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A good player will take into account the odds of drawing specific cards when designing a deck. Exceptional players can work out the odds of drawing specific cards in each hand, and take that into account during each game. Don't worry about meeting the latter too often at Warlord tournaments; they're far more likely to be winning a fortune in a Casino playing poker! (edit: well, except for Breathweapon and Malexin, who do both in between writing stuff for us)- MatB Pete VG did some maths on the odds of drawing cards for your opening hand. He uses this to demonstrate the advantages and disadvantages of 50 and 60 card decks, to great effect. First he works out the odds of drawing a specific card during the first few turns. Then he attempts to find which size deck gives you more characters in your opening (and subsequent) draws. The last section explains Pete's conclusions. He's a mathematician, I'm not, I won't argue with his math; I will say that I broadly prefer 60 card decks, he prefers 50. (edit: in the more recent ampaign format, the differentials in deck size are more important to think about, certain decks (especially of the Healing archetype it appears) very much benefit from a 60 card deck. It does, however, depend on what you want your deck to do, as Pete has capably shown; he plays Tooth Fairy combo decks, I prefer armies of solid dependable Dwarves! (and, 3 years on, still do...) Mat Specific Card Is it better to have 50 cards or 60? Players seem divided. Here are some numbers that might help clarify your thoughts: Say you have three cards in your deck. You want to know the chance of drawing at least one of those cards in your opening hand. 'Tis easier to calculate the chance of not drawing the card and then subtracting from 1 to get the chance of drawing at least one card...and such is what I did. 50 cards: 1 - 41/44 x 40/43 x 39/42 x 38/41 x 37/40 = 1 - 0.69 = 0.31 = 31% 60 cards: 1 - 51/54 x 50/53 x 49/52 x 48/51 x 47/50 = 1 - 0.74 = 0.26 = 26% If you feel like number crunching (and for some reason I did on this dark and gloomy morning in California), you can calculate the chance of getting at least one of the card in the first 10, 15, 20, etc. cards...
I'm fairly confident that most Warlord games are not going to last beyond the 3rd turn once the environment matures. Cutting your deck down to 50 cards gives you a 10% edge in drawing the card that you want by the third turn, provided that you have three in your deck. That means that a 50 card deck'll perform better than a 60 card deck in approximately 1 out of 10 games. Opening Characters The argument for a 60 card deck is that you have a greater proportion of characters left after you remove the starting 6, and this is good, since characters are the best cards in the game. The question is whether the advantage conferred by having slightly more characters in your deck outweighs the disadvantage of not drawing the right character at the right time. Here're some more numbers, based on the assumption the deck consists of 50% characters: % Chars in a 50 card deck = 19/44 x 100% = 42% % Chars in a 60 card deck = 24/54 x 100% = 44% Likelihood of drawing at least one character in the first 5 cards: 50 card deck: 1 - (25/44 x ... x 21/40) = 1 - .049 = 95% 60 card deck: 1 - (30/54 x ... x 26/50) = 1 - .045 = 96% Thus far, it's not looking like there's much of a difference between a 50 and a 60 card deck as far as drawing at least one character in the opening hand is concerned. The 60 card deck only performs better in about 1 of every 100 games. Compare this to 1 in 10 games for the 50 card deck drawing a desired card by the 3rd turn, and the 60 card idea isn't looking too sound. To complete the comparison, one would really have to calculate the likelihood of drawing 2 - 5 characters in the opening hand.... The chances of getting in your opening hand (assuming 50% characters): [A full breakdown of Pete's math can be found here.]
So...you have roughly a 7% better chance of getting more characters than actions/items (at least 3) with a 60 card deck than with a 50 card deck. Part one shows that you have a 10% better chance of drawing a "3 of" card by the third turn with a 50 card deck. In constructing your deck, you've gotta decide which is more important: drawing lots of characters in the opening hand, or drawing that Nimble Fingers before the game is over. There are more paths to investigate here...you might compare the chance of drawing x number of characters by the third turn with that chance of drawing a specific card by the third turn, or you might look at the chances for cards that you have 2 or 1 of in your deck. I'm through with number crunching for now, though. Other brave souls may continue if they wish... Conclusion Most Warlord decks, IMO, want to see the cards that make the deck work by turn three. Most speed decks should've drawn their kill cards by this point, and most stall decks will want to have their heels dug in. If it has three of a specific card in the deck, a 60 card deck has a 63% chance of seeing at least one of those by the third turn, provided that you're drawing 5 cards per turn. A 50 card deck has a 73% chance of seeing a "3 of" card in the first 15 cards. Here, the 50 card deck has an edge. The difference is 10% - The 50 card deck will perform better in about 1 out of every 10 games. Another significant number is the number of characters you draw in your opening hand. A 60 card deck has a 44% chance of getting at least 3 characters in its opening hand, whilst a 50 card deck has a 37% chance. Here, the 60 card deck has an edge. The difference here is 7% - affecting roughly 7/100 games. (This is about 2/3rds of 1/10, for comparison.) Both decks have roughly a 95% chance of drawing at least one character in the first five cards, which means that both are basically equivalent at avoiding character screw (though a 50 card deck *is* probably more likely to draw that big character that you can't play, given the assumption that a 60 card deck will play a higher proportion of weenies to fill out its ranks.) There are other factors that come into play here. More number crunching would reveal how great a difference there is between 50 and 60 card decks as far as the number of characters drawn by the third turn goes. Also, slower decks will want to avoid running out of cards, and so might go to 60 cards. These numbers are just to get people thinking in more concrete terms about the 50 vs. 60 decision, and whether it fits your specific deck. Fare thee well, ~ PeteVG Rogue Elf Bringing you Dark Lores of Revenge(tm) for more than six generations. Appendix The chance of getting exactly 1 character in the opening hand in a 50 card deck is: 5!/(4!1!) (19 x 25 x 24 x 23 x 22)/(44 x 43 x 42 x 41 x 40) = 5 x .044 = .22 = 22% The chance of getting exactly 2 is: 5!/(3!2!) (19 x 18 x 25 x 24 x 23)/(44 x 43 x 42 x 41 x 40) = 10 x .036 = 36% Exactly 3: 5!/(2!3!) (19 x 18 x 17 x 25 x 24)/(44 x 43 x 42 x 41 x 40) = 10 x .027 = 27% Exactly 4: 5!/(4!1!) (19 x 18 x 17 x 16 x 25)/(44 x 43 x 42 x 41 x 40) = 5 x .018 = 9% Exactly 5: 5!/(5!0!) (19 x 18 x 17 x 16 x 15)/(44 x 43 x 42 x 41 x 40) = 1 x .011 = 1.1% So, chance of getting... At least one character: 1.1% + 9% + 27% + 36% + 22% = 95% At least two: 1.1% + 9% + 27% + 36% = 95% - 22% = 73% At least three: 73% - 36% = 37% At least four: 37% - 27% = 10% At least five: 1.1% For a 60 card deck, the calculations go as follows: Exactly 1: 5 x (24 x 30 x 29 x 28 x 27)/(55 x 54 x 53 x 52 x 51) = 5 x .038 = 19% Exactly 2: 10 x (24 x 23 x 30 x 29 x 28)/(55 x 54 x 53 x 52 x 51) = 10 x .032 = 32% Exactly 3: 10 x (24 x 23 x 22 x 30 x 29)/(55 x 54 x 53 x 52 x 51) = 10 x .025 = 25% Exactly 4: 5 x (24 x 23 x 22 x 21 x 30)/(55 x 54 x 53 x 52 x 51) = 5 x .018 = 18% Exactly 5: 1 x (24 x 23 x 22 x 21 x 20)/(55 x 54 x 53 x 52 x 51) = 1 x .012 = 1.2% So, chance of getting... At least one character: 1.2% + 18% + 25% + 32% + 19% = 95% At least two: 95% - 19% = 76% At least three: 76% - 32% = 44% At least four: 44% - 25% = 19% Five: 1.2% |
TaKtiX@TaKtiX.Org Pete Vander Giessen is a California based player. A friend of DadofDavid, he can usually be found playing L5R and Warlord in the Pasadena Games Zone. |
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