I'd like to hear what people have to say concerning how often a knowledgeable bj tournament player will advance in a typical blackjack tournament round using a table advance format compared to random chance. Clearly there are lots of variables. How bad are the other players? How strategy friendly are the rules? Just how good is the knowledgeable player? Maybe it matters whether we are talking about one player advance situations versus two player advance situations? Do any of you keep careful records of tournaments that you have played in so that you can provide empirical results for your actual playing? If not, how about some opinions? If you want a more concrete example to work with, suppose we have five players at a table with one advancing. How often should the knowledgeable player expect to advance? Is it 25% of the time, 30% of the time, 40% of time,...?
First, we have to define Knowledgeable player. You have two types blackjack experts and tournaments experts. A blackjack expert, compared to a novice player, will only have minimal advantage. So, in your example maybe 25% compared to random of 20%. A tournament expert will have a higher % probably around 40% compared to random of 20%. These are just guesses, though.
First of all, we must acknowledge that none of us will ever play enough tournaments in our lifetime to record results that will be statistically valid. With that said, there is one particular tournament which I have played 75 times and for which I have records for my results both as a knowledgeable blackjack player and a knowledgeable tournament player. The first round of this tournament is a 2 advance from 7 format, so by random chance one advances 28.57% of the time. Here is the breakdown of my results for 75 actual entries: Overall: 19/75 = 25.68% --- almost 3% below expectation As a knowledgeable blackjack player, but before I started to learn about tournament strategies: 3/27 = 11.11% --- well be low expectation. One might even say that my chances of success were reduced because I thought I knew what I was doing, but actually didn't. I had figured out on my own about correlating bets in order to protect a lead, but not much else. On the other hand, I actually won the tournament during this phase by using a progressive betting scheme (not martingale) as my main strategy and correlating on the final few hands. This proves that anyone can get lucky enough to win a major tournament. Since I began studying the game (about 9 years) my results are 16/48 = 33.33%, which is above expectation. In the past 5 years my results are 12/22 = 54.55% -- well above expectation. I have finished second during this time period. As I said, we can't draw any meaningful statistical conclusions, but there does appear to be a trend of increasing success for me in this event as my experience and knowledge grows.
From a statistically valid point of view, my software has a tournament module which allows me to model the actual tournaments that I play. I also have a large number of tournament bots, each of which plays different strategies and end games. I am able to allow the bots to compete against one another over the course of millions of tournaments to see which ones tend to perform better for different formats and conditions. Some of these bots are smarter than others and I can say that the smarter ones do out perform the others and often achieve advancement rates far above par.
There is no way we can ever answer Kelly's question using an empirical analysis of actual tournament play. We could never get enough data from actual tournament play to develop a statistically meaningful model. The best we can do is to develop software bots like gronbog's and then run simulations over billions of tournaments. Some question the validity of bots in simulations because actual human beings aren't computer programs. However, thoughtfully designed bots tested over billions of tournaments in simulations are probably very accurate facsimiles of what the aggregate of human behavior would theoretically be over billions of trials.
There are simple ways to add some humanity to the bots. For example, random heuristics can be added so that the bot makes certain errors with a certain probability. Having said that, it is also useful to see what the potential of perfect or near perfect play is. I would also like to add that the best early/mid/late round strategy for a given tournament often depends on the general skill level of the rest of the field. After I have played an event a few times, I am able to seed my simulation of the event with bots which correspond by percentage to the general skill level and actual strategies that I observe while playing it.
