Arbusers

It happens very often that multiple value bets in different markets are present on the same match at the same time. They cannot be treated as separate events, because the outcome of one bet is usually strongly connected to the outcome of the other bet. One recommendation would be to only bet only once per match. It is tempting to bet multiple times on different markets per match, with overall increased stake. Somehow I believe that this way, I can assume the same risk and increase the turnover, but maybe I am fooled.

Example:
A soccer match offers 2 valuebets:

1. O 3.5 at odds 2.1
2. away team O 1.5 at odds 2.1

The probability of each of these two options to happen is 50%.

So instead of wagering 1.000 whatever currency (w$) at the first option, I decide to wager on 500 w$ on each of the two options, believing that I just reduced my risk according to an evaluation of the probalilities.

• both win: 40 %
• both lose: 40 %
• one loses, one wins: 20%

So the question is:

Does splitting your stake on multiple bets on the same match, reduce, maintain or increase the risk?

I think its all about total stake in a match. Does not matter what line. If some line has better value normally it matters. I would do it as a separate project with less bets. So you do value bets in one project. And second project may contain second line bets only. But since the number of bets in second project will be less you should see its profits and statistics every six months and not each month.

Actually, I was thinking of it just a thought experiment.

So suppose you have 1000 w$ and two options on the same game with equal EV and odds, would you bet it all on option 1, option 2 or split it on both? I am in doubt what is better.

It depends on bookie some put red flag if you bet 2 different lines on same event. Almost all put red flag for high stake. So it depends from bookie to bookie. Valuewise i think is the same because most of lines are related for same reason they both have same EV.

I think Vida is asking about the theoretical answer, not considering any other factors. In such case, splitting the bet you are clearly reducing variance (risk), and in your example you maintain expectation.

In fact, a single bet is the maximum variance you can get: either you lose all, or you win all. By splitting the stake of that bet into 2 you will reduce risk, even if the second bet were an EV- one (pointless to do of course, since the first goal should be to maximize expectation and minimizing variance should come only in second place).

are you talking about value bet risking ? If you are reducing the risk to make losses from this value bet? Or risk to not be paid or to be limited from a bookmaker?

barbero wrote: I think Vida is asking about the theoretical answer, not considering any other factors. In such case, splitting the bet you are clearly reducing variance (risk), and in your example you maintain expectation.

Exactly. It is purely a theoretical discussion. If someone is doing shop betting or if using multiple bookies for those bets, other factors don't matter anyways.

I am thinking of this case as if splitting the stakes is actually going to matter in terms of variance vs expectation, or if it is just some kind of paradox? In the hypothetical example variance is clearly reduced as barbero points out, but since it is now a win-win in only 40% of the cases instead of 50% (single stake), maybe the expectation got reduced by an equal amount? Additionally, there is now the 20% case, win-lose, where a small amount will be returned, just to increase confusion even more.

Expetation stays the same but why not bet both lines full amount and make a side project with second lines in same match. This way you make more profit. And at the same time you make another research if the events with 2 lines or more with value are good to bet or not. You can test the side research with low stake.

In my opinion those are two outcomes where each of them has their own probabilities and EVs. They don't exclude each other too. If you base your staking plan on your EV, I don't see why you wouldn't stake the same amount on both. Everything else is pure speculation.

Another thing is if they would exclude each other. In that case, it would be foolish to take both. I'd probably think about taking the one with the higher EV in that case.

@tom I believe whether they exclude each other or not should not be a factor to decide whether to bet on both or not. If they exclude each other, meaning both can't happen (let´s call it anti-middle), and both bets have value, you will necessarily be getting a juicy surebet and making profit in the long run. It all comes down to whether you are sure that both legs have value, which is an entirely different discussion, but if you are, it shouldn't matter if they are exclusive or inclusive imo.

Consider a football game where the probability of exactly 2 goals being scored is 20%, under 1.5 goals is 50% and over 2.5 goals is 30%. These are the real probabilities and you happen to know them. You get offered the bets under 1.5 @ 2.5 and over 2.5 @ 4. These are exclusive bets, but surely betting on both should produce the highest return on the long run.

@Vida if you just bet 100 in one of the bets, you get

E = outcome_win * probability_win + outcome_lose * probability_lose = 110 * 50% - 100 * 50% = 55 - 50 = 5

On the other hand if you bet 50 on each bet, you get

E = outcome_win_both * probability_win_both + outcome_lose1_win1 * probability_lose1_win1 + outcome_lose_both * probability_lose_both = 110 * 40% + 5 * 20% - 100 * 40% = 44 + 1 - 40 = 5

You maintain your expectacion and you obviously reduce variance since by splitting your bet into two you get other possible results (one win and one loss) in your probability distribution apart from the extreme values that were all you had in the first case, where you either won all or lost all (and these new possible results fall in between the extreme cases). Variance calculation is a bit too much to be written here but a spreadsheet with its functions comes in handy

Thank you all.

@wolfie
The reason I want to keep this question theoretical, is because I am myself basically unlimited in terms of stake size (shop betting) so bot betting full amount doesn't make sense in this context. So it is assumed that it is a regime with NO limits, only the limit set by the stake plan. When discovering several value bets as the case I described, it would be nice to have a notion of whether it theoretically makes a difference in terms of variance vs expectation by putting more money on the table on several interdependent lines that all have positive expectation.

@tomkruiz
Yes, those are are two outcomes with own prob and EV, although they have equal value in this case for simplicity. Although they are still interdependent, neither do I see why I shouldn't stake an equal amount on both. The question is how much compared to the single bet case? Same is too much, half is not enough.

@barbero
Exclusive bets occur often during large swings, but mostly not simultaneously. I am often reluctant to make a second exclusive bet, but maybe it is mainly because of human psychology - it takes away the excitement. This behavior should stop, as the juicy surebet must be the better option in the long run.

Bravo! Your calculation is very convincing and it seems obvious that distributing the same wager onto several lines is indeed reduced variance/risk. What is needed now is a measure of how much overall stake can be increased in order to maintain the same level of variance/risk. If anyone has any ideas to this approach, please speak. I like numeric approaches, so maybe I will run simulations of this case of both methods with varying increases in stake, to see if the observed variance and profit reveal something.