Triple card draw in a row

naabaldan

We all know card draw is completely random and there is a chance to draw the same card three times in a row.

But as far as I can say this happens more often than it should, especially at the beginning of a new game.

This was reported by members of my coalition also.

I may be wrong - please correct me if - the chance to draw three times the same card in a row at the beginning of a game is

0,04% ((40*39*38)/(4*3*2) = 24/59280=0,0004048583). To pull a masterpiece from the kaladesh block has a higher chance ;-)

Some screenshots available.

Naabaldan

EvilDead

Too bad that luck isn't happening when you open packs!!!

Feden

Although still small, I think it's actually 0.4% to draw any card 3 times and you gave the chance of drawing a specific card 3 times.

Either multiply by 10 (for each of the 'successful' outcomes) or you can just ignore the first card, since any card has same odds to be drawn first and you really just care if the next two match the first one.  Then the probability that the second matches the first is 3/39, and then 2/38.  So 3/39*2/38 ~= 0.4%

naabaldan

You are wrong. Sorry. Duplicate cards are considers chances are multiplide. First chance is 10%. Second is 7.7% and third is 5.2%. The chance to get three in a row is 10%x7.7%x5.2% approximately. Or 0,04%.

Laeuftbeidir

Whether it's 0,4 or 0,04 - it means you can expect it to happen once in 250 or 2500 matches. Regarding all the matches played, it's totally possible that one player sees this happening several times,so more people have to report it to make a big likely - I mean, we've actually had that issue a year ago.. I'll monitor it for myself.

ertaii

You're basing your calculations on actual paper decks. I think the drawing events are uncorrelated since sometimes you get to draw more than 4 identical cards. Basically that means that every time you draw a card you get one chance out of ten to drawing any card. So, choose any card for you first card. You've got one chance out of ten to draw it a second time, and equal probability for the third draw. That gives you 1% chance to draw three times in a row the same card. Which would fit more the fact that this happens quite often.

Laeuftbeidir

ertaii said:

You're basing your calculations on actual paper decks. I think the drawing events are uncorrelated since sometimes you get to draw more than 4 identical cards. Basically that means that every time you draw a card you get one chance out of ten to drawing any card. So, choose any card for you first card. You've got one chance out of ten to draw it a second time, and equal probability for the third draw. That gives you 1% chance to draw three times in a row the same card. Which would fit more the fact that this happens quite often.

That's not correct. You start with a 40 card deck, whenever you reach the end of it, another one is generated. Fetching specific cards is a way to get more than 4 copies in hand, but it'll not likely happen naturally.

We had that theory and did some crowdresearch that proved the 40 card deck.

Bubbles

This started happening after the last major update when a lot of things went buggy. I have way more duplicates now, often the same 3 cards over and over for the first 10 rounds. 

naabaldan

Your assumption is not correct. When the deck is initialized it has 40 cards 4 of each one. Later in the game, when you draw more than 4 of one card the deck gets invalid and is refilled. that way you can get more than 4 cards of one. even if you calculate that you have the same chance every draw its 10%x10%x10% = 0,1% of a chance.

But this is not true.

Volrak

Feden said:

Although still small, I think it's actually 0.4% to draw any card 3 times and you gave the chance of drawing a specific card 3 times.

Either multiply by 10 (for each of the 'successful' outcomes) or you can just ignore the first card, since any card has same odds to be drawn first and you really just care if the next two match the first one.  Then the probability that the second matches the first is 3/39, and then 2/38.  So 3/39*2/38 ~= 0.4%

Feden is correct.

If 4/40 * 3/39 * 2/38 was the chance of drawing any unspecified card three times in a row in your opening hand, then it would follow that 4/40 * 3/39 would be the chance of two of the same unspecified card, and 4/40 would be the chance of drawing any unspecified card one time in a row.  It's hopefully obvious that the chance of drawing 1 unspecified card once in a row is 100%, not 4/40.

Skiglass6

Mathematically it would be correct to ignore the first card if calculating any three of the same card pulled instead of a specific three.  However, the OP can not disregard the probability of the first card drawn. The OP would need to evaluate the deck and calculate probability of pulling a card that is not useful in the beginning of the match. I doubt OP would be posting this if Summoner’s Pact was the card pulled three times in the beginning, an off color match still plays all three cards and gets a turn 2 kill from it.