# outs calculation

• Silver
Joined: 25.01.2009
hope u r doin well, Collin.
i know well u r a pro both in poker and maths.
for instance, i have a flush draw on flop, and normally they count that i will have my flush 9 times of 47 on turn and 9 times of 46 on river. But...
Don't u think we should take into account, namely discount the outs because they may be dealt to our opponents and thus i will never hit them. in case of a spade flush draw on 9-max table it means that i will miss 4 spades of 9 on average because 16 cards held by my opponents will contain 4 spades on average.
let me know yr email, and I will submit my calculation.

appreciate yr being explicit and convincing when pointing out at my mistakes.
• 10 replies
• Bronze
Joined: 03.04.2011
It is 9/47 on the turn and 9/46 on the river, because that is the expected chance of hitting a flush. In reality it might be 0/31 if every space is dealt to the players already, or it might be 9/31 if zero spaces have been dealt to other players than you - you will never know for sure.
When calculating your outs, I believe it is best to only focus on what you know. You dont know your opponents cards, therefore you have to see it as there is 47 unknown cards left and 9 of those will make you hit the flush.
• Moderator
Moderator
Joined: 27.01.2013
Hi Goget,

We don't have to take those cards villains might hold into account. It is true that your opponents will hold some amount of spades on average, but it doesn't matter. There are 47 unknown cards and 9 of those are spades. So the probability that the next card is a spade is 9/47.

You can basically take that into account if you want to but it makes this too complex without a reason. It is true that your villains will be dealt 4 spades on average if all cards are unknown. Since there are 4 cards known already (your hand + 2 on the flop) there are only 9 flush cards left. From those 9 flush cards your villains will be dealt only 3 cards on average, not 4. And since we take those cards into account we have to remove villains 16 cards from the deck also. This leaves us total of 6 outs on average in a deck on 31 hands. 6/31 is roughly the same than 9/47.

I'm not very good at math. I hope I'm correct when I say this and I hope it is not too difficult to understan.

Regards,

la55i
• Moderator
Moderator
Joined: 27.01.2013
Originally posted by Malendes
It is 9/47 on the turn and 9/46 on the river, because that is the expected chance of hitting a flush. In reality it might be 0/31 if every space is dealt to the players already, or it might be 9/31 if zero spaces have been dealt to other players than you - you will never know for sure.
When calculating your outs, I believe it is best to only focus on what you know. You dont know your opponents cards, therefore you have to see it as there is 47 unknown cards left and 9 of those will make you hit the flush.
It is 9/47 OTF and 9/46 OTT. On the river we don't have any outs anymore since there are no cards to come. There are 52 cards in the deck we have 2 and 3 are on the flop so total of 47 unknown.
• Bronze
Joined: 03.04.2011
Originally posted by la55i
Originally posted by Malendes
It is 9/47 on the turn and 9/46 on the river, because that is the expected chance of hitting a flush. In reality it might be 0/31 if every space is dealt to the players already, or it might be 9/31 if zero spaces have been dealt to other players than you - you will never know for sure.
When calculating your outs, I believe it is best to only focus on what you know. You dont know your opponents cards, therefore you have to see it as there is 47 unknown cards left and 9 of those will make you hit the flush.
It is 9/47 OTF and 9/46 OTT. On the river we don't have any outs anymore since there are no cards to come. There are 52 cards in the deck we have 2 and 3 are on the flop so total of 47 unknown.
Yeah I know. I said it wrong I guess - what I meant was "it is 9/47 chance on hitting OTT and 9/46 on hitting OTR"
• Bronze
Joined: 01.05.2012
Hi Goget,

Malendes has it right. The cards that are dealt to your opponents are distributed at random, so it doesn't matter if the unknown cards are in the hands of your opponents or at the bottom of the deck. They are unknown, and thus treated as such.

If you have a good reason to believe that a player has one of the spades in his hole cards (the most obvious example would be a player accidentally flipping over a card in a live game), then you may of course include this in your calculation. Otherwise, you'll have to treat them the same way as any other unknown card in the deck.
• Coach
Coach
Joined: 09.07.2010
I wondered the same thing when I was younger. And I calculated how often opponent has 0, 1 or 2 spades, what are the changes then and in the end the average % was the same as with 9/47.

If you don't believe, just do the math yourself. But treating unknown cards as unknows is the correct thing. Don't make it too complicated.
• Silver
Joined: 25.01.2009
TO ALL:
Thanks for responding guys, but all you say is nothing new to me.
of course all cards are unknown, and villians can hold from 0 to 9 spades. that's why i say at 9-max they will hold 4 spades on average on the assumptions that every 4th card is going to be a spade on average.
most important: the probability of coming spades from the left deck/pack is some probability. the probability of coming spades from the dealt cards is zero, but in yr approach you claim there is some.
i want to offend noone, but what u all have said so far is not convincing to me.
the difference in 2 types of calculation (example of flush draw) is about 6% for turn + river!!! 39% vs 33% which is considerable.
i am really eager to look at opinions of people who really excel in theory of probability; i think mr. Collin Moshman is one of them.
• Moderator
Moderator
Joined: 27.01.2013
It doesn't matter how many cards villains do hold on average.. It is irrelevant when calculating probabilities. Only thing that matter is the unknown cards.

You can do it the more difficult way as I explained earlier.

You said that villains have 4 spades on average in their total of 16 hands. Where did you get this? I guess you thought that 1/4 of the cards are spades so from villains 16 cards 25% -> 4, are spades.

Actually when you already know 4 of them because you have a flush draw, there is 9 spades left in the 47 unknown cards. So from those, villains do not have 1/4 spades, they will have 19.1% spades, which is 3,056 spades on average..

So your total outs are 9 - those villains have on average (3.056) = 5,944
Cards left on the deck = 31

5.944/31=0,1917
9/47=0,1914

So as you can see, this is the same calculation. You are only making it too complex without any reason. It can be achieved much easier.

So the difference between your two calculations is there because you thought there are 4 spades on average out there. But that would be true only if all of the spades would be unknown = you don't have a draw.
• Silver
Joined: 25.01.2009
thanks.
• Silver
Joined: 25.01.2009
I really made a mistake with the number of spades villains have on average in their total of 16 cards.
With both calculations the numbers are not even close, they are the same - 19,1489361702128%