Rolling in Teamfight Tactics

A note from SIG: Andy is a Duke University graduate and Quantitative Trader at SIG. Despite starting TFT only a year ago, Andy had the best average placement in NA across all three Dragonlands events and has become first North American representative for the Dragonlands Championship!

Introduction

Before going into some puzzles and the ways that we can solve them in TFT, we need to review some basics of the game and the tools that we use to play. If you’re experienced with TFT feel free to skip this section:

• Gold: You gain some amount of gold each round and can use it in many ways (we will discuss these)
• Level: You can spend gold to level up to play an extra unit on your board and get better shop odds for expensive units.
• Units: You play them on your board in combat. Units cost between 1 and 5 gold (except dragons), and usually stronger units are more expensive. If you get 3 copies of a unit, you can upgrade a unit, and you can do this up to 2 times.
• Shops: Shops contain 5 slots that each contain one copy of a unit that you can choose to buy. Every round, your shop will refresh with new units, but you can also buy shop refreshes with 2 gold at any point (this is “rolling”).
• Combats: Each stage has five rounds where you fight other players and one round where you fight neutral monsters.
• Health: You start with 100, and health goes down when you lose against other players, losing more health when more of the opposing units survive. You are out when your health goes to or below 0, and your placement in a game is the reverse order of the order you were knocked out (8^th to 1^st).
• Augments: On stages 2-1, 3-2, and 4-2, you get a choice of 3 augments (choose 1) that improve your board.

Of these resources, gold is the resource that is most flexible and, for that reason, most of the important decisions in the game are about spending gold.

What Gold Can Buy

At any point in the game, we can use gold to:

• Level Up: You can buy experience at a rate of 4 gold per 4 experience points. The levels go from 1 to 9 and require more experience the higher the level you are.
• Roll: To improve your board, you need to find rare units and/or upgrades to your current board by getting many copies of the same unit. To do this, you can refresh the 5 slots in your shop at any point for 2 gold.
• Buy Units: Units cost gold, and units you aren’t playing on your board can be put on your bench (up to 9 units).
• Make More Gold: There is an interest system in TFT, where for every 10 gold you hold in your bank (up to 50 gold), the next round you will collect an extra 1 gold of income.

For the rest of this post, we will consider decisions that mostly debate the options of leveling up and rolling.

Purpose of Rolling

When we roll, we are effectively buying five slots that are each randomized according to our level. For example, at level 6, the chances are (25%, 40%, 30%, 5%, 0%) to get 1, 2, 3, 4, and 5 cost units. It is positive EV to roll when the “value” of these options together is more than the 2 gold we spend. The value comes from units that we would buy to play on our board, but it’s a hard thing to quantify exactly. Before they decide to roll players assess the game state to look for factors that might make rolling higher EV. This could be:

• Board Strength: If your board stinks and your opponents’ boards are strong, rolling to potentially turn some losses into wins or save health can raise your expected placement.
• Cost of Upgrades: If there are a lot of units you can hit in the shops that can make your board better (for example, if you have a lot of “pairs” and another copy will make an upgrade), getting board strength becomes relatively cheaper in gold since the shops are more likely to contain units that make you stronger.
• Health Totals: If you are low health, you need to consider spending your gold before you die to make sure you are as strong as possible.

With this in mind, let’s look at some of the spots I found myself in during the final days of the Jade Cup and see if you agree with my reasoning!

Case 1: Day 4, Game 2, Stage 3-2

Here, you should notice a few important things about my game state. The first is that I am the lowest health in the lobby, and by a good amount. I am in this spot because I opted on stage 2 to sacrifice my board strength to maximize interest. I am now sitting on a mountain of money, with 82 gold on stage 3-2, but my board has almost no upgraded units and is much weaker than that of the rest of the lobby.

This is a spot where I need to roll to make my board stronger, since I am already low and will keep losing a lot of health if I keep playing this board. I have two ways of doing this:

1. Roll on level 6 to hit big upgrades like Tristana and Jinx (our carries) and Tahm Kench (our frontline).
2. Level up to 7 using 36 gold and roll to hit one copy of stronger carries, such as Corki, frontline like Idas, and support like Sona (all 4-costs).

In this spot, I go with option 2. There are a couple reasons for this. From the previous section, I know that rolling is more attractive when board upgrades from shops are relatively cheap. Here, I am not sitting on a pair of Tristana, my main carry, and only have two pairs that I can hope to hit in a reasonable amount of gold.

There are a lot of units that I can roll for on level 6, but on level 7, it becomes 3 (5% to 15%) times as likely to roll 4-cost units in my shops, which are units that will be strong enough at one copy to get me through stage 3, and strong enough when upgraded to play for level 9 and a strong finish. Going level 7 also lets me add another unit that we can find since we are rolling anyway, and with the cannoneers board I am building, there are lots of units that I can throw in that will be strong and synergize well. If I could hit one Corki and Sona, that board would be stronger and relatively cheaper to find than my upgrades on level 6. After leveling, I had 46 gold left, and rolled to get this board:

This was a lucky set of rolls, as I found my Corki, an upgraded Ornn (4-cost frontline unit), and even a Soraka (5-cost, 1% chance on level 7). It left me with about 20 gold (including bench). This rolldown set my board up well to get through the rest of the game, and I ended up finishing in first.

Case 2: Day 3, Game 2, Stage 3-5

In this spot, while it looks like I have lost almost no health, I have lost nearly every fight up to this point. I only look healthy because one of my augments gives me 30 player health. My board here is strange: I have some upgraded frontline and support units (Shen, Gnar, and Lulu), but these units do not synergize, and I am still using an un-upgraded Karma (1-cost) as my carry.

Despite having a weak carry now, I see this as a bad spot to spend money to roll in. Including bench units, I am sitting on 41 gold and have no pairs. If I roll, I am only rolling for a better carry like an Anivia (3-cost), which makes upgrading this board very gold inefficient. I can use the health that I got from my augment to basically buy myself more time so that I can get more gold and level up to 7 so I can roll for more units (1 copy of some 4-costs like Neeko and Shi Oh Yu can help improve this board) alongside a better carry like Anivia or Daeja.

A theme you see in a lot of games is the idea of sacrificing health by waiting to roll in exchange for gold. In both examples so far, my board was much weaker than the rest of the lobby, but this time, I had much less gold and needed to get to an amount that I could roll and get board strength with. I have the time to do this since I have much more health to “trade” away.

Case 3: Day 4, Game 3, Stage 5-6

This spot comes much later in the game, where my board is almost as strong as it will ever get, and all the players are much lower in health. Here you see that I am around middle of the pack with just 15 health left. Losing by 6 or more units on stage 5 will knock me out, so I need to be careful. In my spot, I have very few upgrades left to hit, and there is only one unit that can make my board much stronger than it is: Shyvana, a 10-cost dragon.

I had two options to consider. I could either wait one round and risk dying on my pile of gold to get to the neutral round and level to 9 (16% chances for 5 and 10 costs like Shyvana) on stage 6-1 with 21 gold, or I could roll all my gold now to try to find one Shyvana (4% probability for 5 and 10 cost units).

To get a better idea of the probabilities, there are 8 different 5/10 cost units, so the chances of hitting a Shyvana is the chances of getting a 5/10 cost unit at the current level divided by 8. With 30 rolls on level 8, the chances to hit at least one is and with 10 rolls on level 9, the chances to hit are (you can reason that you would need about 4 times the rolls on level 8 as on level 9 since the chances are 4 times higher).

On the surface, it looks like the decision is close, and with the risk of never getting a chance to go to level 9 if hit hard enough this round, it can be tempting to say I should just roll the dice and try before I die.

A few factors pushed me toward risking it though. The first is that Shyvana is a dragon and takes up two slots, so to fit her in, I would have to drop either Ornn or Lee Sin along with Soraka, losing key stats from their traits on my Sett (my carry) and the Tempest stun. If I went 9, I could fit her in just by dropping Soraka and keeping useful stats on my carry. The other reason is that Soraka, when she casts her spell (once per combat), heals player health by 2, making it so I would need to lose by 7 whole units to die on this turn if she casted. Since most players only have 7 or 8 units on their board at this point, I thought the odds of my dying on this round were extremely low.

In the end, it looks like I could have used some work on my forecasting, as I died by exactly 7 units and did not get a chance to spend my gold, finishing in 6^th. It might be right to sweat the risk, but it won’t always work out.

TFT is a complicated game, and even amongst the examples I chose here, there could have been other reasonable courses of action. If you think that you disagree with some of my ideas and have a different take, drop them down in the comments below.