Highest Bidder: Theories of the High Score

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In my time playing Highest Bidder I have only experienced a player scoring all three cards of a round a handful of times. Naturally, this is a rare occurrence and a single player scoring all cards in an entire game is not only highly unlikely, but close to impossible. That said, in this post we’re diving in to the possibilities of high scores. What would it take to break the score record in Highest Bidder, and what is the highest score possible?

Note that this applies to the base game of Highest Bidder. The Art Auction version includes some advanced cards that take away points but those are not addressed here.

What is the highest possible score?

Theoretically, the highest possible score in Highest Bidder is 149 points. This would require a single player to win all 14 bids and that the two X2-cards (double points) are played on the five highest scoring cards – one in each round. Also, the 7-point card would have to appear during the very last round when it is already worth double points (for a total of 56 points).

Remember, in a standard game these are the 14 point cards:

  • 3x 1 point
  • 3x 2 points
  • 3x 3 points
  • 2x 4 points
  • 2x 5 points
  • 1x 7 points

A somewhat more realistic scenario would be for one player to take one card in each of the five rounds. If those cards happen to be the highest possible cards as outlines below, the total score with the two X2-cards would be 128:

  • Round 1: 4 points x2 x2 = 16
  • Round 2: 4 points x2 x2 = 16
  • Round 3: 5 points x2 x2 = 20
  • Round 4: 5 points x2 x2 = 20
  • Round 5: 7 points x2 x2 x2 = 56

Possible outcomes without the X2-cards

The likelihood of the X2-cards appearing together is slim. In a two player game, odds are that only one or none of the X2-cards are even dealt. The more players there are, the more likely it is that the X2-cards are in play however it also becomes more likely that they will be played on two different point cards.

Equally, it becomes more likely that the half points card (there is only one in a standard game) is in play. For the sake of argument, we are not going to look closer into that and assume that the half points card is never in play or at least never affects the point cards we are theoretically aiming for.

Without the X2-cards, the highest possible score if a player wins all bids (and there are no half point cards) is 55. If the last round is not automatically worth double points, it would instead be 43.

If a player wins one bid every round, which is more realistic, the highest possible outcome is 32 assuming the 7-point card appears during the last round, thus scoring 14 points.

Is there a high score sweetspot?

I think we can establish that there are a lot of variabilitets in play. Here are a few:

  • The number of players: Fewer players increase the likelihood of any given player winning a bid, but decreases the likelihood of the double points (X2) and half points cards appearing. On the other hand more players would likely spread the X2 cards out across multiple point cards.
  • Whether or not the X2-cards and half points cards are in play.
  • Whether X2-cards are played as intended or if they “misfire” (someone other than the player who played the card wins the bid), and the risk of them being deemed invalid as a result of other effect cards.
  • Whether the highest card (7 points) appears in the last round or not.
  • How the point cards in general are spread out across the rounds, for example if one round has a lot of high cards and another round has only 1 and 2-point cards. Ideally, in the cases suggested above, each round would have one high card and two low to maximize the effect of the X2-cards, however that in turn would increase the likelihood of all players going “all in” with their bids on the same card , making it less likely that one player wins all of them.

Is there a way to find a sweet-spot for high scores? What is the most likely highest score to ever be reached? This is beyond my comprehension but from experience a good score is somewhere around 40-50 points. A very good score is around 60-70 points. Certainly possible and not extremely unlikely. I doubt that the theoretical highest possible score will ever be reached, however I would like to see a score above 100 points one day.

Final example – an attempt at finding a likely highest score

Based on everything we’ve covered above, I would like to end this post by attempting to find a likely high score that might one day actually be reached. A score that is close to unbeatable, but not entirely unrealistic. I don’t have any hard statistics to go based on and I’m not sure of the math behind the likelihood of certain cards appearing (and being played as intended), but I’m going to assume the following:

  • Our player wins one card during each of three rounds and two cards during two rounds (so seven cards total). It is too unlikely that all of these will be the five most valuable cards, so let’s instead say that he’s lucky but not TOO lucky: 7, 5, 4, 4, 3, 3 and 2.
  • The last card (automatically worth double points) is NOT the 7. To increase the likelihood of it actually happening, I will instead assume it’s the 5.
  • During the last round, both X2-cards are played on the 5.
  • During the last round, our player actually wins both cards. Let’s assume the second card is only a 3, again to make it more likely.
  • During all other rounds, the score is doubled three times in total. In this case I will assume that it’s the highest remaining cards, so 7, 4 and 4.
  • None of the plays backfire and other players effect cards don’t “ruin” it for us.

The total score with the above assumptions: 81 points. Here’s the math:

  • Round 1: 2 points (no X2-cards)
  • Round 2: 3 points (no X2-cards)
  • Round 3: 4 x2 = 8 points
  • Round 4: 4 x2, 7 x2 = 22 points
  • Round 5: 5 x2 x2 x2, 3 x2 = 46 points

Unlikely, but not impossible, and not entirely unrealistic.

What are your highest scores, and do you have any input on the above arguments and reasoning?

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