In Texas Hold 'Em:
In hand you have A and 10 of diamonds.
The “Flop” has two additional diamonds.
What are the odds of either filling the flush or getting another A are more than 50%?
(My thought is ~51% chance - 9 possible diamonds remaining, 3 additional As, out of 47 unknown cards, or 12/47 + 12/46 =~51%)
Would you go all in with that?
Your analysis seems correct to me.
What’s the question?
Just want to confirm my analysis, and see what the poler pros think of going all in with those odds.
Would I go all in with it? As with most questions regarding poker, the correct answer is it depends. Is it a tournament or a ring game? If it’s a tournament and I lose, am I out? How far away from making the money am I? How’s my opponent been playing? Is he a rock who raised before the flop? Is he a maniac? Could he have made a straight or two pair on the flop, meaning that the three Aces aren’t really outs? Do I maybe have some sort of backdoor straight draw as well?
If I’m first to act and I think I can move my opponent of the hand with the chips I have in front of me, and the pot is big enough to be worth it, then sure, I can make that semi-bluff. If I’m calling, or if going all in lays my opponent the right price to call, then I’m less likely to. Calling all in isn’t in and of itself unreasonable, but it’s almost always better to be betting/raising all in.
Let me ask another poker odds question. What is better against AA, another pocket pai or suited connectors?
The following is the correct method for determining the odds for your situation. But we need to note two assumptions for this specific case:
First assumption: you do not mind if both the turn and the river cards are diamonds, increasing the chance of another player having a flush, because you have the ace, giving you the highest flush.
Second assumption: you also certainly don’t mind if both the turn and river cards are aces.
Therefore, the calculation is easily made. First we determine the probability of not getting the flush and also not getting at least one more ace. The joint probability for these 2 possibilities is equal to the product of the probabilities. We then subtract this joint probability from 1, giving your answer.
The equation is : 1 - (35/47 * 34/46) = aprox. 45%.
Well, I meant the probabilities of not getting any of your desired cards on both the turn and the river. You multiply these two together.
Suited connectors. More straight possibilities, more flush possibilities, more two-pair possibilities. You’re still a huge dog, but with suited connectors you’re slightly less huge of a dog. You’re about 20% to win with a pocket pair and about 25% to win with suited connectors.
See! I knew I was doing it wrong.
Thanks misterdls.
Poker odds calculator. Won’t help determine the odds question for the OP but it will help GO answer his.
AsAd vs 9h8h: Aces are approximately 77% to win.
AsAd vs 8c8h: Aces are approximately 80% to win.
The odds will change slightly if the pairs or the connectors share a suit.
If the Pair can share a suit I’m not playing with your deck 
He means if the pair of aces shares a suit with the lower pair, or the pair of aces shares a suit with the connectors.
Misterdls gives you correct answer for your specific question, but in case you want to catch the next fish yourself, here’s a useful principle:
When you’re calculating probabilities, it’s correct to multiply the chances of two independent events occurring to determine the odds of them both happening. It’s not correct to add them together to calculate the odds of either occurring.
For instance, what are the odds of a drawing a red card from a fair deck in two draws? Is it 26/52 + 26/51? No, that would give you ~1.01, a statistical impossibility. It’s actually 1 minus the chances of drawing a black card in both draws, or 1 - (26/52*25/51) or ~0.755.
Go all in how? In response to a bet that would put you all in? Or are you betting all in, with some hope that your opponent will fold?
How big is the existing pot?
If you’re calling a bet that would put you all in, then at slightly less than 50/50 to hit your hand, the existing pot has to be big enough to push the odds in your favor (assuming you’re heads-up here).
If you’re betting all-in, there are other considerations. Let’s say there’s no way to buy the pot, because there’s a calling station in the hand. Then betting all-in with a big draw may cost you action you actually want. For example, someone with a small pair. On the other hand, if there’s a chance to win the pot outright, that’s worth a lot.
Incidentally, in your odds calculations, you have to factor in the possibility that you’ll hit your hand and still not win. You could make your flush with a card that pairs the board and makes your opponent a full house. You could hit your Ace, but it could give your opponent two pair, or he could already have that beat with a set or two pair.
For that reason, I’d downgrade the value of hitting an ace substantially, and downgrade the flush draw a little. So to call an all-in bet I’d want the pot laying me perhaps something like 65-35 instead of 45-55.
Another factor is the size of the bet in relation to your bankroll. One of the biggest mistakes young poker ‘professionals’ make is that they overbet their bankrolls. This is guaranteed to bust you out of the game eventually, even if you’re a winning player. Pro blackjack players know this, and spend a lot of effort working out optimum bet sizes in relation to their bankrolls. Poker players don’t, and it’s why so many good players wind up busted out of the game from time to time. So if that all-in bet is a significant fraction of your bankroll, sometimes you have to just let it go. But then, if calling an all-in bet would be overbetting your bankroll, you shouldn’t be in the game in the first place.
Without running it through the odds calc, I think the best hand against AA is 67suited. Higher suited connectors can make straights that eventually run into the A, causing you to lose the hand.
It should also be noted that RAISING all in is different from CALLING an all in.
Also, if you are holding the A10, there are straight possibilities that you may need to be factoring into the equation as well.
Also we need to know the texture of the flop. As Sam said, a paired board means you have to worry about your A as an over card not mattering, as well as your flush card making a boat. It’s also feasible that with a flop of 8d6d2c, that your 10 can be counted as another out or two.
Also, we need to know the preflop play. You could also be facing a player with AK, AQ, or AJ, all of which mean your A is dead. If they managed to pair the other card on the flop, both of your hole cards are dead, and all you have is the flush(or a backdoor straight draw, which you really cant count)
AA vs 98s - AA 77.22% 98s 22.47% tie 0.30%
AA vs 87s - AA 76.83% 87s 22.87% tie 0.29%
AA vs 76s - AA 76.81% 76s 22.87% tie 0.32%
AA vs 65s - AA 76.76% 65s 22.87% tie 0.37%
Watching some poker tourney I heard “the number of outs for your hand X 2” gives you a rough idea of your % chance to win the hand.
Good or bad poker math?
CMC fnord!
Number of outs times 2 times the number of cards left to come.
Bad. The difference in odds with two cards to come varies dramatically depending on how many outs you have.
But time for a small rant: New poker players today spend FAR too much time talking about percentages and odds. This is natural for a couple of reasons - one is that percentages are easy to show on TV, and a lot of new players get their exposure to poker this way. Second, a lot of hardcore poker wannabe’s are techie types who gravitate towards math in the first place.
But focusing too much on math will kill you. It is simply not important to know that your hand wins 23% of the time in a showdown vs 27% of the time. The difference between those two numbers is totally swamped by the intangible factors you should be paying attention to. The guy who is wrapped up in calculating the pot odds he needs for his draw may completely miss the fact that the other guy’s play indicates he doesn’t have much and might fold to a bet. Or that his betting pattern indicates that you are drawing completely dead.
You should learn relative hand strengths in a general sense. Know that a four-flush with two cards to come is almost always a playable draw in a limit game, and that a gutshot straight on the flop is only playable when the pot is fairly big. That’s good enough. Here’s a little quiz that illustrates this:
A good player limps in from early position. You call with 89s in late position. The flop is T73. The player bets into you. What should you do?
A) Fold. You have a straight draw, but there’s only 3.5 small bets in the pot.
B) Call. With implied odds, you should be getting the odds to draw to your straight.
Before you answer, hang on. Here’s what you should REALLY be asking at this point: What would a tight player be limping with from early position that he can bet into that flop? He would have raised with AK, AA, KK, QQ, and probably JJ. Are there any hands he could have that have a ten in them? Hmmn… Maybe ATs. But the odds are that he’s got AQ, AJ, KQ, or maybe a smaller pair like 99 or 88.
So the options I’d be weighing would be:
A) Call, with the intention of possibly raising him on the turn if a scary card for him lands. I’m in late position, so I could have anything. If he checks to me, I’ll consider either betting or checking, depending on what the next card is.
B) Raise. If he just calls, then if a scary card for me comes (A,K,Q) on the turn, I may just check and take a free card. If a scary card for him comes (T, 7, 8, 9), I’ll bet again.
Neither of those decisions has a whole lot to do with pot odds, other than the strategic raise that I might use to get a free card on the turn. WHat I’m really thinking about is what HE is holding, and what that means to my ability to win the pot.
And even on a straight odds calculation, it’s important to remember implied odds. The difference between 23% and 25% is not nearly as important as my understanding of whether I’ll be able to extract another bet out of my opponent if I do hit my hand.
When you’re in multi-way pots, the really critical thing to understand is what kind of draws you are up against. Too many players spend all their effort trying to figure out what the odds are that a flush will come in, without considering that a flush card that pairs the board may kill them, or that they’ll make a flush on the turn a fourth flush card will kill their hand, or that someone else is drawing to a higher flush.
When you have a made hand like top pair with no secondary outs (i.e. no 3 flush or 3 straight), and it appears that you are up against multiple draws, sometimes the best thing to do is to check and fold, even if you think you have the best hand. But the only way to know is to have an understanding of the kinds of cards your opponents will play from their position, and therefore how many big draws you may be facing.
Poker is a game that’s all about making the best decision in a sea of unknown information. The person who is the best at this will win the money. Spend your time honing your inductive reasoning so that you can eliminate those unknowns and outplay your opponents, rather than memorizing tables of exact odds.
Facing a good, tight player who limped from early position, I would raise with 89s pf. I think it is much easier to take the pot down on the flop if you have raised pf. I think also the limper is less likely to probe into a flop that you raised into if you have position, unless he has hit the flop, as the danger that you will reraise should slow him down. In either case, flopping a open ended straight draw is a raise post flop as well. 1)it will disguise the straight when it hits, and 2)since that flop most likely missed him, the raise probably takes the pot down immediately. If you are playing to raise postflop, I feel you have to raise it preflop as well, to make it worth betting on the draw.
I think it’s relatively easy to put the limper on AJ or AQ in EP. Any big pair is raising(except on partypoker, where every clown who gets AA UTG wants to limp in for some reason). Betting the draw on the flop should push out anyone sitting there with two overcards, so if he is calling the flop bet with 99 or 88, you can reasonably bluff As or Ks that hit on the turn or the river and push him out there too.