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Market Making

Market of Cards – Group Market Making Game

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Market Making Game ~10 min Guided tutorial
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Play Now Access includes a guided tutorial for your first game
Overview
Market of Cards is the classic group market making game, actually played at some trading firms on their final-round super day, where candidates make markets against each other at the office. In this single-player version you trade against adaptive AI bots. Every card in play, your two private cards, each bot's two private cards and the shared centre cards, adds up to a hidden true value. You and the bots take turns posting a bid and ask that the rest of the table trades against, a centre card is revealed after every round of quotes, and when the last card flips your trades settle against the true total. Your only private information is your own hand, so the game is about estimating the true value better and faster than the bots.
Example: your turn to quote
You see your own two cards and the centre cards revealed so far. Everything still face down you have to estimate. On your turn you post a two-sided market on the total value of every card on the table, and the other traders decide whether to hit your bid or lift your offer. When they quote, you get the same choice.
Cards are worth ten times their rank, with red picture cards positive and black ones negative.
Game Phases
1
Value your hand Number cards 2 to 10 are worth their value times 10 in any suit. Face cards depend on colour: red Jack, Queen and King are +110, +120 and +130 while black ones are negative. The ace follows your setting, always +10 in lowest mode or plus and minus 140 in highest mode. Memorise these, fluent valuation is the whole game.
2
Estimate the true value Add your two cards to the expected value of every card you cannot see: the bots' hands and the unrevealed centre cards. A quick estimate using the average value per card beats a slow exact calculation, because in trading you rarely have time for the precise number and it barely changes your decision.
3
Quote your market On your turn you post a bid you will buy at and an ask you will sell at, with a spread of at most 20. Centre it on your estimate of the true value and skew it to manage your position. Quote too close to your own information and you give it away; quote at the table average and you risk trading in the wrong direction. Taking too long costs a 50 point penalty.
4
Trade, reveal, adapt When a bot quotes, you get first shot: buy at their ask when your value is above it, sell at their bid when it is below, or pass. After everyone has quoted, the next centre card is revealed, so re-estimate before the next round. The AI bots adapt their markets to your quotes and to each other, exactly like opponents in the live group game.
More Practice

Market Making Games

Probability Betting Game Fruit Market Making Game Free Make Me a Market – Facts & Guesstimates Example Cards Game Example Dice and Cards Game Basketball Game ETF Challenge Next Card Betting Fermi Questions The Marble Olympics
  1. How do you go about calculating the standard deviation in the dice and cards game in your head? Is there any trick to do that calculation mentally or do you have to consider every single outcome?s
  3. Do firms actually use these card values (or similar) in their superdays? The scoring feels very odd since normally the EV per card is 7 or 8 (depending on the Ace value). The difference between that and this is big enough (for example, black face cards being negative) that I don’t feel like I’m gaining good intuition for the more likely scoring system (EV per card is 7 or 8).
    1. It’s actually usually the opposite. The 7 or 8 is too straightforward, so this is the type of alternative scoring systems the firms use. Firms use different ways to change the scoring system, of which the one in this game is one of them.
  4. The bots have deterministic behavior AND do not take into account inventory or other player’s pricing on their own pricing. This makes it very easy to know at which prices they’ll quote after you’ve seen their first quote. Memorizing the pnl is very hard, but the game becomes trivial once you know that.
  5. How long do they usually give before starting rounds. I understand that the time between rounds for buying/selling is probably a couple of seconds but how much time do they give to calc EV before a round starts? I was wondering for both the group market making game and especially the EV card game for market event scenarios (ex. if only cards under 9 are being played) since we would be calculating the EV by hand.
  6. [16:06:35] My own hand value: 120, Total expected value: 500.8
    [16:06:41] You quote: 490 at 510
    [16:06:41] AI 1: “Mine at 510”
    [16:06:48] AI 1 quotes: 584 at 604
    [16:06:54] You: “Yours at 584”
    [16:07:26] AI 2 quotes: 429 at 449
    [16:07:29] You: “Mine at 449”
    [16:07:31] AI 3 quotes: 415 at 435
    [16:07:33] You: “Mine at 435”
    [16:07:34] My own hand value: 120, Total expected value: 508.5
    [16:07:49] You quote: 500 at 520
    [16:07:49] AI 1: “Mine at 520”
    [16:07:56] AI 1 quotes: 592 at 612
    [16:08:00] You: “Yours at 592”
    [16:08:03] AI 2 quotes: 437 at 457
    [16:08:05] You: “Mine at 457”
    [16:08:06] AI 3 quotes: 423 at 443
    [16:08:07] You: “Mine at 443”
    [16:08:08] My own hand value: 120, Total expected value: 506.2
    [16:08:31] You quote: 498 at 518
    [16:08:31] AI 1: “Mine at 518”
    [16:08:36] AI 1 quotes: 589 at 609
    [16:08:39] You: “Yours at 589”
    [16:08:40] AI 2 quotes: 435 at 455
    [16:08:41] You: “Mine at 455”
    [16:08:42] AI 3 quotes: 421 at 441
    [16:08:43] You: “Mine at 441”
    [16:08:44] My own hand value: 120, Total expected value: 533.8
    [16:08:56] You quote: 523 at 543
    [16:08:56] AI 3: “Yours at 523”
    [16:09:11] AI 1 quotes: 617 at 637
    [16:09:13] You: “Yours at 617”
    [16:09:14] AI 2 quotes: 462 at 482
    [16:09:16] You: “Mine at 482”
    [16:09:17] AI 3 quotes: 448 at 468
    [16:09:18] You: “Mine at 468”
    [16:09:27] It turned out that the total value of the table is 580
    [16:09:27] 
    Your PNL 937 points
    AI 1 PNL 130 points
    AI 2 PNL -477 points
    AI 3 PNL -590 points
    How is this PNL even calculated? Simply doing Sells-Buys is not giving the PNL value
    1. From your log, I see the following.

      Your buys:

      • 449
      • 435
      • 457
      • 443
      • 455
      • 441
      • 523
      • 482
      • 468

      Your sells:

      • 510
      • 584
      • 520
      • 592
      • 518
      • 589
      • 617

      So, 9 buys, 7 sells. Cross out 9 buys versus 7 sells to get a PNL of:

      • (510-449) + (584-435) + (520-457) + (592-443) + (518-455) + (589-441) + (617-523)
      • 61 + 149 + 63 + 149 + 63 + 148 + 94
      • 727

      The remaining two buys are at 482 and 468, while the table value turned out to be 580:

      • (580-482) + (580-468)
      • 98 + 112
      • 210

      So, the final PNL for you is 727 + 210 = 937.

      This is exactly what the log tells as well, so the game calculated the PNL correctly. Does the calculation in this reply help? If not, don’t hesitate to reach out.

      1. Thanks for the Explanation!
        Are we supposed to do these calculations simultaneously while making the market? There are a lot of calculations involved to do simultaneously. Or can we just give some approximate answers during the interviews?
        1. During an interview, with a group game like this, the trades will usually be logged. Sometimes you might need to make calculations in-between rounds, other times just at the end. So, normally you can use pen, paper and the logs all together to easily do the mentioned calculations.
    1. Did you have a look at the example here: https://www.tradinginterview.com/courses/market-making/lessons/market-making-interview-set-up/

      It shouldn’t be 6,740,000, because you need to add the 6,740,000 on top of the average price of your open two positions (as you mentioned, pos size +2). If after crossing out your lowest sells against your highest buys (to calculate the max guaranteed loss) your remaining positions are, for example, long at 3 million and long at 1 million, your average price being long is 2 million, so you add that on top of the 6,740,000.

      Example:
      buy at 10 mil
      sell at 1 mil
      buy at 8 mil
      sell at 2 mil
      buy at 6 mil
      buy at 4 mil

      1. Here, your max guaranteed loss is (10-1 + 8-2) = 15 mil.
      2. The remaining 2 long positions are on average long at 5 mil.
      3. If you sell 2 lots at 15/2 + 5 = 12.5 million, then you break even.

      Proof:

      Buys:

      • 10 mil
      • 8 mil
      • 6 mil
      • 4 mil
      • Total: 28 mil

      Sell:

      • 1 mil
      • 2 mil
      • 12.5 mil
      • 12.5 mil
      • Total: 28 mil

      Hope this helps, let me know if anything is unclear.

      1. I see, thank you!
        For calculating the max guaranteed loss, are you supposed to remember all the prices at which you bought & sold, or are you allowed to write things down?
        1. It depends on the company, for example at Optiver you are often expected to complete these task mentally, including breakeven points and such. It’s a big plus if you are able to do this.
          1. Sorry, one more question, I am not sure why my position would my position be 1
            I had the following game:

            Please make me a next market with a maximum spread of 5.

            I will buy

            Please make me a next market with a maximum spread of 5.

            I will buy

            Please make me a next market with a maximum spread of 5.

            I will buy.

            Now I will quote the next market. I want to buy 4 lots at 605. Do you want to trade?

            Yes, I will sell 4 lots to you (me)

            .Please make me a next market with a maximum spread of 5.

            I will buy.

            Please make me a next market with a maximum spread of 5.

            I will sell.

            This was the final round, now I will ask a few questions about your position.What is your position? (Example: if you are 2 short, write down -2. If you are 3 long, just write down 3)Position

            Your position is incorrect, the correct answer is 1

            If I sold 3 times, then sold again 4 times (since it asked to buy from me 4 lots), then sold again, and then it bough from me only 1 time, how can my total position be 1?

    1. If someone else says ‘Mine’, then that person is buying (vice versa with ‘Yours’). If you quoted a bid and an offer, it means the buyer who said ‘Mine’ is buying your offer, so you are the selling party.
  9. Hi! For some reason I cannot start the market making simulator with facts or guestimates. While in the market of cards games at the bottom I get prompts to sart game or go back to course, in the simulator I see only the back to course option. Am I missing something?
    1. Depends on which EV you mean – your own EV or the EV around which your opponents are quoting?

      Your own EV: no, this is just the EV as it is. It’s up to you if you use it as a mid-market or take on a different strategy.

      Your opponents mid market: yes, they take into account their own real-EV, but also include what others quote as well to adjust it.

      1. Hey Tolga, thanks for the response! I’m referring to the in-built one in the website that updates after round as the community cards reveal. The website tells me what my own EV should be but I don’t quite understand how it works?
          1. Done! Please have a look and let me know if it clarifies the calculations. As elaborated on in the lesson: we use the quick and efficient way to calculate the EV. For the game decisions, it makes no sense to go into too much details, such as the fact that cards aren’t replaced in the deck of cards. It will slow your calculations down too much without having a significant effect on your final decision on where you put your mid-market.
  11. What would be an appropriate strategy for this game? Should I set my new price based on my EV, or what my opponents are setting? Should I try keeping an inventory?
    1. At the end of the game, the card on the table are all visible. Now, you check the total value of the table. Let’s say it’s 300, and your trades were:

      buy at 200
      buy at 240
      sell at 150
      sell at 350

      The PnL per trade is:
      300-200 = 100
      300-240 = 60
      150-300 = -150
      350-300 = 50

      Total PnL = 100 + 60 -150 + 50 = 60

        1. During the interview, with a group game like this, the trades will usually be logged. So, you can use pen, paper and the logs all together to easily do the mentioned calculations.
  13. How is the expected value calculated? For example if I have 8 and black King then that is -50 points with 9 cards still covered. If I play with rules where Ace is 10, then expected value of each card we can’t see would be 55 points since it is average of Ace through Ten and pos/neg jack – king cancel each other out. Hence wouldn’t the expected value be 55 * 9 – 50 = 445. However the game says it is 330.8?
    1. I think you mean Ace is 1? Good question, this is a commonly made mistake: you are taking the average of 1-10 because J, Q, K cancel each other out, however, they are still there. Therefore, you need to add 3 zeros and divide the total by 13, instead of 10. So, with ace low, the average card value is

      10*(1+2+3+4+5+6+7+8+9+10+0+0+0)/13 = 42.3.

      -50 + 9*42.3 = 330.8

      Important to note: this off course doesn’t take into account that two cards are now out of the deck, and so the expected value per card should have slightly changed. However, the EV just serves as a rough estimate of where your mid-market could be. It would take too much time to constantly calculate the EV too accurately, considering the fact that those exact decimals won’t change your game play. In real life, you won’t have time to calculate it that precisely: the method above is the quickest/ most efficient.

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