AQT8 has 26 "outs" (or actually cards that dodge the villains outs) but needs to hit one of the 26 cards on turn & river both in a row, AK66 wins by hitting one of the 15 outs on turn OR river.
Simple calculation, but to get the equity for the AK66 hand it’s easier to calculate the probability that this hand will NOT hit an out and win. We know 11 cards, so there are 41 left in the deck. On the turn, 26 are losers, so the turn is a loser with probability 26/41. Similarly, on the river we now know 12 cards and assuming the turn was a loser, there are now 25 losers left. Therefore the river is a loser with probability 25/40. The probability of both of these cards being losers is the product of these two 26/41 x 25/40 = 130/328. So the equity is 198/328 (1 - loss probability) or 60.4%.
The difference between this value and the stated 59% likely comes from runouts where AK66 hits an out but loses anyway, such as a K turn and a J river (neither being a spade), which gives AQT8 a straight.
I came to poker already knowing most of the math necessary to play. (I have a BS degree in Chemistry with a mathematics minor). The basic probability calculations were just applications of things I’d already learned — expected values, equities, pot odds vs card odds, etc. But don’t let these intimidate you; such calculations are really not that complex; they just require clear thinking about the problem at hand, much like the OP situation where the key is to realize that one player wins if he hits an out on either card and the other must have a favorable outcome in both cards. Certain probabilities come up repeatedly in poker - how likely is it that I will hit my flush draw? How likely am I to flop a set when I have a pocket pair?, and so forth.
For situations where you have counted outs and need to translate that into an equity, there is a handy approximation that even a math dunce can use - the rule of 2 (or 4). This rule says that if you have x outs, the probability that the next card will be one of them (expressed as a percentage) is 2x. For example, if you have a pocket pair with flop overcards and myou believe your opponent has made a higher pair, you have two outs. The probability that you will make a set on the next card is approximately 4% (which is why you should fold in most cases - you need to get 24:1 odds to make a profitable call). If you have a flush draw you have 9 outs, so the probability of hitting it on the next card is about 18%, meaning you need about 4:1 odds to call profitably.
The rule of 4 part comes (in case you havenÂ’t already guessed) when you have two chances to hit your out. In that case you multiply your number of outs by 4 to get the percent chance that you will hit your out on either of the two cards. For the set, you have about an 8% chance of hitting it on the turn or river. For the flush draw itÂ’s about 36%. Note that the rule gives about 60% in the hand you posted, so it still works pretty well for 15 outs, but it obviously becomes less good as the number of outs increases. For example suppose we were to play a game where you guess black or red, you get two cards, and you win if either one is the color you guessed. The rule of 4 applied blindly to this game predicts that you have a 104% chance of winning, which obviously is absurd (you have 26 outs; 26x4=104). For most practical poker situations this wonÂ’t be an issue - you rarely have that many outs.
What you should be careful of is misusing the rule of 4. In the spot you posted, for example, you should really be more concerned with the chance of hitting an out on the turn, unless one player has shoved the flop. That is because if you miss you may have to call another bet in order to see the river. You may be forced to fold if you donÂ’t have proper odds to continue, meaning that you donÂ’t actually realize all of your equity. The proper time to use the rule of 4 is when one player is all in on the flop; then you are guaranteed to realize all of your equity.
How are you assigning suits? Can't have two 6c .. and .. if clubs are covered then AQT8 can't get to 48%
Also .. PLO 'drawing' may be tainted if not to the nutty side of the draw.
Also, also .. the Nuts on the Flop may not be able to improve, which leaves any holding susceptible to getting out-drawn with no backdoor equity to retake the hand on River.
The concept that NL players struggle with is that in PLO you may have the equity/odds to draw to the Turn but not necessarily take the lead in the hand. You're paying to 'maintain' your equity so you can continue to the River. Yes, some of your draw may require run-run but as long as you're equity correspondes to getting 2 to 1 (and hopefully getting paid off some of the time) you're +EV to continue. Hit a few of these and your opponents will be grumbling and you'll be set up for some big sessions. GL
i think you are confusing and falsely amalgamating "outs" and "being ahead"... sort of ok with 1 card left. but not with 2 cards left
lets simplify (and i rounded thimgs to make.math.intuitive)
1 card left, 45 cards not accounted for.. 15 outs for player B. then 33%_chance,of winning.. simply easy
2 card left.and ignore redraw possibility... then B has 30_outs. so 67% win.... the outs,doubled but "A leading" didn't double as they aren't outs.
technically B's chance of winming = 1/3 plus 1/3 time 2/3 = 5/9 or 55% as hitting two outs doesn't increase his chances of winning (given our assumptions)
IRL, there is redraw... with all money in, the redraw can actually be on the turn... more like it beats B hitting a draw.. and you need to separate clean outs from contested outs
so it's "A ahead" ---> "B outs" ---> "A redraw outs"... don't consider "A ahead" as "outs"... and A's "redraw outs" have value ONLY IF B hits an out
AQT8 has 26 "outs" (or actually cards that dodge the villains outs) but needs to hit one of the 26 cards on turn & river both in a row, AK66 wins by hitting one of the 15 outs on turn OR river.
hadn't thought of it this way mathematically vis a vis A player
player B has 15 outs, 2 cards to come so 67% chance of win. but 2 outs hitting don't help his winning % over 1 out hitting.. so 5/9 chance of winning (see my earlier.comment).. outs are "OR"
player A has 30 "safe cards" so 2/3 on each card.. needs to hit "safe card" twice... so 2/3 squared = 4/9... "safe cards" are "AND"
5/9 + 4/9 = 100%....
"AND" and "OR" are.the cornerstones of probability math and/or.math logic. this is first lecture of first year university course (although i think grade 8's could learn it"
