working out the maths

Hi I have been playing a bit of poker and although i know the odds for certain hands such as AK vs QQ etc i was curious about the maths behind these odds.

lets say if my opponent flops top pair but i have two overcards. with the turn and river to come who is the fave. or say if my opponent flops two pairs and I have nut flush draw with two cards to come who is the fave. or say u have one overcard vs pocket pairs.

how is the maths behind all these worked out? Thanks in advance. Just like to know if im the fave when im putting my money into the pot :)

it's just probability.

say you have AK and the flop is 367 or something like that. you have nothing except ace high. there are 2 more cards to come. you have 6 outs, the 3 aces and 3 kings. if this was heads up, there are 45 cards left unseen. so the probability of you hitting a A or K on the next card would be 6/45.

turn or river would be
6/45 + 6/44

turn AND river would be
(6/45) * (5/44)

those are the basic ideas anyways

so would i be rite to say with my AK against a small flop with someone holding a pair I would be roughly a 4 to 1 underdog to win the pot since 6+5/45 gives me roughly those odds? do i need to take into consideration his outs as well of hitting two pair or a set? thks

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Originally Posted by schenk

so would i be rite to say with my AK against a small flop with someone holding a pair I would be roughly a 4 to 1 underdog to win the pot since 6+5/45 gives me roughly those odds? do i need to take into consideration his outs as well of hitting two pair or a set? thks

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yeah pretty much. an A or K will flop i think around 30% of the time. so almost 1 in 3 you'll have TPTK on the flop, which will hold up to the river most of the time.

but if you were all in preflop, it's roughly 50% that either a A or K will come by the river. this is why AKs is ranked higher than QQ. i think it's something like 51% favourite for AKs. AKo is like 49% :P

if you have the button, you can bet to try and take the pot down right there, or try a free card on the turn to see both turn and river for 1 bet. it kinda gives your hand away if you take the free card though.

Immensely helpful - I think Fnord recommended this site:

http://simulator.pokertips.org/simulator.php

I highly recommend running some common scenarios through it so you can get a feel for various odds pre and post flop. I also recommend trying some with multiple hands, even if you just put in random garbage hands, because they will always reduce your winning percentage somewhat. (i.e. if you go all in with AA against AK suited, you're 87% to win... but if you throw in one idiot with 27 offsuit, suddenly you're just 76% to win. And funny enough, 27 guy wins 1% more often than AK guy.)

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And funny enough, 27 guy wins 1% more often than AK guy.

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AA dominates AK. 27 guy can catch two pair, trip 2's or 7's, fill in one gap straights, etc. AK must either make a straight, flush or catch a few kings to win.

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so would i be rite to say with my AK against a small flop with someone holding a pair I would be roughly a 4 to 1 underdog to win the pot since 6+5/45 gives me roughly those odds? do i need to take into consideration his outs as well of hitting two pair or a set? thks

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Now wait a minute. There is a huge difference between (6/45)*(5/44) and 5+6/45. 2% v 24%. Why the seeming hypocrasy?

(Would be the first time I have missed something) :roll:

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but if you were all in preflop, it's roughly 50% that either a A or K will come by the river. this is why AKs is ranked higher than QQ. i think it's something like 51% favourite for AKs.

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How does being all-in change your probability of an A or a K comming by the river? That just doesnt make sense. I think Phil Hellmuth's is like the only thing I have read which states that AK is better than QQ. I will take QQ any day. You have a made hand. Unlike the Ak that is drawing out. I always look at AK about the same way as I do TT. But thats me and not you.

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Originally Posted by ihategnomes

How does being all-in change your probability of an A or a K comming by the river? That just doesnt make sense. I think Phil Hellmuth's is like the only thing I have read which states that AK is better than QQ. I will take QQ any day. You have a made hand. Unlike the Ak that is drawing out. I always look at AK about the same way as I do TT. But thats me and not you.

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it's 50% because that's the prob. an ace or king will come by the river. it's different when you are not all in because after the flop you'll either be way ahead or way behind. AKs is ranked higher than QQ because of it's flush making ability which slightly puts it ahead of QQ.

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Originally Posted by ihategnomes

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but if you were all in preflop, it's roughly 50% that either a A or K will come by the river. this is why AKs is ranked higher than QQ. i think it's something like 51% favourite for AKs.

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How does being all-in change your probability of an A or a K comming by the river? That just doesnt make sense. I think Phil Hellmuth's is like the only thing I have read which states that AK is better than QQ. I will take QQ any day. You have a made hand. Unlike the Ak that is drawing out. I always look at AK about the same way as I do TT. But thats me and not you.

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How the hell can you play AKs the same way as TT, thats just stupid. TT isnt even an excellent pocket pair, and most of the time the board is going to hit an overcard which somebody is bound to have.


-anto

I play TT like AK becuase most of the time with AK the board will flop unders and someone is bound to have one.

Every hand is situational and just becuase a scarey card falls doesn't mean someone else will hold it. You should play both TT and AK for a raise preflop in hopes of going heads up so that you can play them properly.

-'rilla

Rilla my point id, what do you rather get; TT or AKs?? If you make an aggresive bet with TT and someone calls you, and ten an overcard hits the flop then someone is bound to have it, and you will have to fold. This is why i dont like TT than much, i dont even feel very confident with JJ.


-anto

If you get it heads up they can only have at most 2 over cards (by my calculations) So if they hold AK and the flop comes Qxx or Jxx, you still have the best of it. You can't shy away from TT or JJ just becuase it might not be the powerful overcard after the flop. You're out flopping two overs 2/3 of the time. And again, my point with AKs is if it doesn't hit on the flop, what's its value? You're in the same spot with AKs and a flop that misses you as you are with TT and a flop with an overcard.

-'rilla

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Originally Posted by a500lbgorilla

If you get it heads up they can only have at most 2 over cards (by my calculations) So if they hold AK and the flop comes Qxx or Jxx, you still have the best of it. You can't shy away from TT or JJ just becuase it might not be the powerful overcard after the flop. You're out flopping two overs 2/3 of the time. And again, my point with AKs is if it doesn't hit on the flop, what's its value? You're in the same spot with AKs and a flop that misses you as you are with TT and a flop with an overcard.

-'rilla

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Rilla, i didnt use to think this way, but you are a much better and experienced player than me, so if you say so then ill believ u :wink: , and ill try to adjust my play to what u just said


-anto

QQ is about equal to AKs. QQ is better heads up, but AKs is better (slightly) multi-way. I think in general TT is about the same, but TT dominated by twice as many pocket pairs.

For limit, i agree. But in NL where it's easier to protect your hand on the flop, i'd say QQ and up are dominant. AKs, JJ, TT are about equal and can be real good but flop-dependant.

-'rilla

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Originally Posted by a500lbgorilla

. AKs, JJ, TT are about equal and can be real good but flop-dependant.
-'rilla

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Rilla i think you hit the nail righ on the head with this statement. If my jacks dont improve, im beat at least one third of the time , this is why i dont make gigantic raises with JJ or TT or AKs, i think 3XBB raises are ok for these hands IMO.


-anto

I am just wondering what you guys think of this play. There are 24 people left in a tourney with about 116 people that started. its a 22 dollar buy in 11-20 place get only $23 only make $1 but first pays about $650. Anyway im about 14th place or so in total chips a few hands previous. Well i get dealt AK off, i am 2 spots to the right of button. first 3 or 4 people folded whatever, so its just small blind big blind in the hand then the person next to me raises to $15,000. at this time the blinds are 1500/3k bb with 500 dollar antes. anyway i have about $38000 in chips left and the other player that raises has about the same, now when the person made the bet before me they took a while to bet the raise to make it 15k so i couldnt put them on aa kk or even qq, so i figured they had AQ or AK or smaller pockets. I reraise to go all in after all i am going to win this tournament not just get in the top 20, i knew that the person already bet $15k and had about $35k so if i reraised they would probaly call. SO i go all in 39k everyone folds back to that person at the table they call. They have pp Jacks. long story short i didnt flop anything to win that hand.
But would you guys reraise AK off when you put someone on lower pp or AK or AQ themselves? This person played tight i knew they had a hand but i really like AK heads up with the person and i was right they did have lower pp Jacks, i know ak off is about 48 percent to win against JJ right? So would you guys play this or fold? you guys think i made the right call? i knew if i could hit something i would double up and be 2nd at my table and after all i was going to try to win this tourney not just place in top 20 since i wouldnt make much money unless i place in top 3 or 5. So i figured near coinflip is a good all in raise by me??

also if someone raised huge early in the tourney preflop to my ak off i will fold. it was so late in the tourney though only 24 left of 115 or so players, its good to move in with AK off when i thought the other person had pp lower than queen or AK or AQ where if they had AQ or AJ they would be drawing near dead to me? The person took so long to bet i even thought they could of had pp 9s or 10s, my guess was pp 9s 10s or Jacks, and they had jacks, but did i still make a good move so late in tourney buy reraising my AK after she bet 12k raise with JJ and i push her all in? i was trying to double up getting late in tourney, i know id still see some more good hands but i mean that will hit near half the time right so its a good call to try to double up and get in top 3 in chips with so little people left? just too bad no A or K hit or 2345 or straight. Id rather it be suited king ace i play but it was unsuit but still decent call? its near coinflip so? just wondering what you all think of this