Great video, really helps to visualize what you're talking about here. I really like the point about limitations on the use of expected value in a single play of a boardgame. In poker, when you make a bet that has good EV you know that, over the course of multiple poker hands, you will come out a winner on enough of those hands that you *should* make a profit on a long enough time horizon. The calculation would have different weight if you knew that this one hand right now was all or nothing. EV would still be informative, but maybe not the only driver of the decision.
I also did some fun thought experiments about the complexity of EV when it comes to Lost Ruins of Arnak. I think its possible to play Arnak without ever adding a card to your initial deck (maybe not a winning strategy, but for the sake of argument it is technically possible to play that way). My question is this: if you never add a single card to your deck, could you say that that your EV of drawing 5 cards is the same each round? I think the answer is technically no, given that the card remaining on the top of the deck is effectively a known value. Practically, the answer is yes bc you're talking about a range of EVs from 3.2 - 3.4 so it won't really feel that different. The act of adding just one additional card to the deck (in this case, the dog) changes these calculations a lot. tl;dr if you're playing a deck building game, EV changes with every card added to the deck and you could spend a whole evening recalculating it every round and not necessarily win the game.
Yeah overcalculating EV isn't going to help you that much or be worth your brain cycles. And you're right that board games often lack "the long run" that poker or investing does!
I think that easier way to calculate in any game when you are looking for, will I draw at least 1 of X is to calculate the odds that you won't draw any and then just know that all other evens mean you drew at least one. So in case of 2 draws from a 2/5 sucess deck you will calculate 3/5*2/4=6/20=30% 100%-30%=70% This way it's very easy to do memory math in the middle of the game. However a big downside to this method is that it's much harder to calculate odds for drawing at least 2 cards.
@10:33 - You really think it isn't intuitive? I would have imagined that in the universe of people who enjoy economic/euro board games the portion who'd find branching paths fairly apparent would be high?
Hmm maybe I'm underestimating folks, and you're right that games have a huge sampling bias but in my experience as a teacher and a student, this is something that many folks struggle to mentally math.
In regards to your Arnak example, would the evaluation of futute turns always lead to the conclusion that you have to draw cards as long as you have at least 1 card with higher value than the base cards? Usually deck builers have the draw card cost integrated (if they don't, they become "broken" like old school MTG draw cards), so we should have the expectation that the extra benefit of having the high value card in the deck would be balanced by the game's cost of drawing a cqrd
I chose dog because it's one of the most powerful and versatile cards - when the relative value of your other cards goes down then the cost paid for drawing a card probably becomes a more significant drawback. So in brief, no, it's not always worth drawing because you might be giving up too many other bennies
Great video, really helps to visualize what you're talking about here.
I really like the point about limitations on the use of expected value in a single play of a boardgame. In poker, when you make a bet that has good EV you know that, over the course of multiple poker hands, you will come out a winner on enough of those hands that you *should* make a profit on a long enough time horizon. The calculation would have different weight if you knew that this one hand right now was all or nothing. EV would still be informative, but maybe not the only driver of the decision.
I also did some fun thought experiments about the complexity of EV when it comes to Lost Ruins of Arnak. I think its possible to play Arnak without ever adding a card to your initial deck (maybe not a winning strategy, but for the sake of argument it is technically possible to play that way). My question is this: if you never add a single card to your deck, could you say that that your EV of drawing 5 cards is the same each round? I think the answer is technically no, given that the card remaining on the top of the deck is effectively a known value. Practically, the answer is yes bc you're talking about a range of EVs from 3.2 - 3.4 so it won't really feel that different. The act of adding just one additional card to the deck (in this case, the dog) changes these calculations a lot.
tl;dr if you're playing a deck building game, EV changes with every card added to the deck and you could spend a whole evening recalculating it every round and not necessarily win the game.
Yeah overcalculating EV isn't going to help you that much or be worth your brain cycles. And you're right that board games often lack "the long run" that poker or investing does!
I think that easier way to calculate in any game when you are looking for, will I draw at least 1 of X is to calculate the odds that you won't draw any and then just know that all other evens mean you drew at least one. So in case of 2 draws from a 2/5 sucess deck you will calculate 3/5*2/4=6/20=30%
100%-30%=70%
This way it's very easy to do memory math in the middle of the game. However a big downside to this method is that it's much harder to calculate odds for drawing at least 2 cards.
Love this trick! I use it all the time especially when trying to figure out worst vs best case scenarios
👍
@10:33 - You really think it isn't intuitive? I would have imagined that in the universe of people who enjoy economic/euro board games the portion who'd find branching paths fairly apparent would be high?
Hmm maybe I'm underestimating folks, and you're right that games have a huge sampling bias but in my experience as a teacher and a student, this is something that many folks struggle to mentally math.
Woohooo! As a statistician, I approve of the video, just wish it translated into me being better at Gloomhaven.
Ha! Well I'm sure you know the odds that your attack modifier deck is going to spit out something you're happy with?
In regards to your Arnak example, would the evaluation of futute turns always lead to the conclusion that you have to draw cards as long as you have at least 1 card with higher value than the base cards? Usually deck builers have the draw card cost integrated (if they don't, they become "broken" like old school MTG draw cards), so we should have the expectation that the extra benefit of having the high value card in the deck would be balanced by the game's cost of drawing a cqrd
I chose dog because it's one of the most powerful and versatile cards - when the relative value of your other cards goes down then the cost paid for drawing a card probably becomes a more significant drawback. So in brief, no, it's not always worth drawing because you might be giving up too many other bennies
Statistics are I really need that 6 and by god I'm going to roll it.
Honestly, this is the best approach for maximum "hell yeah"s
Now for the religious question...frequentist or bayesian?😂
Fortunately I don't have to answer this question in my day to day but I'm closer to a bayesian :)