2 of 3 system: the bookmaker's variant

We study here a variation of the 2 of 3 system in sports betting. The system 2 of 3, or 2/3 method, secures a bet by significantly increasing the chances of winning, and therefore reducing the chances of losses.
As always, this security is done in counterpart of the overall gain: in a certain way, part of winnings is put aside to cover part of the losses.
With this insurance in place, we are now interested in a way to increase the gain. We thus finally come to a mathematical method which simply reduces the chances of losing your bet, while maintaining the odds of winning.
Of course this is not an effortless miracle method, all this costs a greater personal investment: making several bets (of the right amount) and this with several bookmakers whose odds you must take the time to study separately .

2 of 3 system calculations

Suppose we are facing an event with the following odds:
Victory   Draw   Defeat
2.45 3.20 2.80
Thanks to the 2 of 3 calculator we find that we can divide 10 euros of total stake into 5.33 euros on the victory with odds of 2.45 and another stake of 4.66 euros on the draw with odds of 3 ,20. In these two cases, victory or draw, the net gain will be a little more than 3.05 euros, or an ROI of almost 30%, whether one team or the other wins!
By betting exclusively on victory, the gain could have been 10×2.45 = 24.50 euros, but with our 2 of 3 strategy, we also win in the event of defeat. We thus transferred part of the gain from victory to defeat. This is the very principle of all insurance, here applied for sports betting.
The chance of winning is significantly increased: you now only lose in the event of a draw.
It now remains to be seen how to do this, while keeping this same method secure, to also increase the gain.
We can find it from the bookmakers, that is to say by putting them in competition.

Bookmaker method

Principle of the method

Whatever the outcome of an event, betting always benefits bookmakers. So you might as well compare them and take the best odds from the bookmaker that offers them.
We then study the odds of several bookmakers by selecting for each the favorite bet.

How to bet: an example

Let's assume that we have odds for the same match from 3 bookmakers, the 1st being the one used in the previous example.
BookmakersVictory   Draw   Defeat
#1 2.45 3.20 2.80
#2 2.25 3.40 2.90
#3 2.50 3.50 2.75
The best odds for victory are offered by bookmaker#3, while bookmaker#2 offers the best for defeat.
We then resume the calculations with the two odds 2.50 and 2.90, again using our 2 out of 3 calculator. We now find that we must divide our 10 euros of total stake (for example) into 5.37 euros on victory with odds of 2.50 and 4.62 euros on defeat with odds of 2.90.
Regardless of the actual outcome, victory and defeat, we have a net gain of 3.42 euros.

This method is also called the arbitrage method, or arbitrage betting, much more general in economics, and which consists, to simplify, of buying at the lowest price and reselling at the highest price (of course not to the same people).

In which cases to use a 2 of 3 bet with bookmakers method

The 2 out of 3 system is a really secure bet: the gain will be less important but more frequent, and the bad vagaries, the whims, of chance can thus be largely blurred.

A mathematically advantageous "2 in 3 chances" formula?

By betting on any two outcomes, you can end up losing every time. So you have to be careful.
We seek to be a winner for sure on the 2 outcomes on which we bet, regardless of which of the two comes true: it is the study and the mathematical calculations carried out for the surebet (inappropriate term here, because it nevertheless remains the uncertainty of the 3rd result).
We saw that to be a winner by betting on the two results with odds of c1 and c2, it is necessary to check the math relationship
1/c1 + 1/c2 < 1

If surebet situations are rare, as here we only look at 2 of the 3 possible outcomes, the situation on the contrary frequently becomes advantageous.
The surebet calculator for 2-way events can be used to see this easily and at the same time determine the distribution of bets which gives the maximum gain.

So, is system 2 of 3 really an advantageous strategy ?

The previous mathematical aspect only concerns the "pure" game of chance. This is not the case for sports betting, which has specificities other than for a dice game or casino roulette.
Indeed, with a little attention, knowledge, sport, match history, statistics, etc., all these elements which allow us to make somewhat informed predictions, the chances of loss are already decreasing.
Well, even a good, professional prognosticator can blame fate by predicting a victory when a draw is ultimately achieved... The 2 of 3 system, with good predictions, can therefore become infallible by erasing residual hazardous events and small errors in prognosis.

Limitations and drawbacks of the system 2 of 3

First of all, obviously, the method can only be adapted for sports whose matches have 3 possible outcomes (2 of 3 ...).
Then, even if it is very clearly a startegy which makes it possible to secure a bet, that is to say to greatly reduce the chances of loss, defeat and the pure and simple loss of the bets made obviously remain possible: it is not a miracle method, a sure winning strategy.
Another disadvantage: betting with this strategy requires a prior calculation, first to know if it is really advantageous, then to calculate the distribution of each part of the stake to be allocated to the two bets. This is a minor inconvenience as this 2/3 bet calculator does all these mathematical calculations automatically.

Finally, to finish, we remember the increase in the chances of winning (we now win in 2 out of 3 outcomes) comes at the expense of the amount of the gain itself: the gain is less important, which is also measured on the overall odds of the bet which is lower. Mathematically, we speak of the math expected value . From a purely mathematical point of view: a game of pure chance without any prediction, the fairly general mathematical rule is that the different betting strategies do not change the expectation ... but it is not a game of pure chance , like a game of dice or roulette at the casino…

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