Expected Value (EV) Calculator

Ok, you may have read some comments I made on the "Today's Show" thread about an EV calculator, and maybe wondered what I was talking about (unless perhaps you looked at my website... )...

...Well, wonder no longer as I aim to explain the intricacies of this quite fabulous tool I've created for (roughly) predicting offers. Firstly, the basics:

The Basics

Ok, firstly I thought about a system based around all the final 2's that it is possible to leave in the endgame, which starts with 231 pairs and then clearly decreases as amounts are eliminated from the board.

For this to work effectively, I then had to think of a way to 'equalise' each potential 2-box offer to provide an 'average' view of a player's expectations from the given board, so I chose the fair deal method designed to provide a 'benchmark' figure as such. With me so far? Good.

In Practice

"So, how did this all work out?", I hear you cry. Or something like that. Well, once I had computed all the fair deal offers (from 4p on 1p/10p to precisely £166,556.94 on £100k/£250k), the Expected Value on the full board came to £17,070.98, which coincidentally used to be about the average winnings a couple of years ago. Oh, how things have changed...

Anyway, at this point it became apparent to me the notion of 'Expected Value' was a lot more complicated than I previously thought, in the sense that most of the time the banker wouldn't offer what the board was worth (unless he was playing a high-risk player, more of which later), as he wanted an edge - the question I was seeking to get an answer to was what should even a low-risk player reasonably expect for the board?

...And then I stumbled across a formula I could use...
(Stay with me, please!)

Median Value

I wanted a way to take into account board instability (as the banker so often does with his offers), but not the typical volatility method. I figured as I was working with pairings, the central (or median) pair value is important to the equation reached; on stable boards of course, this is closer to the expected value, and it stands to reason that on instable boards most players will get significantly less than the expected value. I had found a way to adjust the final 'estimated offer' figure, brilliant!

So, just to explain this a bit further, on a full board, the median pair value (that is, the 116th highest pair) is £5,070.96, which divided by the £17-ish EV figure I mentioned earlier, gives an 'instability rating' of 3.37. The 'estimated offer' figure is reached by calculating the midpoint between the 2 figures, so the starting value is £11,070.97. Let's think of this figure as a 'buy-the-box' offer for the time being, so for the first 2 or 3 offers, typically the banker will offer about 66% of this figure as he's not that interested. At 8-box, this figure tends to be much more reliable though. You still awake? See, I told you this was complex!

Summary

Of course, it can never be an exact science with the offers, but what it can give is an indication as to the type of player the banker feels he is up against; the way to look at is a medium-risk player will likely receive close to the figure given, a low-risk player will receive more towards the 'median pair value' figure, and a high-risk player will receive close to the 'expected value' figure. Of course, you occasionally get exceptions off the scale either way, like Corrine and, er, Richard, but it serves as an interesting guide I think...