This question relates to my field of experience being roulette, and flat staking play in particular. Recently I have encountered several surprisingly different interpretations of 'winning edge'. Can you please provide some clarification for us ? The easy one is the house edge which is a fact in European Roulette and of course larger for double zero roulette, but what about the one where a player has an edge over the house ( having overcome the house edge) based on a statistically significant sample of live bet experience and the consistent application of one particular bet methodology and strategy?

At present I use a percentage expression/definition based on a sample over many sessions ( average duration say 100 spins) with total spins in excess of say 5000 spins. It seems to me there is a 'trading range' within several sample sizes of 5000 spins and at present I strike the midpoint as a guide, qualified by a guideline range either side. Of course within a sample itself there can be sessions which are losses, but in the greater scheme of things it appears there can be a positive outcome for several bet types.

The context for this question is work on an ever more 'efficient' bet. I am grateful to Sqzbox and others for this terminology and participation in this research, and also to Xander for putting forward his own interpretation and definition of 'edge'.

As I understand some of the variables that may qualify any answer let me add that although I recognize  the most efficient bet may be a single bet (ie one chip placed upon one target) for reasons of time availability I compromise a little and actually stake 9 targets for every bet application. Hence if struck on the first attempt I earn +27 units. I keep going until a hit or stop loss at -54 units and resume later with a fresh attack when appropriate.

Good question - hopefully there will be some good responses and we can all learn lots.

For myself, I did a little bit of research and discovered the following that is based on winnings vs. investment so is focused on the money aspect rather than spins.

It has been defined that "The player's edge is the expected return divided by the initial bet". So, for example, on a 9 chance bet the calculated theoretical players edge, based on the odds of the game, would be –

Expected return = outlay x odds where outlay is 9 and odds are -2.73% = 9 x -0.0273 = -0.2457
Initial bet = 9 of course.

So the theoretical players edge for this bet works out to be 9 x -0.0273 / 9 = -0.0273 = -2.73%. No surprises there.

However, if your question is about the players edge based on your actual results (and I suspect that it is) then probably I would use the definition for EV. Quoting blackjackinfo.com -
"I think you are wanting to calculate w/l% ie: %Win/Loss – Also called EV or IBA (Initial Bet Advantage.) This is the amount won or lost divided by the initial bet. this is how QFIT's simulator help describes expected value, errhh your edge over the house."

So if you invested 100 units and got 120 back then your return is 120 – 100 = 20 and I would calculate the edge (for that particular data set) as –

20 / 100 = 0.2 = 20%

Thanks

yes it is based on results.

So what about measuring % return per spin.

Take for example the recent RNG test with 385 spins and a net return of +459 units.

The approx +120% ratio is a measure of sorts but not pure edge per se over the house?

Even though 385 spins were observed it does not mean that I played all of those spins***. In fact I played about 55% of those spins with 9 targets, ie 212 spins, ie outlayed  1908 units to result in 2367 units, ie + 459 units.

Using EV/IBA that would be  2367-1908 = +459 and divide that by spins 385, ie 1.19 , so what is the edge?

Surely not 1.19% ( seems like a lot of effort for little edge), or 11.9% , or back to my original ratio 120%.

Instead following your advice,  459 divided by total outlay ( a sort of measure of bet efficiency) 2367 gives 0.194

ie bet edge of +19.4% ( less -2.7% overcome?)     for this session result alone of course.

Is this correct?

*** let me throw a small spanner in the works here...

I actually played 96 spins but recorded 98.  Also I played this simultaneously on 4 independent sets of targets, some times playing sometimes observing and waiting and in one case 97 spins were used.

So adding all the results for every set together added to 385 spins and the net result was a fortunate +459 units on 212 spins that were actually played.

120%? Where did that come from?

I'd calculate like this -

459 (profit) / 1908 (investment) x 100 (to make it a percent) = 24.0566%

As for return per spin, I suppose you could look at it as 1.19 units earned per spin but I'm not sure that that can be converted into a player's edge.

Anybody else?

Ah yes thanks, I used the wrong figure for outlay ( I used income). Apologies.  +24% it is then.

120% came from +459 divided by 385 spins, a sort of efficiency percentage measure, or 1.19 efficiency ratio.

It  seems there can be various ways of viewing which may assist the player, but in the end all that matters is the net profit where possible.

Oh, OK. So that is the return per spin then - your 1.19 as mentioned, but multiplying that by 100 to get a percentage (actually 119%) would seem to be a bit of a stretch - not sure what that tells us.  In any case, to calculate percentages your units of measure of the operands have to be the same to give a meaningful result. So you can calculate a percentage of units-in vs. units-out, or spins played vs. spins measured, and so on, but not when the units are, for example, units for one operand and spins for the other.

Thanks.

I will use the ratio as 1.19 as a measure/ benchmark of bet relative efficiency in future. Goodness me, if the same result could have been achieved with a single chip outlay as opposed to nine chips, what a leap!

The triple digit bet edge is wishful thinking evidently ( although can be witnessed in short cycles of 20-30 spins sometimes).

Still not sure whether the 'house edge' figure should be deducted or is that irrelevant?

This has been most helpful.

I think I would be inclined to use only the spins invested on.  That is, as a measure of efficiency the 1.19 is not really all that good because it is units per spin over ALL the spins - which includes the spins where no bet was placed. I'd be more inclined to use "units profit / number of spins bet on" as a measure of return per spin, or "earning rate". So in this case 459 (profit) / 212 (spins where bets were placed) = 2.165. This would be a measure of earning rate per spin "played" - or, IMO, just "earning rate". I'm personally of the view that spins where no bet is placed is irrelevant to mathematical calculations of earning rates and efficiencies and so on. Only where the answer is specifically relevant to these would I include them - such as, the ratio of spins measured to spins played, or perhaps earning rate OVER ALL SPINS CONSIDERED, which would be the 1.19 of course but is explicitly stated as such. If you were just quoting rates without qualification then I would assume (as most would I suspect) that you were including only those spins where bets were placed.

The house edge is not really all that relevant (IMO) when measuring success. If you wanted to measure how well you did in terms of beating the house edge then of course it would be relevant. But generally I think most would only be interested in how well did you do, what was the earning rate, what was the apparent advantage, and so on, and none of these would include reference to the house edge.

All this is just my opinion of course and I would be interested to hear from others.

If someone says that they've won 511 units in 384 spins you need to know on how many numbers they are betting at each spin.  Here's an example with various bets...

Take units won, divide by the number of spins, and then divide by the number of numbers on which you bet.

For example:  If you're on:

9 numbers... 511/384/9 = .148  or about a 15% edge
5 numbers... 511/384/5 = .266 or about a 27% edge

but...if you're only on one number.... then 511/384/1 =133% edge

Knowing the true edge and how many units you can expect to win IS important in order to calculate the ideal progression.


-Xander

Knowing the TRUE edge is not an easy job.
Math part is not difficult.
You first must know wether youhave got an actualedge or not.
Suppose you pick a dozen and play 200 spins winning 200 units, you won 8.333% of total money wagged.
Does it mean you have got 8.33%? no
Not yet to be more precise.
True edge comes after long studies and data. The more experience you have the less data you need.
This realm can be developed by  actual APs.