8. Advanced Topics

8.1 Converting Between Binary Prices and Decimal Odds

Converting from binary binary prices to decimal odds is relatively straightforward - simply divide 100 by the binary price. For example: a binary price of 50 is the same as 100 / 50 = 2 in decimal odds; a binary price of 25 is the same as 100 / 25 = 4 in decimal. Converting in the other direction is the same - just divide 100 by the decimal odds to calculate the binary price.

If you are used to purely decimal odds then it may be handy to keep in mind certain "marker" points:

8.2 Combining Both Selections for Betfair Binary Markets

Since any binary market by definition has only two possible outcomes, any bet on one selection has an exact equivalent inverse bet on the other selection. For example, a back of £100 at 1.5 in decimal odds on one selection is exactly equivalent to a lay of £50 at 3.0 on the other.

Calculating the equivalent bet on the opposite outcome when using decimal odds can be rather tedious - you have to compute both the odds and the adjusted stake. For binary prices, calculating the equivalent bet on the opposite selection is easy - just subtract the odds from 100. So, a binary price of 80 on the first selection is equivalent to a binary price of 20 on the other. The stake remains the same.

One of the revolutionary ideas behind BDI is the combination of the binary prices of one selection with the equivalent binary prices of the other selection into a single concise view of the binary market.

8.3 Binary to Decimal Mapping

Since Betfair natively uses purely decimal odds, BDI has to do some fairly advanced calculations in order to make the mapping from binary to decimal as seamless as possible. When viewing Betfair markets which are "unzoomed" (i.e. units of 0.5 in the ladder), each binary price in the ladder is not an actual price which can be traded directly; instead it maps to a range of decimal odds on one or both of the two underlying Betfair selections. For example, when viewing a Betfair binary market:

• The binary price of 99.5 in BDI corresponds to a range of decimal odds from 140 to 1000 only on the second underlying selection.
• The binary price of 99.0 corresponds to decimal odds of 1.01 on the first selection, but also a range of decimal odds from 80 to 130 on the second selection.
• The binary price of 98.5 corresponds to a range of decimal odds from 60 to 75 only on the second selection.
• …and this pattern repeats similarly all the way down the ladder.

This is probably the cleanest way of mapping binary to decimal odds when using a uniform difference of 0.5 across the whole ladder, but since it naturally involves approximation it leads to several important implications:

1. There are many binary prices in the ladder which do not map to both underlying selections.
   Any binary prices which map to decimal odds only on the non-favourite selection (i.e. with decimal odds of greater than 2.0) are coloured grey. In the example above, both the 99.5 and 98.5 map only to ranges of decimal odds on the second selection (i.e. the non-favourite), and therefore appear grey in the ladder, whereas 99.0 maps to both selections and so appears white. Also note that when viewing a multi-selection market, the ladder is used to trade one selection at a time, so any binary prices which do not correspond to a range of decimal odds are blacked-out.
2. For binary markets, when submitting small binary orders at binary prices near the top or bottom of the ladder, the orders can get rejected if they are for a grey binary price.
   The order is trying to be placed for a grey binary price so this means that it will normally correspond only to a bet on the second underlying selection, i.e. the non-favourite. For grey binary prices near the top or bottom of the ladder, the decimal odds are much higher on the non-favourite selection. Higher decimal odds will mean a lower decimal stake for a fixed binary stake and thus BDI will reject your order if it corresponds to a decimal stake which is below the minimum allowed Betfair stake. The solution is to raise your binary stake, or choose a white binary price.
3. BDI chooses the worst value decimal odds in the range when placing an order.
   This is the reason why when placing an order at a particular binary price on the ladder, the actual binary price of the submitted order is usually slightly worse in value. The main design decision behind this is to protect the user from "queue jumpers" on Betfair - people who beat your order by one decimal tick on the Betfair website. By submitting an order at the worst value decimal odds in the range, anyone who tries to offer slightly better value will show up on BDI as an order in the next binary price bracket, thus making these tactics easier to spot.

We recommend using the "zoom" mode (Ctrl + Z) to show all possible binary prices in the ladder for more precise trading, especially on slow moving markets. It then means that each price in the ladder corresponds to just one decimal odds value. Note that when zoomed in to Betfair binary markets, the grey/white colouring of values in the Price column of the ladder is used to indicate which prices correspond to the favourite and which correspond to the non-favourite.

8.4 Arbitrage Opportunities for Betfair Binary Markets

In this diagram there is an "overlap" between the best buy at 55.5 and the best sell at 54.5 meaning that a profit can be obtained if you manage to quickly buy at 54.5 and then sell at 55.5. On fast-moving in-play markets these situations are very common and the overlap can be much greater than one percentage point - it’s just down to you to work out which of the two overlapped prices is out of line, hopefully before anyone else!

These opportunities are also visible on the Betfair website but are harder to spot as the user has to check to see if the percentage overround for the "Back" side is less than 100%, or if the overround is greater than 100% on the "Lay" side.

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