A Self-Weighting Strategy Is Sometimes Best

Years ago, Mason Malmuth distinguished between self-weighting and non-self-weighting strategies. His thoughts on this topic are still available in his book Gambling Theory. Basically, a self-weighting strategy (SWS) consists of making a large number of bets of approximately the same size. This leads to a result that approximates your average advantage or disadvantage. A non-self-weighting strategy (NSWS) is one that makes some smaller bets and then makes occasional large bets. A successful NSWS makes large wagers when the player has a big advantage. As a simple example, a blackjack player who flat bets will end up losing between one-half and one percent of the total amount of his wagers. A blackjack card counter makes small bets until the remaining cards are good (lots of high cards) and then makes large bets. This will allow a skilled player to gain an overall advantage since his total bets with an edge outweigh his bets with a disadvantage. A simplified NSWS for successful poker players consists of trying to get more money into the pot when they have an edge, and also playing for higher stakes when the competition is weaker.

Thus, we see that in many situations an SWS is inferior to an NSWS. This isn’t always the case. Daily grinders often successfully follow a macro SWS by playing the same game at the same stakes. Even within this limited situation, the use the NSWS technique of trying to get more money in the pot when they have an edge. They may add another NSWS component to their game, by taking occasional shots at higher stake games when they appear to be particularly weak. During the World Series of Poker, however, I frequently see players abuse the idea of NSWS by wagering the most in situations where they have little or no advantage. In fact, they may take the most risks when they are underdogs.

Let’s look at tournaments first. A disciplined tournament player with a small edge can follow an SWS strategy by playing in tournaments with approximately equal buy-ins. I think a range of $500 to $1,500 makes sense. Even after you have played 100 of these, there is still a large luck factor, but your overall result will often be representative of your advantage. Suppose instead the player adopts an extreme NSWS, and adds in a few high roller events, such as the two WSOP $50,000 events. Now their overall result will correlate strongly with their results in these two events. Look at this exaggerated example. They play in 100 tournaments with an average $1,000 buy-in, and double their money, but fail to cash in the two high-roller events, and thus break even overall. 100 wins and two losses lead to breaking even. Someone else fails to cash in 100 small tournaments and one high-roller, but logs one reasonable finish in the other, ending with a $200,000 win, and a net profit of $50,000. But in this case 1 win and 101 losses lead to a small profit. Remember the two events, which had the most influence on their result, also consisted of the best players trying their hardest.

I also see cash game players make a similar mistake. They are consistently grinding out a medium stake game, like $2-$5 or $5-$10, but then one-night leap into a nosebleed game like $50-$100 or $100-$200. Usually they make this error on a night when they are losing and steaming. Thus, they adopt the NSWS at a time when they are probably not playing at their best. As with the high buy-in tournaments, high-stakes cash games contain the best players.

The takeaway is this: Follow a non-self-weighting strategy if you can risk the largest percentage of your bankroll when you have the biggest edge. It is okay to take a shot when you are a huge favorite. Avoid the NSWS when your largest wagers will occur when you have the smallest advantage or even a disadvantage. You generally find the best players in the higher stake games and tournaments. So, when it comes to selecting games or tournaments, a simple non-self-weighting strategy may be your best choice. ♠

Steve ‘Zee’ Zolotow, aka The Bald Eagle, is a successful gamesplayer. He has been a full-time gambler for over 35 years. With two WSOP bracelets and few million in tournament cashes, he is easing into retirement. He currently devotes most of his time to poker. He can be found at some major tournaments and playing in cash games in Vegas. When escaping from poker, he hangs out in his bars on Avenue A in New York City -The Library near Houston and Doc Holliday’s on 9th St. are his favorites.