Gambling Theory and Other Topics

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Product Details

  • ISBN-13: 9781880685037
  • Publisher: Two Plus Two Publishing, LLC
  • Publication date: 5/28/1999
  • Edition number: 4
  • Pages: 313
  • Sales rank: 1,013,950
  • Product dimensions: 5.40 (w) x 8.50 (h) x 1.20 (d)

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Non-Self-Weighting Strategies

What is the most important gambling concept that there is? Which concept separates the winners from the losers? What is the one idea that permeates all successful thinking and theorizing on the subject of gambling? In my opinion, it is the little-known statistical concept of self-weighting versus non-self-weighting gambling experiences.

A self-weighting gambling experience is when your expectation and variance are the same from play to play. But what does this mean, and why is it so important? To answer these questions, let's start with a simple example.

Suppose you make a trip to Las Vegas, walk up to a craps table, and start betting $1 every time you roll the dice. You do this for 10,000 rolls, and then suddenly on the next roll you pull $1 million out of your pocket and put it all into action. Now how many times have you rolled the dice? Well, there are two answers, both correct. The mathematicians will say 10,001 times, but the statisticians will say one time simply because your results are all clustered around that one big bet. Notice that during the first 10,000 rolls of the dice, we were looking at a self-weighting gambling experience. But after that $1 million bet came along, we had a very non-self-weighting gambling experience. Incidentally, and this is important, all successful gamblers are statisticians, not mathematicians.

Why are all successful gamblers statisticians? To answer this, think about the games that can be beat. This includes poker, blackjack, sports betting, and progressive slot machines, just to name a few. It does not include roulette, craps, baccarat, super pan nine, and non-progressive slot machines. The reason the games in the first group are beatable is that successful non-self-weighting strategies are available. This is not true of the second group. Their self-weighting characteristics mean that the player will never have the best of it. To understand this, let's take a closer look at poker.

Suppose you are a Southern California poker player. Your game is high draw, jacks or better to open, played with a joker that either counts as an ace or can be used to complete straights and flushes. You are dealt a pair of aces. How should they be played?

The typical player plays this hand in a very straightforward manner. If no one has yet opened, he will open; If someone already has opened, he will call. Notice that this is a self-weighting strategy. In other words, there is very little difference in how this hand is played. Also notice that self-weighting players are very predictable opponents, and very predictable opponents are the easiest to beat. This is true in all forms of poker.

Now what about the expert high draw player? How does he play a pair of aces? Well, most of the time he will open when he is in an early position, but not all the time, especially if his other cards are small. (The small cards maximize the chances that someone else will be able to open the pot.) If someone else already has opened, the expert will call most of the time, but not all the time. If his opponent has opened very late, where most players are likely to play any minimum opener, such as a pair of jacks, he will raise. If a tight player opens early, the expert knows that he is (1) up against a quality hand and (2) less likely to be against a pair of aces, since the two aces in his hand reduce the chances that his opponent is also holding a pair of aces by 70 percent. (Not 40 percent as many people think. This is because there are 10 ways you can pick two aces out of five, while there are only three ways you can pick two aces out of three.) Consequently, there is a good chance the opener has a pair of aces badly beat. The expert player would throw his hand away in this situation, especially if several players still remain to act behind him.

It should be obvious from this example that the expert player is following a non-self-weighting strategy. Even though he does not play as many hands as his self-weighting counterpart, the expert still puts about the same amount of money in the pot. This is because he gets full value for some of the hands he plays, while his typical self-weighting opponent does not.

By the way, it doesn't matter what kind of poker game it is. The expert players, who consistently take home the money, all follow non-self-weighting strategies. One claim I've made is that the low-limit jackpot games in California can easily be beaten. Most people believe just the opposite, simply because the house takes a lot of money out of the pot to pay not only for the game, but for the jackpot as well. (For those readers unfamiliar with jackpot poker, a player wins the jackpot when he has a powerful hand beaten such as aces full or better in high draw or a six-four in lowball.) These jackpots become quite large, sometimes as high as $40,000 in certain games.

The jackpots have a unique effect on almost all players, turning them into self-weighting opponents. What happens is that typical players now have an incentive to play many more hands. Also, they don't want to make marginal (value) bets and raises - where the real money is won in limit games - simply because they are more interested in survival and shooting for the jackpot.

Remember, the more self-weighting your opponent is, the poorer he plays. An extension of this is that the more self-weighting opponents you have, the easier a game is to beat. As we have seen, in the typical jackpot game, almost everyone follows self-weighting strategies. This is why I argue that an expert player, who follows non-self-weighting strategies, can easily beat these games. The drop and the rake should be a small price to pay for the privilege of going home a winner. Summarizing, we see that in games with a jackpot, there are non-self-weighting strategies available that allow the expert player to compete with a positive expectation. The non-self-weighting player waits until he has the best of it and then takes maximum advantage of the situation. That is, he will make as big a bet as possible and take advantage of a very small edge if that is all the edge he has.

However, even though you have the best of it, this doesn't mean that you are going to win. In addition, following a non-self-weighting strategy has the statistical effect of decreasing the overall sample size. This leads to two related topics that will be covered in Part Two of this book: fluctuations, which every skilled gambler suffers from, and the "extremely silly subject of money management."

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Table of Contents

Foreword by David Sklansky V
Introduction 1
Using This Book 5
Part One: Gambling Theory 7
Introduction 8
A Good Bet 9
Non-Self-Weighting Strategies 10
Non-Self-Weighting Strategies Revisited 14
Sequencing 20
Non-Self-Weighting Poker Ideas 24
Afterthought 27
Part Two: Theory in Practice 29
Introduction 30
Fluctuations 31
The Extremely Silly Subject of Money Management 34
Special Note From Mike Caro 39
How Much Do You Need? 41
What About the Losers? 54
Computing Your Standard Deviation 60
Win Rate Accuracy 64
What if You Play Blackjack? 66 Two Tales: The Bullfrog and the Adventurer 75
Free Bets and Other Topics 81
Skills Required to Hit the Big Time 93
Traps to Avoid 99
Supplemental Skills 103
California or Nevada? 106
Jacks-Back 113
Seating and the Interclass Correlation Coefficient 118
Betting and Game Theory 121
Which Count Is Best? 125
Tipping 128
Afterthought 130
Part Three: Pseudo Theory Exposed 131
Introduction 132
Lottery Fallacies 133
Dangerous Ideas 146
The Myth of the House Advantage Revisited 164
Bingo System Fallacy 169
Afterthought 171
Part Four: Poker Tournament Strategy 173
Introduction 174
To Rebuy or Not To Rebuy 175
Tournament Strategy 184
Settling Up in Tournaments: Part I 200
Settling Up In Tournaments: Part II 204
Settling Up in Tournaments: Part III 208
Afterthought 212
Part Five: New Games 215
Introduction 216
Preliminary Pai Gow Poker Information 217
A Few Pai Gow Poker Observations 223
Pai Gow Poker Tournament Strategy 226
Pan Nine Strategy 230
Afterthought 240
Part Six: Gambling Fantasy 241
Introduction 242
The World's Greatest Semi-Bluff 243
The World's Greatest Gamblers 248
The World's Worst Gamblers 255
Self-Weighting Disasters 261
The Adventurer in Action 265
Some Creative Bad Beats 268
Building Pyramids 273
Afterthought 275
Conclusion 277
Appendix A: Opinions of Various Books 279
Poker 280
Blackjack 296
Other Topics 302
Appendix B: Maximum Likelihood Estimator for the Mean and Standard Deviation 311
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