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Is there an equation that represents the odd of hand Vs hand.

So for example

Heads up all in play

Player 1 AA Player 2 A3 off suit

Flop 2,4,Q Turn 5 River 9

What would be the odds of player 2 hitting the straight against player 1's pocket aces, and is there an equation to work this out?

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Pre flop there is not an equation. They run simulations.

AA was like 93% pre flop. That was a bad beat. Cover the top card with a pair is the most dominating hand. After the flop only needing the 5 changes things up to like 83%.

Search the web for poker equity calculator.

After the flop there are 47 unknown cards of which 4 are need so 4/47 = 8.5% on the turn.

Turn or rive is a little more complex but you can nominally double that.
Actually 4/47 + (1 - 4/47) x 4/46 = 16.5%

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As mentioned by Paparazzi, player 1 has 93% equity against the other player's 7%. So 93% of the time player 1 makes a move he will have the best hand.

Flop

2-4-Q

At this moment player 1 has 83.14% equity against a possible straight (2, 3, 4, 5 and Ace) or a backdoor set draw if a three comes up on the Turn, leaving to player 2 exactly 4 outs and 16.66% equity.

Turn

5

Well player 2 definetly hit the jackpot with this perfect turn card. With a completely plot twist in the game, player 2 now has 96.5% equity against player's 1 3.41% to river a three and chop the pot up.

River

9

With the nine on the river, player 1 is drawing dead with pocket aces against a straight with Ace high, leaving the player 2 exactly 100% equity.

Conclusion

There are some good and free softwares available on the internet, that you can use to understand better some poker hands, one good example is Equilab which by the way I use frequently, it's free and very efficient (although you can pay for some exclusive features as well).

DO NOT USE THIS KIND OF SOFTWARES IN ONLINE POKER, POKERSTARS FOR EXAMPLE, PROHIBITS ITS USAGE AND YOU'LL GET A STRIKE, IF YOU DO SO YOU'RE TAKING THE RISK OF LOSING YOUR ACCOUNT.

Also there are two way for you to find your equity, the first and the most simple way is the rule of 4 and 2, which on the flop you take your number of outs and multiply it by 4. So in this case with A3o you have 4 outs, therefore, 4 * 4 = 16% and on the turn you multiply your outs by 2, so assuming that you still have 8 outs, it would look something like 4 * 2 = 8% equity.

The other one is the most accurate but harder way to get it right while playing, that is to divide the number of cards that WILL help you by the cards that WILL NOT help and multiply the result by 100.

So in total there are 52 cards, let's say you're playing against nine players, everyone gets 2 cards, therefore, 18 cards won't help you already, leaving us with 52 - 18 = 34 cards. There are 3 cards on the flop, at this moment you have 34 - 3 = 31 cards available in the deck, of those 31 cards only 4 cards will help you (your outs), therefore 4/31 = 0.129032... then multiply it by 100 and you'll get 12.9% exactly.

It's up to you to choose which one to use, I personally use the second one only in very hard situations, in general I tend to use the 4 and 2 rule because most of the time the result is going to be sufficiently accurated.

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  • That is not correct. You don't know what cards the other players had. You don't know they did not have a card you need. – paparazzo Aug 25 '17 at 17:46
  • @Paparazzi you never know. That's why it's called probability, there are 4 outs that will help you but you can't know if they'll come at the end of the day it still poker and a bit of luck is needed. – João Brgai Aug 25 '17 at 19:28
  • Still not correct. A down card is a down card. Never mind. – paparazzo Aug 25 '17 at 19:33
  • @Paparazzi you can't base your judgement only by watching TV streams, because they know your exactly hole cards that's why there is more accurated results. Suppose you raise with QQ on the CO, the HJ actually folded Q8o, BT calls and the blinds fold. On the flop you don't know that the HJ had a queen, so you need to assume that you still have 2 outs for a set, otherwise you won't have any math judgement to help in your decisions. – João Brgai Aug 25 '17 at 19:34
  • @Paparazzi unless you know something else about your opponent which tells you the opposite. But anyway, how would you do then? – João Brgai Aug 25 '17 at 19:35

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