12 replies to this topic

[Naismith]

I feel stupid asking this since I feel like the answer should be easy -- or at least easy to find.I know how to figure out the odds of the next card hitting. For instance, if I'm holding KQ diamonds and the flop comes J-10-X with two diamonds, I know that I have 15 clean outs out of 47 remaining cards.My question pertains to figuring out the turn and the river. In the above scenario, I'm looking at hitting the turn 1 in 3 times, roughly. If I miss, it's still about 1 in 3 on the river. How do I figure out the odds of hitting on the turn OR river as opposed to just one or the other?I'm sure I can find the correct answers to the odds in one of my books, but I'm more interested in getting the actual math equation.Peace,Jay

[JaysonWeber]

Your odds to improve to ATLEAST a straight holding an open ended straight flush draw is 54%.Is that what you were asking?

[Naismith]

I wasn't asking for this specific situation, just using it as an example. I was looking for the math equation to figure it out...in that specific situation, to improve to a straight or flush, it's about 33 percent on the turn. I trust your 54 percent number for the turn and the river...I just don't know the math formula to figure it out.Thanks for your response. Hope I explained it better.Peace,Jay

[UglyJimStudly]

Naismith said:

How do I figure out the odds of hitting on the turn OR river as opposed to just one or the other?

Rough guide that's close enough for government work: count your outs after the flop, and multiply by 4. That is pretty close to the percentage chance that you'll hit on the turn or river. So if you flop an open-ended straight draw (8 outs), you have roughly a 32% to hit on the turn or river, which works out to close to 2-1 odds. If you paired one card on the flop and figure someone else has a bigger pair, then to win you need to either pair the other card or make trips; that's five outs (three to pair your other card, two to give you trips), so roughly a 20% chance that it occurs, odds of about 4-1 against making it.This shortcut isn't quite exact, but is usually close enough for betting purposes since you're looking for advantageous pot odds anyway - i.e. you don't want pot odds of 4-1 when you're making a 4-1 draw because that's just a break even situation, you prefer the pot to be at 5-1 or more so you can make some money.A similar shortcut works on the turn, there you double the outs to figure out your percentage.

[Abbaddabba]

You have 15 clean outs, firstly.4 aces, 4 9's and 13 diamonds minus the four you see on the board and in your hand, minus 2 for the fact that one of the aces is a diamond and one of the 9's is a diamond.Clean meaning that you're assuming someone doesnt have a higher flush draw and assuming someone doesnt hit a full house, even if you hit. Those should be factored in, but first you want the PR of hitting.15/(52-5) = 31.91% ... worse than a thirdAssuming a hit on the turn, you have a 100% chance of completing a straight or flush by the river. Supposing you miss on the turn, there is one fewer card in the deck (52-6)If you did not hit on the turn, you ahve a 15/(52-6) = 32.6% chance of hitting on the river, weighted by the probability of needing the river in order to complete it (meaning that you didnt hit on the turn).The weighted average would be .3191*1 + [(1-.3191) *(.3260)]= .3191 + .22197= .5411In other words, you have roughly a 54% chance of completing one of your draws by the river, with the given knowledge on the flop.

[Abbaddabba]

With that kind of a draw, you are favored to virtually anything out there heads up. Only a set and POSSIBLY nut flush draw with a pair, has you.The probability of you beating a set is (and makes the working assumption that the pr of quads given knowledge of a set is roughly as probable of going runner runner for higher trips).[1-.5411 * 0] + [(.5411) * (pr of board pairing up) * (0)] + [(.5411) * (1 minus pr of board pairing up) * (1)]The probability of the board pairing up need only be 7.5% in order to make it favored to you, and im fairly certain that it is at LEAST that likely even without calculating it.It's actually a lot more complex than that, when you consider that some of the events are potentially mutual and others cannot be. Ie: connecting for a full house and hitting the flush in the same card.

[jogsxyz]

Naismith said:

If I miss, it's still about 1 in 3 on the river. How do I figure out the odds of hitting on the turn OR river as opposed to just one or the other?Peace,Jay

It's all done backwards. It's one minus the chances of missing on both cards. On the turn you have 32 ways to miss out of 47 and on the river you have 31 ways to miss out of 46.32/ 31/ /47 times / 46 = 45.91 - 45.9 = 54.1But usually you chances of winning is a little bit less. Sometimes the other guy makes a boat when you make your straight or flush.

[Naismith]

Wow, thanks for the responses.I guess I was wrong in my initial assumption that it was simple! :)Peace,Jay

[randomization]

There are a couple of different questions. If you just want to know the chance that a certain card (or one of a group of cards) falls by the river, you do: 1-(chance of hitting on the turn) x (chance of hitting on the river). So with your 15 outs, that's 1- (15/47) x (15/46). That's pretty easy with a calculator. Another question is what your chance of beating a certain other hand is. That's pretty easy to find out, but obnoxious to calculate. If you just want the answer, try www.twodimes.net/poker/ which will give you answers when you specify hands. As for doing it yourself, I'd suggest you find a website or book on probability. They'd explain better than I would (and you'd understand what you were doing better than if you just got a recipe).

[Naismith]

Again, thanks for the help.I know somewhere around the house, one of my books lists all the odds of hitting a specific number of outs by the river after the flop. I'll be damned if I remember which book it is, but it's something I'll try and find and memorize the stats for.I wanted to have the math equation so I could do it on the run, but I'm not so sure I'm capable! :)As for the odds of it beating a specific hand...that's not exactly what I was looking this time, but I appreciate the link!Peace,Jay

[MrConceit]

There are multiple ways to figure this out, just like most math questions. :)Possibly the easiest is jogsxyz's method of doing it backwards.Another way is Abbaddabba's which certainly works, but to me seems complicated.I prefer my 3rd way.To explain it in words first, you do first the obvious 15/47 you have to hit on turn, then you add that to your chance of hitting on the river TIMES your chance of having missed on the turn.In math it is:15/47+15/46*32/47 which is 54 percent.For flush draws it works the same to get you the correct answer of 35 percent.9/47+9/46*38/47I didn't bother putting in ( ) since order of operation makes it obvious here. :)And sadly yeah, it's not as simple as you'd first assume it to be. Though once you get used to doing this kind of stuff, it does become not too hard. You just have to get the method down, whichever method you choose to use that is.[Edit]Oh laugh, I'm an idiot. Before you mock me Abbaddabba, I did just realize I'm just saying the exact same thing you are. Though I did think you made it sound more complicated than it has to sound! But when I reread yours - I'm just repeating you. SORRY!

[Naismith]

Well, I tried to figure out how to do this in my head, but then remembered that I'm an idiot. I don't think I'd be allowed to pull out my cell phone and use the calculator on it while at the table. So...http://www.texashold.../odds_chart.phpI'm cheating. :)Thanks for the responses. I'm glad I at least know the formula now!Peace,Jay

[Abbaddabba]

Unless you really know your math and stats, intuition is probably a better tool to make your decisions with. It's easy to plug one number in incorrectly and come to a ridiculously high or low miscalculation, resulting in an bad decision that could have been avoided on base intuition.I see plenty of people "calculating" the pot odds in ring games, only to come up with a ridiculously bad decision despite what they think is perfectly rational. Common mistakes include neglecting your draw losing to a better draw (or made hand), failing to realize the magnitude of a bet relative to the pot (though you have to be a bit of a 'tard to do that), failing to acknowledge the potential for additional raises from players yet to act (effectively raising the value you need to invest to go for the draw, miscalculating fold equity if you miss your draw, miscalculating the implied odds of if you do hit your draw, misreading what you think someone else has... the caveats are endless. I sincerely doubt that even the biggest pro's go through rigorous mathematical operations like that in their head, except in rare circumstances where it's they're heads up and ready to call an all in, and they feel as if they have an incredibly strong tell.Play enough hands and you'll build up a better intuition, so you have to rely less on calculations that (unless you're a math genius) will result in errors, left right and center.