over cards

below is some info i've collected on over cards,
as a general rule of thumb for non gifted in math (me)
is this chart a good over all to remeber
reguardless of # players
or if not, then what about 6 or 9 players
or what would be good over all % to remeber
chance of at least one over card coming on the;
you---flop---trn.& riv. combined
kk-----23%------17%
qq-----41%------32%
jj-----57%------45%
1010---69%------57%
99-----79%------68%
88-----87%------77%
the % for turn river separtae are not really nessecary
but would be really to have. thanks.

[anatta]

When I first started playing holdem about five years ago, I read a book by Lou Krieger where he said something to the effect that I don't raise with JJ in a multiway pot since I know that I will see an overcard most of the time...

This really is nonsense, as our boy Ed Miller in his great book Small Stakes Holdem says, its all about the EV.

What I am trying to say is its nice to know the percentages or have a feel for them, but it really is all about making the correct decision. For example, your turn and river percentages for TT...this shows a pair of tens is vulnerable to overcards more that KK, duh! But how this effects your play...ie do you raise the flop to protect your hand, do you wait to see the turn in late position with many callers before you raise with TT, see if a good card comes, and then raise with the higher expectation of only one to come, etc.

Finally, I have to question your percentages. Every friggin' time I get KK...

[AaronBrown]

The number of players doesn't matter. Your figures for the turn and river are unconditional, that is they are the probability of getting an overcard on the turn or river regardless of whether or not you got one on the flop.

The unconditional probabilities are easy to compute. For each potential overcard rank, there is an 8% chance of an overcard on each board card dealt. So with KK there is one overcard rank (Ace). There is an 8% chance of getting an Ace on any specific board card. With QQ and two overcard ranks (Ace and King) there is a 16% chance. With 88 and six overcard ranks, there is a 48% chance.

With AA, it's not a bad approximation to multiply 8% by 3 to get the probability of flopping an overcard, and by 2 to get the probability of getting an overcard on the turn or river, regardless of whether or not you got one on the flop. But as the probabilities go up, the approximation gets worse. And even for Aces, multiplying 8% by 5 to get a 40% probability of an overcard somewhere on the board is not accurate, the correct answer is 35%.

The problem is the cases where you get more than one overcard. You have an 8% chance of getting an Ace on the turn, and an 8% chance of getting one on the river. The chance of getting Aces on both the turn and river is 0.5%, so the probability of getting at least one Ace is 8% + 8% - 0.5% = 15.5% (not the 17% in your table).

Here are the correct values for (in order) the chance of flopping an overcard, the chance of getting an overcard on the turn if you did not get one on the flop, the chance of getting an overcard on the river if you did not get one by the turn, and the chance of any overcard on the board.

KK 23% 7% 6% 35%
QQ 41% 10% 8% 60%
JJ 57% 11% 8% 76%
TT 69% 10% 7% 87%
99 79% 9% 5% 93%
88 83% 7% 9% 97%

thanks aaron for your time
slowly but surely adding math to my over all game package,
when i first started playing i couldn't add 2+2 and get the 4, now i can swat common outs like flys(by repetive reading). when it comes to the cards themselves i do see the need to have a feel of what to expect to or not to happen in in a mathamatical expectation.i think i got everthing i need on starting card
expectations, say i have suited conn. max. strech from a mathimatiacl point i may flop a flush draw about 11% time,open end straight draw 7% time,a pair 29% time and etc... same holdings, and so fourth with other starting hands
yes i do get its only from pen and paper point of veiw and not always reality. i can read material such as the psychology of poker once and go ok no problem. but when i see (even as simple to some floks) 9x9+2 i get a head ache
my next math project is to try and grasp some pot odds stuff.then i think i will be in good shape( at least for me). i think i know but i don't understand, say my oppoent is on a flush draw i'm supposed to bet some much of the pot to make it wrong for him to call. i have got some of the pot odds (taken ) from a book and i have looked at it some,
but??? anyways that for a future post(i will lok at pot odds and try to get it on my own first). ive looked at poker stove, but man i just.............
by the way im not to lazey to punch in the numbers my self but i just do not relate to doing math, i can some what understand the finllay answers though.