Odds vs Hold em hand 6 consecutive cards of the same suit and a bit of strategy
January 27th, 2015 at 2:34:49 AM
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First off I am new to this site so if I have misplaced this question then I'm sorry, I looked at "Probability" but thought it fitted in here the best.
In any case perhaps someone can answer me two questions? I am sure the folk around here when they see my imbecile question will be thinking to themselves "Duh! What a dullard! That's is a really simple case of factoring of combinations" or whatever, I am sure this will not be a taxing mathematical problem for most interested in odds and probability, but it sure is beyond my current abilities!
I play Hold 'em pretty much non-stop in my spare time online (in UK). Last night the most interesting hand I have been involved with came up, and I would like to know two things.
1. The odds against the sequence of cards that came up.
2. Whether my decision to play the hand was strategically sound considering my stack size, probability, whatever, from a mathematical perspective.
I shall try to keep it as simple as I can.
It was nearing the end of an MTT (100/5000), and I had been in the top 10 for most of the night. Unfortunately I lost a big pot with my A8 vs villain's A7 all in. So at the time this hand occurred I was down to about 8 big blinds and significant antes. I was on the button with 9s10s. About 3 players before me flat called the big blind (everyone else had well over 10 big blinds). I figured that I had a hand that a) was likely to flop well a decent amount of time, and b) was a multi way pot so if I got lucky and was somehow able to get a couple of stacks to come along for the ride, and I won, I'd be back in business. So rather than push all in I flat called, leaving me with just over 6 big blinds. My reasoning being that if I lost the 1.5 so big blinds I was going out only a little sooner than if I stayed with 8 big blinds by not playing the hand at all.
1. Is that reasoning sound mathematically, or should I have pushed all in or not played the hand at all?
The flop came 9h8s7s which to say the least fitted alongside my 9s10s very nicely to say the least. The cut-off shoved, I called and the small blind also called.
Cut off had AsQs
Big blind had 5c6c
So for the sake of clarity I had a draw to the straight flush, BB had the 9 high straight, and Cut off had a draw to the ace high flush. So obviously I'm now hoping NOT to hit the spade!
The turn : (9h8s7s) 5s giving the cut off the ace high flush, and dropping my win probability to 4.8% (and breaking my heart). Now the only cards that could save me were the Js or...
River : (9h8s7s5s) the beautious bountiful 6s!
Great so I hit my third ever straight flush. Whatever...no great shakes. However...
2. No matter where I look, probably because a six handed hold 'em hand is a misnomer(at least I think it's one, I never knew exactly the proper application of that word), I cannot find the odds vs SIX consecutive cards of the same suit falling.
I know we aren't going to need to call the Enigma codebreakers in for this one, I know it is a simple math question, as a layman I am just interested in how the extra card in the sequence expands the odds. I know the odds vs a straight flush are 1:64,974, an I am guessing this extra card is going to increase these odds alot. I might be wrong.
Many thanks,
softshoedancer.
In any case perhaps someone can answer me two questions? I am sure the folk around here when they see my imbecile question will be thinking to themselves "Duh! What a dullard! That's is a really simple case of factoring of combinations" or whatever, I am sure this will not be a taxing mathematical problem for most interested in odds and probability, but it sure is beyond my current abilities!
I play Hold 'em pretty much non-stop in my spare time online (in UK). Last night the most interesting hand I have been involved with came up, and I would like to know two things.
1. The odds against the sequence of cards that came up.
2. Whether my decision to play the hand was strategically sound considering my stack size, probability, whatever, from a mathematical perspective.
I shall try to keep it as simple as I can.
It was nearing the end of an MTT (100/5000), and I had been in the top 10 for most of the night. Unfortunately I lost a big pot with my A8 vs villain's A7 all in. So at the time this hand occurred I was down to about 8 big blinds and significant antes. I was on the button with 9s10s. About 3 players before me flat called the big blind (everyone else had well over 10 big blinds). I figured that I had a hand that a) was likely to flop well a decent amount of time, and b) was a multi way pot so if I got lucky and was somehow able to get a couple of stacks to come along for the ride, and I won, I'd be back in business. So rather than push all in I flat called, leaving me with just over 6 big blinds. My reasoning being that if I lost the 1.5 so big blinds I was going out only a little sooner than if I stayed with 8 big blinds by not playing the hand at all.
1. Is that reasoning sound mathematically, or should I have pushed all in or not played the hand at all?
The flop came 9h8s7s which to say the least fitted alongside my 9s10s very nicely to say the least. The cut-off shoved, I called and the small blind also called.
Cut off had AsQs
Big blind had 5c6c
So for the sake of clarity I had a draw to the straight flush, BB had the 9 high straight, and Cut off had a draw to the ace high flush. So obviously I'm now hoping NOT to hit the spade!
The turn : (9h8s7s) 5s giving the cut off the ace high flush, and dropping my win probability to 4.8% (and breaking my heart). Now the only cards that could save me were the Js or...
River : (9h8s7s5s) the beautious bountiful 6s!
Great so I hit my third ever straight flush. Whatever...no great shakes. However...
2. No matter where I look, probably because a six handed hold 'em hand is a misnomer(at least I think it's one, I never knew exactly the proper application of that word), I cannot find the odds vs SIX consecutive cards of the same suit falling.
I know we aren't going to need to call the Enigma codebreakers in for this one, I know it is a simple math question, as a layman I am just interested in how the extra card in the sequence expands the odds. I know the odds vs a straight flush are 1:64,974, an I am guessing this extra card is going to increase these odds alot. I might be wrong.
Many thanks,
softshoedancer.
