Odds for Hitting Outs on Turn AND River

[Mastershake73]

I am an Engineer and for some reason, having a terrible time understanding the odds for calculating outs on the turn and the river (2 cards to come).

I could just memorize the odds charts, but I won't be able to believe it until I understand the calculation.

Assuming 4 outs (gut shot straight) the chance of hitting that hand on the turn is 4 /(52-5) or 8.5%

If you miss on the turn and need to hit on the river, the chance of hitting is 4 / (52-6) or 8.7%

What I can't grasp is why those odds are not added to get the chance of hitting on the turn or the river.

I read that the difference is due to the times that you hit the card on both the turn and the river.

Could someone please explain this to me?

[JocK]

P(miss_draw) = P(miss_turn) * P(miss_river)

or:

1 - P(hit) = [1 - P(hit_turn)] * [1 - P(hit_river)]

so:

1 - P(hit) = 1 - P(hit_turn) - P(hit_river) + P(hit_turn)*P(hit_river)

or:

P(hit) = P(hit_turn) + P(hit_river) - P(hit_turn)*P(hit_river)

that's all...

(If you would simply add hitting probabilities, you would double count the cases where you hit both on the turn and the river...)

[alphatmw]

[ QUOTE ]
I am an Engineer

[/ QUOTE ]wtf?

[smbruin22]

if you add the two, it gives you total number of expected outs, but you just want the odds of hitting. hitting it twice won't help you.

so if you're 20% to get them on each street..

then, it's 20% + 80%*20% = 36%... and 4% of those times you'll hit it twice, but it's already included in the 36%

and this series will go asymptotic at 100% if you do it many times. (assuming 20% each time, and not running out the 52 card deck)

hope that wasn't too confusing

EDIT: alternatively, you can look at the chance that you miss both, which is 80%x80% = 64%. so 36% chance that you hit either one street or both streets, but in terms of you making it, it doesn't matter if you hit once or twice (certainly matters in the actual hand, but that's unrealted to question)

[vozzie]

the actual chance is

chance you hit 4th and not 5th + chance you hit 5th (and not 4th) + chance you hit 4th and 5th

(4/(52-5))* ((52-6-3)/(52-6)) + ((52-5-4)/(52-5))* (4/(52-6)) + (4/(52-5))*(3/(52-6)) = 16,47% when you have four outs, so your pot odds are 6.07

That is just basic statistics and if you are an engineer you should have paid more attention I guess

[godofPOPOV]

i came up with this formula and it seems to work:

x: (#of outs / #of unseen cards) [turn]
y: (#of outs / #of unseen cards) [river]

1 - [ 1 / ((x) + (y)) – ((x) * (y)) ] = odds to hit your draw by the river


so for example lets say you have 6 outs:

(4/47 + 4/46) - (4/47*4/46) = .165

then divide it by one and subtract 1 from it to get the odds:
1- (1 / .165) = 5.01 : 1






thats a pretty easy form.

now go ahead and memorize all the numbers so you dont have to calculate that at the tables!

[peten2toms]

Can any none genious post this in moron terms? I believe I read somewhere once that you simply double your outs, so say a 12 outer becomes 24 outer? So you simply go from a 3-1 dog to a 1.5-1 dog wrong or write?

[doctorjae]

i might be wrong, since i'm new to poker as well, but i believe that on the turn,it's the number of outs X 4 = %odds
and on the river it's the #outs X 2...

therefore 10 outs on the turn = 40%
and on the river 10 outs = 20%

i guess that means you're 40% and 20% to win the hand...

i'm sure i'll be corrected if i'm wrong...

[godofPOPOV]

edit: i meant to say subtract 1 from it, not the number from one. (otherwise it would be negative)

[warbler]

The doubling method works like this;

take your outs (4 in the case of a gutshot) and double it for your chance to make it on the next card (the turn - if your on the flop OR the river if your on the turn) which would give us an 8% chance to make our straight on the next card.

If you are paying to see two cards then double it again 4 doubles to 8 and that doubles to a 16% chance.

This method is a quick and dirty method of calculating your pot odds at the table and it is resonably reliable within a certain range i.e. from about 4 to about 14 outside of this range it begins to lose accuracy.

I used to hate this method and use more precise ones however I have long since been converted to it. I am curious as to what methods are predominatly used by the players here??