Magic Online (MTGO) has needed to fix tournaments payouts for a while now. In the last two years the economy has literally fallen apart with a consequent decrease in tournament attendance. The reasons behind this decline are hard to evaluate but I think this article gets pretty close to the truth.

Magic Online is not a free-to-play game. On the contrary, it is quite expensive, so the possibility for players to even partially repay themselves by playing well is crucial in order to maintain a large crowd of active non-casual players. I think a change was necessary, and I believe that with this new policy (you can find the announcement here) Wizards of the Coast is also stating that there is a problem that must be fixed.

The direction WotC is taking seems quite promising, though there are a couple of problems that I want to discuss with you all.

With this article, I will walk you through my thoughts, analyzing the pros and cons of the new and the old system. Before going deep into my considerations, though, I want to introduce you to a base concept that I often use when I need to analyze MTGO tournaments. That concept is called Expected Value, or EV.

## Expected Value (EV)

Let’s assume that a friend of yours asks you if you want to play a game set like this: you pay $10 to roll one dice; if the number that comes out is between 1 and 4 you lose, if it’s 5 you earn $20, and if it’s 6 you earn $30. You might want to know if it’s worth playing or not. Tossing aside whatever gambling inclinations you may have, there’s a parameter that is possible to calculate that can estimate if such a proposal is worthwhile or not. This parameter is called expected value and it determines how much you can earn on average each time you roll that dice.

Considering the odds of each number as 1/6, we can make this table.

Buy-In = $10

Numbers | % | Payout

1-4 | 67% | 0

5 | 17% | $20

6 | 17% | $30

The EV is calculated by adding all these numbers together using this formula: EV=P(1,4)*(Payout(1,4)-Buyin)+P(5)*(Payout(5)-Buyin)+P(6)*(Payout(6)-Buyin)

We can plug the numbers in our table above into the formula to get this: EV=4/6*(0-10)+1/6*(20-10)+1/6*(30-10) = **-1.6667**

You can see that the final EV in this scenario is negative 1.6667. So what does it mean that you have a negative EV?

It means that on average every roll is making you lose money. In this case, over the long term, you would be losing about $1.67 every time you rolled the dice. Of course, it’s a game of probability so while it remains possible to win in a short run, in the long run you will almost certainly end up with less cash than when you started.

## How is EV related to MTGO?

MTGO works the same way as the example that I used above: we can calculate the EV for every tournament we decide to participate in to help us understand if it is worth playing in them or not. Let’s understand how we can compare it with our dice experiment. We can try to draw the same table we did before, for instance we’ll look at an MTGO Daily Event (DE) with the old system.

Buy-In = 6 tix

Results | % | Payout

x-2 | ? | 0

3-1 | ? | 6 boosters

4-0 | ? | 11 boosters

As you can see the only thing missing is the % likelihood of each result. This probability is related with our win rate.

What’s the win rate, you might ask? Well it’s the probability of winning a game of Magic against an unknown opponent. It is not possible to calculate this number in advance, but we still can evaluate how daily events compare to other tournaments by looking at a variety of win rates to understand which events are more convenient, or simply to try and determine if the new system is better than the previous one.

On of the factors to consider is that the higher is the payout, the less we need in terms of win rate to have a positive EV. The opposite is true as well; the lower the payout, the higher our win rate should be, assuming the same buy-in. Let’s see how is possible to calculate the probability (P) to make a 3-1 or even a 4-0.

- Winning a game of Magic on MTGO is like flipping a coin; you can only win or lose. The only thing different is that the probability of these two events are different so while the odds of having tail or heads is 50% the chance of winning is WR% (win rate) and losing is 1-WR%.
- Calculating the chance of making a 4-0 is pretty simple, you just have to toss your coin 4 times hoping that you win the roll every time. Therefore

P(4 wins)=(W〖R)〗^4. - We have 4 different ways in which we can achieve a 3-1 (WWWL,WWLW, WLWW, LWWW) so the formula is P(3 wins)=(WR)^3*(1-WR)*4.
- The rest of the cases are the X-2s but we don’t care to differentiate those as much, so the probability is calculated like this P(2 wins or less)=1-[P(3 wins)+P(4 wins)].

The same formula used to calculate our EV before is still applicable for our DE:

EV = P(4w)*[Payout(4w)-Buyin]+P(3w)*[Payout(3w)-Buyin]+P(2w or less)*(-Buyin)

Let’s fix three different values for the price of booster packs (3 tix, 2.5 tix, and 2 tix), and see how the EV is different with a change in our win rate and/or payout.

As in our previous example, this graph could be read as follow: with an 80% win rate in the 3 tix curve we will expect an average 15 tix gain per daily event; or at a 53% win rate in the 2.5 tix curve the EV will be 0 and we will break even. As you can see the higher our win rate the higher the EV, but the less the payout the less the EV. The more value we see in our booster packs (payout) then the lower our win rate can be while still maintaining a positive EV.

Now that it’s clear what Expected Value is and how it works, I’ll continue my analysis comparing Daily Events and 8-man tournaments in the old and the new structures.

## Daily Events – Old vs New

Let us first look at Daily Events with both the old and new models.

### Old System

- Buy In = 6 tix
- 3-1 finish gets 6 boosters, 4-0 finish gets 11 boosters

Dailies are the backbone of constructed Magic on MTGO. They retain the highest EV possible and for years (I assume) they have worked well. The boosters a player won could be sold on the secondary market for tix. However, in the last two years the market was saturated too quickly with unwanted boosters and consequently the prices of those boosters plummeted.

This is the price trend of KTK boosters over time between their release and the release of Dragons of Tarkir. The price went down from 3.9 to 1.4 tix and significantly lowered the EV of daily events. For simplicity let’s consider only the period of time when dailies where paid with KTK boosters only, from October (3.9 tix each) to February (2.2 tix each), and see how the EV decreased over time for 3 different win rates.

As you can see the 55% win rate curve was earning 5 tix per event in October but by February was merely breaking even. Any win rate lower than 55% was losing money by February! The system needed a fix. Let’s see how things will change with the new system.

### New System

- Buy In = 12 tix OR 120 Player Points
- 3-1 finish gets 3 boosters + 180 Player Points, 4-0 finish gets 6 boosters + 360 Player Points

This new system features the introduction of Player Points: an untradable way of paying for tournaments. This appears to be an attempt to fix the variable EV of daily events caused by booster price fluctuations, but is it really that convenient?

As you can see this system will cause you to lose less money if boosters are decreasing in value (the slope is less high), but in the end on average has a lower EV than the old system.

This is not, however, true for all the win rates. In fact, for win rates higher than 64%, this new system is actually more profitable. I believe this is due to the fact that increasing the buy-in and consequently the payouts really helps players with a higher win percentage.

Overall, though, this new Daily Event system should be revisited. Let us see, for instance, what could happen with a different payout. What if a 3-1 finish gets 3 boosters + 240 Player Points while a 4-0 finish gets 6 boosters + 480 Player Points?

This payout system gives you a lower EV for Win rates under 52% and provides a lower risk of losing money if booster pack prices drop extremely low. I think it’s a better transition from the old system because it keeps the same EV for average win rates while decreasing the difference in EV between release dates.

Moving on from daily events, let’s take a look at 8-man events.

## 8-Man Events (5-3-2-2) – Old vs New

Here is what the buy-in / payout breakdown looks like in the old and new systems.

### Old System

- Buy-in = 6 tix
- 3-0 finish gets 5 boosters, 2-1 finish gets 3 boosters, 1-1 finisher gets 2 boosters

### New System

- Buy-in = 6 tix OR 60 Player Points
- 3-0 finish gets 2 boosters + 140 Player Points, 2-0 finish gets 1 booster + 60 player points, 1-1 finish gets 60 players points

Let’s take a quick look at our EV in daily events vs 8-man events in the old system.

The problem with 8-man events is that when boosters are less than 3 tix each your first win no longer allows you to repay the buy-in for your next event. Looks like WotC had this problem in mind when reshaping the payouts. In fact, so long as you win one match it’s guaranteed that you can join another tournament.

To evaluate if this new system is better or not we have to consider three different booster pack price scenarios: booster prices under, equal to, and over 3 tix. Let’s look at EV based on pack prices of 2.5 tix, 3 tix, and 3.5 tix.

Looks like WOTC really nailed it! The EV in the new system is far less dependent on the booster price and is even a little bit higher than in the old system. I guess now we will be encouraged to play 8-man events a little bit more.

## Other considerations

There are a few other considerations that I want to point out in conclusion:

- Doubling the Daily Event buy-in is beneficial for grinders (who tend to have a higher win rate) because the payouts are also increased. Having higher payouts means that other tournaments like PTQs and Drafts are actually cheaper in proportion. This change is detrimental for casual players, however, who tend to have a lower win rate and now they have to pay double the price they were paying before.
- Adding Player Points as a reward will decrease the number of boosters packs in circulation and will hopefully ensure that they will better maintain their value. This might actually be bad for single card prices but I’m not sure yet which factor will be dominant.
- Not having Player Points available for trade means that really good players will have a stock of actual junk, because they will earn too much compared of what they need. WotC should implement more ways for players to transform their player points into something with value, like boosters in the store, promo cards, or something similar. Finally, with less tix at our disposal and a plausible increase in card price, it may become more costly to collect the single cards needed for constructing decks.

Magic Online is a complex financial system, and instead of doing nothing I’m actually glad that WotC is trying to shake up things a bit. Based on the changes they’re making now, it is my opinion than daily events still need some revision while 8-man events saw a substantial improvement.

Thanks for reading, and that’s all for now. Hope you enjoyed the article!

Until next time, Mattia

PS: You can find my excel sheet with all the calculations here.