Table of contents
Competing Against Players at All Tables
This chapter applies to the situation where you are competing against more than just the players at your table; you are trying to finish with a higher bankroll than players at a number of tables.
The strategy is to pick out a goal bankroll size that will win. Then go all out for that number or zero. Either bust out or hit your goal.
Succeed or Bust
A large part of your edge comes from applying a simple money-management strategy: Either advance to the next round or bust out. The succeed-or-bust strategy is easiest to understand in tournaments where you know what bankroll total will allow you to advance to the next round. For example, at one tournament contestants buy in with $500 and know for certain that finishing with $1000 or more will put them in the second round. You maximize your chance of advancing to the second round by maximizing your chance of turning your initial $500 into $1000. Your average ending bankroll is about the same no matter how you bet your money, and is equal to your beginning bankroll less the casino edge on the bets you make. It also is equal to your probability of finishing with more than $1000 times the average bankroll you end up with if you finish with more than $1000, plus your probability of finishing with less than $1000 times the average bankroll you end up with if you finish with less than $1000. Maximizing your probability of finishing with more than $1000 means stopping as close to $1000 as you can when you make it, and going bust if you do not finish with at least $1000. If you do that, you have almost a 50% chance of turning your initial $500 into $1000 or more.
Setting Your Goal
There seems to be a simple square-root relationship between the proportion of contestants moving on to the next round and the bankroll required to be one of those lucky ones. For example, if one fourth of the contestants are going to advance from round 1 to round 2 of the tournament, a good estimate of the bankroll required is double the starting bankroll. The ratio of entrants to number moving on is 4, and the square root of 4 is 2. When playing in such a tournament, try to double your starting bankroll or bust out. This relationship holds best for large numbers of contestants advancing to the next round; when twenty or fewer contestants advance, the square-root relationship breaks down. By being among the last to register for the tournament, you probably can get in the final playing session. This allows you to monitor the earlier sessions to set a better target. As more and more players learn to go for bust or advance to the next round, the cutoff score will be higher.
Probability of Attaining Your Goal
A good approximation of your probability of achieving any particular target bankroll is the ratio of your present bankroll to your target. Think of it as conservation of expected value. Suppose you need to triple your present bankroll. What is your probability of doing it? Answer: approximately 1/3. Suppose you need to multiply your present bankroll by ten. What is your probability of doing it? Answer: approximately 1/10.
Attaining Your Goal
Try to avoid getting stuck with chips you cannot bet. If you cannot bet a $2.50 chip and the minimum bet is $10, avoid making a bet of $15 or any other odd number unless you are going all in. When the minimum bet is $5 and you cannot bet a $2.50 chip, bet $5 anyway and do not worry if you get a chip you cannot bet.
If Your Goal Is Within One Max Bet Of Your Bankroll
Start out betting a proportion of your bankroll equal to your advantage. Most of the time this means betting the minimum. If you are counting cards and the count is so high (or the rules so liberal) that you have a 2% edge, then bet 2% of your bankroll or less. You might be able to drift into your goal without having to make a big bet. This happens frequently at tournaments where 50% of the field advances to the next round.
If Your Goal Is One To Two Max Bets Above Your Bankroll
You will not be able to drift up to your goal with minimum bets. So if you can count cards, bet the minimum on negative or zero counts and make a large bet on positive counts. If you do not count cards, then bet aggressively whenever you feel like it. You are going to have to make some big bets sometime.
If Your Goal Is More Than Two Max Bets Above Your Bankroll
If your goal is many maximum bets above your current bankroll, then bet aggressively from the first hand. For example, in a winner-take-all tournament with a $100 buy-in and $100 max bets, it is best to go with max bets starting on the first hand. If your bankroll is greater than the maximum bet but less than double the maximum bet, then bet half your bankroll. For example, if you are trying to turn $600 into $9000 and the maximum bet is $500, start out with a bet of $300.
Last Five Hands
To be able to advance despite finishing up with a string of losses, you would like to be a minimum bet above your goal with a hand to go, two minimum bets above your goal with two hands to go, etc. For example, if you want to finish with at least $600 and the minimum bet is $10, you can smile if you have $650 with five hands to go. But if you have $620 with five hands to go, you are out if you lose all of the last five hands. In the example of $620 with five hands to go, you can use a progression and finish with $600 or more if you win any one of the last five hands, even if you lose the other four. Bet $20 on the fifth-last hand; if you win, switch to $10 bets and if you lose, you have $600 with four hands to go. If you have $600 with four hands to go, bet $30 on the fourth-last hand; if you win, switch to $10 bets and if you lose, you are down to $570 with three hands to go. Then bet $50; if you win, switch
to $10 bets and if you lose, you are down to $520 with two hands to go. Then bet $90; if you win, switch to $10 bets and if you lose, you are down to $430 with one hand to go. A bet of at least $170 on the final hand gives you your last chance to get to $600. If you win any one of those last five hands, drop to $10 bets the rest of the way and finish with at least $600. Do not double down or split a pair if losing a doubled bet would leave you short of your goal.
On the final hand of a tournament in which a fixed percentage (example: 50%) of the field advances to the next round, bet either the minimum or make a big bet. If you think your score minus a minimum bet will qualify you for the next round, bet the minimum. If you think your score might be short, you might as well bet big and qualify for sure if you win your bet. Don not try to fine-tune it to the point where a slight error in judgment makes you a high-scoring non-qualifier.
In some tournaments involving hundreds of contestants, the prize structure rewards the single highest bankroll so highly that you should try only to have that highest bankroll. Register late so as to get into the final session, and find out what the earlier session winners achieved so you can set your goal precisely. Some tournaments have required turning $600 into $6000 or more. To have a chance in such a tournament, you must bet big virtually all the time. Bet small only if you have reached your goal for the round. With a maximum bet that is small in relation to your goal, you may not get a big enough random fluctuation to reach your goal. For example, starting with $600 at a game with no house edge and playing until you have zero or $10,000, you have a 6% chance of reaching $10,000. But with play limited to 100 hands and with a $500 maximum bet, you have a 3.4% chance of reaching $10,000 and a 5.1% chance of having some cash left but less than $10,000. On marginal doubles, double down. On marginal hit/ stand, such as sixteen against 10, stand. If you are counting cards, split 10-10 at an index number one less than usual, which yields more splits of 10-10. These plays increase your variance, and thus increase your chance of reaching your goal.