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入正题：

Introduction to SNGs

Measuring success

In cash games, players quote their profit and losses in terms of big bets per 100 hands, or sometimes big bets per hour. This allows comparison of win rates across different limits. In SNGs, win rates are quoted as a percentage, called Return On Investment, or ROI. This is simply total profits divided by total buyins, including the vig. For example, if you have made a profit of $660 over 100 $50 5 SNGs, then your ROI will be 660/5500 = 12%.

Standard prize distribution

In most 10-man SNGs, 50% of the prize pool is paid to the winner, 30% to second place and 20% to third place. This prize structure will be assumed throughout this book.

The difference between tournaments and cash games

In a cash game, if a player stands to either lose $500 or win $500 on a given hand, with an equal probability of each outcome, then his expectation is exactly neutral. The axiom underlying this is that a dollar is always worth a dollar, in any context.

In tournaments, chips are not always worth the same amount. Consider a 10-man $100 buyin SNG where everyone starts with 1,000 chips. In total, the 10,000 chips in the tournament therefore have a value of $1,000. At the end of the tournament, someone will have 10,000 chips, but they win only 50% of the prize pool. The value of those 10,000 chips has diminished to $500.

To determine the correct plays in tournament situations (especially in SNGs), we need a way to find out the exact value of chip stacks in a given tournament situation. This will enable us to answer questions like how many chips we should be willing to put at risk to achieve a theoretical gain of 500 chips. Answering these type of questions is the purpose of equity modelling.

Equity modelling

A player’s equity in a tournament is her expectation at a given point at the tournament expressed as a fraction of the prize pool. This is calculated by multiplying together the percentage chance that she finishes in each paid position and the percentage of the prize pool which that position pays, and then summing the resulting numbers.

For example, say a player has a 20% chance of finishing first, a 25% chance of finishing second, a 30% chance of finishing third, and a 25% chance of finishing out of the money. Her equity is:

0.2 * 0.5

0.25 * 0.3

0.3 * 0.2

= 0.235, or 23.50%. The decimal and percentage can be used interchangeably, but in this book we will be expressing it as a percentage.

The total amount of equity in a tournament is constant, because the sum of all players’ equities should always be 100% - the whole prize pool. Therefore, any play which increases one player’s equity must necessarily decrease the equity of one or more other players.

Since your equity is a summary of your money expectation in a tournament, it goes without saying that the goal of every play you make in a tournament should be to increase your equity. You should never “play for first”, or “play for third”. Always aim to simply increase your equity and you will be winning money.

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