Probability Mechanics behind the FastDraw System.
For sometime I have has players that say unusual things while playing Qi. “Yeah I’m at a 1 point Disadvantage that’s right where I need to be” or “down 2? Great, that’s the sweet spot”, are not uncommon. Some players actually take penalties just to get rid of the Advantage. Does this strategy work, other than the desire to be the heroic underdog? The answer is sometimes. Let’s explore the mechanics behind the FastDraw bidding system.
First, every character has a Bid comprised of the total of their Skill and the Statistic it is based on. That Bid is in most cases between 1 and 10, with 1 representing an untrained ability and no aptitude and a 10 for a total mastery of the ability. Can Bids go beyond 10? Yes, using the proper tools, taking additional time or even supernatural levels of skill can take the Bid above 10 and make even impossible tasks child’s play. When two opposing Bids are compared, the difference between them is the points of Advantage. If your Bid is greater than the other Bid, you have the Advantage. If not, you are at Disadvantage. When at Disadvantage your draw number must meet or exceed the total of your opponent’s draw number and the points of Advantage they have in the test. The Advantage can range from a +5 Advantage or Overbid down to a -5 Disadvantage where your opponent Overbids you. It never gets better or worse than that, just +/-5. The test then moves on to the draw, where each player “draws” a number between 0 and 5. If the total of the draw numbers is 5 it is a “Critical Successes” assigned to the player with the lowest draw number. If the draw numbers match (1&1, 2&2, 3&3,…) the player at Disadvantage wins.
That is the system but how does all this compare in game play? How does the math really work behind it? OK, here goes…
With each player able to Draw a number between 0 and 5, there a 6 options for each player. With 2 players there are 36 possible permutations (62). For each permutation there is 6 possible levels of Advantage, 0 to +5, the only thing that changes is if the player is Advantaged or Disadvantaged, but the number of possible results is the same, 216.
Of those 216 possibilities;
6 are Matching Draws at 0 Advantage (a Stalemate).
30 are Matching Draws with an Advantage (Disadvantaged player wins these).
18 are Critical Successes for the Disadvantaged player.
18 are Critical Successes for the Advantaged player.
Of the remainder there are
38 are Wins for the Disadvantaged player.
106 are Wins for the Advantaged player.
Overall, there are 124 Advantage player solutions or 57.4% of the time, 86 Disadvantaged player solutions or 39.8% of the time and 6 Stalemate solutions or 2.8%.
Great math, but I bet your still asking how do I win. The trick is in shifting toward the most favorable advantage position that limits your odds of losing. In addition to the odds of a Stalemate where nothing happens, the chances of success or failure are not linear in the FastDraw system.
From -5 to -1, a players odds of winning rise sharply from 25% to 58%, so yes there is a better chance of success at -1 than at 0, +1, or +2. The player would have to push the advantage to +3 to increase their odds of winning over 58%. Many maneuvers allow you to add a +1 or +2 as well as the +1 bonus of each additional attacker. Here is what we refer to as “The Bat Wing”, a chart of the percentage change in the chance of success between the different levels of Advantage.
At a 0 Advantage, it is not that you have a better chance to lose, it is that you are so evenly matched that neither you nor your opponent can win, i.e., a Stalemate. At +1 the Stalemate percentage becomes the probability that the Disadvantaged player can match your draw number, 1 in 6. From there the odds of success rise again but note how the percentage change in success drops again sharply between 3 and five. This is an effort to prevent players from being completely blown out by high-end advantages.
The key is to use maneuvers and modifiers to push your advantage around the “survival zone” between 0 and +2. Having backup can increase your odds by as much as 11%. You can use many of the maneuvers including grapple and sweep to shift into or out of the “survival zone” or just hold your opponent in that zone until your buddies show up to push you to +3. Remember no matter how bad the opponent is the odds are never worse than 1 in 4.
For example, say you are at a -3 against an opponent. Your odds are better than 1 in 3 or 36%. If you take the opportunity to Defend (+1 cumulative) for a round instead of attacking, your odds increase to almost 1 to 1, 47%. Do it again and you have a 58% chance to hit. Or try a Sweep maneuver and your opponent is -2 (for Prone) and your are +1, a total of +3 in a single round. Maybe you find yourself stuck in a Stalemate, backhand your opponent with your off-hand. It takes you to a -1 Disadvantage but your odds go up almost 17%. Also remember, you are not required to Bid your full ability. Pull your punches and save a few points, especially in the initial engagement. When your opponent tries to maneuver to get the +1 Advantage, you can raise your bid after the draw (as long as you actually have the points) and turn the tables on them. What other RPG lets you Rope-a-Dope?
Bidding and Draw strategy is not about min-maxing and dealing your max damage as fast as possible. It’s about maneuvering, taking the advantage, exploiting opportunities, and being the last one standing. Grapple to reduce your opponent’s options. Sweep them to the ground and run away. Fastdraw your opponent’s gun when they get in your face. Throw people at other people or Disarm them when they rely too heavily on their really cool toys. Take cover, use suppressive fire, and take time to aim and pick your shots. Sometimes it pays to fight smarter not harder.