How to find your True Max

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A True Max Bid is the absolute most that you would ever pay for an item. This is a bid that is so high that you know for certain that you would never ever (ever) bid more or pay more, no matter what. If you bid this amount, then you will either win or you will lose to somebody that you know for certain was willing to pay more, and you will not feel that you could have won if you had a chance to bid more, since you would never bid more anyway.

How do I know how much I would pay for something? Well, it's not that hard for most items. As with most things, you need a plan. One idea is to start at $1.00 and go up by 1 cent at a time. Would I pay $1.00? Would I pay $1.01? $1.02? $1.03? If you're buying a house, we could be here a while. :-) Fortunately, mathematics has given us a better way.

The technique I use to determine my True Max bid is called semi-logarithmic stepping. I just made up that name, but it describes the process fairly accurately. All we need is a starting point, and we're ready to begin.

I believe that most eBay items sell for under $500.00, so that's usually my starting point. I've never paid over $400.00 for anything, so that's a pretty safe bet.

When stepping through this algorithm, ask yourself a variety of questions at each stage. Am I willing to pay this much? Can I afford it? It's important to bid as high as you are willing to pay, but it's also important not to bid more than you can afford. Also, close your eyes and pretend that you're at the auction.

Imagine in your mind that the minimum bid is the number you are currently considering. The only way to bid is to enter that number. You MUST bid this much or you can't have the item. Would you bid? Can you afford it?

To be safe, unless you can answer "yes" to all of those questions, then your overall answer is "no".

Stage Explanation
Get your first bracket. Start with the question "Would I pay $500.00 for this item?" Depending on whether the answer is yes or no, move up or down in semilogarithmic steps. That is, if the first digit is a 5, double it or divide by 5. If the first digit is a 1, then cut it in half, or multiply by five and keep going until you get an answer that is the opposite of what you first answered.

Go up in steps of 500, 1000, 5000, 10000, 50000, 100000, 500000, 1000000 and so on. For eBay items, you will rarely go over a million, although some items on eBay are worth more than that. You could also go down in steps of 500, 100, 50, 10, 5, 1, 0.50, 0.10, 0.05, 0.01. If you won't pay 1 lousy penny for an item, then I suggest a second job. :-) You can see that you are basically going up and down in multiples of 10, but you're taking half-steps each time, in series of 1, 5, 10 or 10, 5, 1.

Sooner or later, probably sooner, you will answer the question differently. At that point, your True max bid is bracketed. In the example I used, I got a bracket fairly quickly. I would not pay $500.00, but I would pay $100.00. Therefore, I know that my True Max is somewhere between those two values.
Move in for the kill. Once you have a bracket, your goal is to get progressively smaller brackets until you know exactly how much your True Max is. If the upper and lower bounds are different by exactly one power of 10, go to the midpoint. If not, then start at the bottom and go up in steps of the nearest power of 10, rounding down. Using my example, I had a bracket of $100.00 and $500.00. The difference is $400.00, so I round down to $100.00 and move up in steps of that many. $200.00 was a yes, but $300.00 was a no. My new bracket is now between $200.00 and $300.00. Because the difference, $100.00, is a power of 10, I targeted the midpoint, $250.00
Repetition is good for the soul. Just keep doing this, over and over. Your bracket will shrink each time, narrowing your range. If you keep doing this correctly, you will eventually arrive at your True Max. I don't do pennies in my bid, so as soon as I get to a $1.00 amount, I'm done.
Here are some stats. I ran a few simulations, and for items under $1000.00 and a True Max bid rounded off to the nearest dollar, you can always get there in 16 steps or less.
I still can't do it. Even using this method, you may run into problems. Many people who claim that they don't have any idea what their True Max bid is may not be able to narrow it down. What if you're sure you won't pay more than $300.00, are sure that you'd pay $200.00, but are unsure about paying every amount in between? Well, all I can say is that if you absolutely cannot define a True Max bid for something, you're going to be at a serious disadvantage on eBay and there's nothing you can really do about, except to push for poor solutions to a problem that doesn't exist.