseudo-name, Rob Singer, was chosen as a parody of the name of his main nemesis, Bob Dancer. If he ever writes to me again with more evidence of his claims, I would be happy to entertain them.