Exact formula for pot odds on turn&river

Here is my problem. I think I get how to calculate pot odds for ONE card on turn or river but in the charts there are always numbers for turn and river TOGETHER. And THIS I can't find out how to calculate.
Here is how I calculate my odds on the turn:
# of outs divided by the number of unknown cards (47). (this seems to match the charts)
I calculate the river by taking 46 as the number of unknown cards.
Now for a two outer the chart says 8.42 for turn&river together.
I tried to add turn and river odds but that doesn't work out. I tried to divide 4 outs by 47 unknown cards; won't work. Tried the same with 46 - no success. All the time I am close but I would like the EXACT SAME value because I don't think the author of the chart just put random numbers in the decimal places.
Please help me out with this.

Also: When do I use turn&river-together-odds? I was thinking that I should just use odds for the next card and not for the next two. If that matters: I play full ring limit hold'em. I thought that it might be if you need runner-runner but I guess those percentages would be WAY lower.

Please help. I have googled a long time but every site (and there are some) which explains odds of course only tells you how to work out odds for the next card and of course they don't tell you how to work out the turn&river-together odds which they have on their chart.

BTW: I am referring here to percantages :)

I think that after about 24 hours of research, posting and asking I have found the right formula. To get the PERCENTAGES for the 'turn&river' columns from the pot odds charts you have to do this:

(# outs/47) + { [ (47 - # outs)/47 ] * (# outs / 46) }

To get ratios:

1. #outs * 46 = A
2. (47 - #outs) * #outs = B
3. 2162 / (A + B) = C

Your ratio is: (C - 1) : 1

I am able to calculate all this but I am not sure when you actually NEED this percentages or ratios. Is it when you go all in on the flop and it is for sure that you won't have to pay anything for the river? If yes, is there ANY other situation where you would need this percentages or ratios?

I am not responsible if people go broke after using my calculations. Confirmation of their correctness or correction of them is very welcome :)

Or you can multiply your outs by 2 (for river) and 4 (for turn+river), possibly add a little something, to get within 1-2% of the real odds.

Quote:

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Originally Posted by jackvance

Or you can multiply your outs by 2 (for river) and 4 (for turn+river), possibly add a little something, to get within 1-2% of the real odds.

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That is exactly how I calculate them as well. You won't have time to be exact when you are at the table (unless you are Jesus Ferguson) so a close approximation is good enough. An example is:

You hold KQo and the flop comes J 10 6 rainbow.

You have an OESD and you think pairing up either of your hole cards will also win the hand, therefore you have 14 outs. You will now hit your hand approx. 56% of the time on either the turn or the river, so you can call just about any bet in limit poker as the implied odds make this a profitable call.

If you miss your outs on the turn you now drop to approx. 28% to win the hand and will now need roughly 4 to 1 odds to make the call.

Quote:

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Originally Posted by Ludanto

(# outs/47) + { [ (47 - # outs)/47 ] * (# outs / 46) }

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Forgot to mention, this is indeed correct. First term is hitting the turn, second is missing the turn and hitting the river.

About the ratio's: your calculations seem correct, but I never liked ratio's. I always use the percentages. Much easier if you're going to be doing calculations and comparing them to what you have to invest in the pot etc.

when I'm on the flop and want to know my equity (ignoring redraws for now), I just do the old (outs times 4, subtracting 1 for every out above 8). So something like a combo draw with a flush draw and a gutshot will have 12 outs, *4 = 48, -4 = 44.. about 44% that I hit.


990 games 0.015 secs 66,000 games/sec

Board: Qh 8c 2h
Dead:

equity (%) win (%) tie (%)
Hand 1: 51.7172 % 51.72% 00.00% { AsQs }
Hand 2: 48.2828 % 48.28% 00.00% { Th9h }

running outs (8+7, T+T, 9+9, T+9) give me some extra equity.

If he had Ah instead of As, his redraw would give him about 6% of extra equity.

An example of using the odds for hitting a draw with two cards to come would be calling on the flop in situations where either you or your opponent(s) will be all-in.

Im kinda transferring to odds rather than percentages now but use

outs x 4 for 1 - 8 outs over turn & river

(outs x 4) - 1 for 9 -12 outs over turn and river

(outs x 4) - 4 for 13-16 outs over turn and river

and anything more than that you always have odds to call anyway.

To get odds for just one street you just divide by 2 so

outs x 2 for 1-8
(outs x 2) -1/2 for 9-12
(outs x 2) - 2 for 13 - 16

I just use:

for turn & river - outs x 4 + 1 = percentage chance of hitting
for river - outs x 2 + 1 = percentage chance of hitting.

I actually checked the above agains tthe proper method and they are pretty close. Some are a bit over, 1-2 % max, some are a bit under by about the same, but when it all comes down to it, it's easy to work out and quick to do too.

J

Ok, I have an excuse to bring this up. Does the amount you have to put in to to pot to call count as part of the pot when figuring pot odds? Some books say it does, some don't. I can't figure out which way is right.

BTW, I also use percentages, I don't get odds at all. When I do sports betting, I always have to figure out that 5 to 2 is really +250.

Formula for the turn and river is W=1-[(47-X)/47*(46-X/)46] where X is the number of outs and W is the win percentage.

The formula for the amount you have to bet for your opponent to have even money odds to call, meaning the amount you want to bet more than (assuming no other callers behind or in front of him) is P*(W/(1-W)), where P is the pot size. Or if you want it directly form the number of outs, it is P*(-x^2+93x)/(2162-93x+x^2).

I think it does.

If you have a pot of 8 bucks and it costs you to 2 bucks to call, then that's a 5:1 pot odds thing (2 dollars to put in to win a 10 dollar pot, 10:2 or 5:1).

So, you take your 5:1/20% pot odds and compare them to the odds of hitting your cards, say a flush at the turn or by the river (turn + river) = about 37%.

Since you have got a better chance of hitting that that required to call by the pot odds, you can call knowing that, in the long run, you'll come out ahead.

Crap. After re-reading this a couple of times, I've confused myself too. Can anyone help out?

J