Chicken
Chicken, also called buzzer chicken or playing (against) the packet, is a game-within-a-game played by competent quizbowl players. In this game, a player recognizes the most obvious answer from a clue or set of clues, and then must decide whether or not to buzz. Games of chicken are very common at tournaments where the difficulty is highly variable within and between packets, or at tournaments where a majority of good questions are combined with a critical mass of bad ones. Hoses and transparent questions increase the likelihood of games of chicken exponentially.
Pseudo-Mathematical Analysis of Chicken
The background to this game comes from analysis of "when to buzz in". Most of the quizbowl world accepts Mike Sorice's assertion that all previously derived models do not take into account the marginal utility of hearing another clue. This analysis looks solely at a single clue off which a player has formulated a guess of "most obvious answer" based on either a set of clues narrowing down the possible answer space or one single clue that the player recognizes but isn't 100% sure he has matched correctly to the answer.
Suppose Team 1 plays Team 2, with Team 2 having a better bonus conversion than Team 1, with each team having a 50% chance to win any given buzzer race. We further assume that each team is competent enough to get the question off the giveaway should the other team neg. Let p be the probability (based on empirical evidence from the tournament) that the "most obvious answer" at a certain point in the question is indeed the answer. Then, we expect the following payoffs (in terms of point differentials) for team 1, and since this is point differentials, the opposite payoffs for team 2:
| Team 1 Buzzes | Team 2 Does Buzz | Team 2 Doesn't Buzz |
|---|---|---|
| Yes | p(0.5(10+BC1)-0.5(10+BC2))+(1-p)(0.5(-5-(10+BC2)+0.5(5+(10+BC1)) | p(10+BC1)+(1-p)(-5-(10+BC2)) |
| No | (1-p)(5+(10+BC1))-p(10+BC2) | 0 |
This simplifies to
| Team 1 Buzzes | Team 2 Does Buzz | Team 2 Doesn't Buzz |
|---|---|---|
| Yes | 0.5(BC1-BC2) | -(15+BC2)+p(25+BC1+BC2) |
| No | 15+BC1-p(25+BC1+BC2) | 0 |
We now look for under what conditions of p different strategies become Nash equilibria, or the set of strategies used by each team attempting to maiximize its point differential regardless of what the other team does.
We find that under conditions of high p, p>(15+BC2)/(25+BC1+BC2), that both teams' best strategy is to buzz. This is consistent with the usually successful application of the Westbrook Method to CBI tournaments, since on CBI questions the answer is almost always the most obvious thing that fits in the category the question's describing.
Under conditions of low p, p<(15+BC1)/(25+BC1+BC2), both teams' best strategy is to wait and not attempt to score any points off that particular clue. In any well-written tournament, the probability that the "most obvious answer" is the right answer switches from near-zero to one nearly instantaneously upon recognition of a uniquely identifying clue that a player can associate with the right answer. Thus, this analysis is consistent with the usually successful application of the McKenzie Method to ACF tournaments.
We also find that the higher the teams' bonus conversions are, the more likely the equilibrium set of strategies is for both teams to wait, which is consistent with most good playing strategies.
Under intermediate p situations, we find that for (15+BC1)/(25+BC1+BC2)<p<(15+average(BC1,BC2))/(25+BC1+BC2), the best playing strategy is for the team with the better bonus conversion to buzz in aggressively and the team with the worse bonus conversion not to buzz in. This supports the viewpoint that teams should not, in fact, buzz aggressively on first inkling of answer against better teams. Under conditions of (15+average(BC1,BC2))/(25+BC1+BC2)<p<(15+BC2)/(25+BC1+BC2), there is no true Nash equilibrium, and the best strategy is for team 1 to do what it thinks team 2 will do and for team 2 to do the opposite of what it thinks team 1 will do.
Chicken occurs when question difficulty and quality is all over the place; thus, the true value of p for a particular point in each question (e.g. the power mark) may be in all four intervals in the span of four questions. In these situations, a team's best buzzing strategy is not based solely on its knowledge base and its impression of their opponent's knowledge base, but also on its best guess of which of the four intervals a particular packet lies on for each clue in each question in that packet. Thus the team is not only playing against its opponent, but also playing against the packet. A team assuming that they should wait for uniquely identifying clues they know may be slow to one too many tossups, while a team who assumes they should buzz aggressively may be disappointed when the packet was not as easy or transparent as they thought. Jerry Vinokurov is known to have exclaimed, "The packet wins again!" after losing battles with the packet, even if his team's superior knowledge base still allowed his team to beat his opponent.