An enlightening discussion from live cash game last night

ianmc38

So the scene is S/E 1/2 Cash Game. Theres a little bit of maths being discussed at the table and for some reason a players asks me the following question:

"Here's one for you: You're holding pocket queens. What are the odds that an overcard will appear on the flop?"

So can anyone give the exact percentage?

I think everyone knows this player. Let's call him say Mr. K Rag

The answer gave me a good chuckle.

Hitman Actual

ianmc38 wrote:

So the scene is S/E 1/2 Cash Game. Theres a little bit of maths being discussed at the table and for some reason a players asks me the following question:

"Here's one for you: You're holding pocket queens. What are the odds that an overcard will appear on the flop?"

So can anyone give the exact percentage?

I think everyone knows this player. Let's call him say Mr. K Rag

The answer gave me a good chuckle.

I think it's 41%.

Edit: sorry, odds = 3/2

ntlbell

ianmc38 wrote:

So the scene is S/E 1/2 Cash Game. Theres a little bit of maths being discussed at the table and for some reason a players asks me the following question:

"Here's one for you: You're holding pocket queens. What are the odds that an overcard will appear on the flop?"

So can anyone give the exact percentage?

I think everyone knows this player. Let's call him say Mr. K Rag

The answer gave me a good chuckle.

This should be good..

Washout

is he STILL going on about that??? same question on FT on Wednesday night.

where he got his maths from i dont know.

opr

lenny_leonard wrote:

I think it's 41%.

Edit: sorry, odds = 3/2

Would that have given you a good chuckle ?

Opr

nicnicnic

off the top of my head I'd say 17/18%

cooker3

I think I remember hearing it was 30% but I am not 100% sure on that.

Bandana boy

Assuming hu
strictly speaking it is roughly 51% chance of an over card on flop to your qq that of course comes down if there is a A or K in play so playing 1 over card roughly 45% and if an ak in play it is 38%

BigDragon

Washout wrote:

is he STILL going on about that??? same question on FT on Wednesday night.

where he got his maths from i dont know.

Same question from him on Tuesday LOL. 60%

Washout

i thought it was 49% assuming that you deal yourself the Queens and no other hands are dealt.

yaledo

Odds that 1 or more overcards appears on the flop = 41.7%

ianmc38

I thought it was somewhere in the region of 33%. However, he insisted that it was 60%. I tried to say that it wasn't even close to 60 but he told me to look it up. I said wow, didnt realise it was that high.

If it was true i'd be cleaning up with AK instead of losin my bollox with it. Lol.

spectre

Lenny is right. Interestingly, this means that in PLHE, AK always has the odds to call a Preflop raise from QQ.

For the non-believers: The Maths

50 unseen cards (8 overs)

Probability of no overs is 42/50 * 41/49 * 40/48 = 0.5857

Therefore Probability of at least one over is 1 - 0.5857 = 41%

ianmc38

Ah yeah i was forgetting those not counted. 40% is about right

Iago

a range of answers...I'd of thought it was around 22-23% or thereabouts.

ianmc38

If you hold AK the chance of an A or K on the flop is ~33%.

Norwich Fan Rob

so its around 47% that AK will beat QQ in a 5 card race, and its 60% that a K or A will come on the flop, interesting theory.

Washout

yaledo wrote:

Odds that 1 or more overcards appears on the flop = 41.7%

i was going (8/50)+(8/49)+(8/48) but that only assumes only card hits.

Washout

spectre wrote:

Lenny is right. Interestingly, this means that in PLHE, AK always has the odds to call a Preflop raise from QQ.

For the non-believers: The Maths

50 unseen cards (8 overs)

Probability of no overs is 42/50 * 41/49 * 40/48 = 0.5857

Therefore Probability of at least one over is 1 - 0.5857 = 41%

this makes more sense

spectre

ianmc38 wrote:

If you hold AK the chance of an A or K on the flop is ~33%.

Indeed you're right Ian. I forgot that for QQ to outflop AK, there are only 6 overs left. So in fact AK will break even trying to outflop Queens in PLHE. Well spotted.

Hitman Actual

spectre wrote:

Lenny is right. Interestingly, this means that in PLHE, AK always has the odds to call a Preflop raise from QQ.

For the non-believers: The Maths

50 unseen cards (8 overs)

Probability of no overs is 42/50 * 41/49 * 40/48 = 0.5857

Therefore Probability of at least one over is 1 - 0.5857 = 41%

Yeah, looks good. I prefer combs meself:

Total flops minus your QQ = 50C3 = 19600
Flops with no A,K = (50-4-4)C3 = 11480

Odds of no A,K = 11480/19600 = 0.5857

So over cards to QQ = 1-0.5857 = ~41%, exactly as above for probability.

*Counterfeit*

I know the answer to this one, believe it or not it's an astonishing 60%

El Stuntman

LOL, I have this vision of play being halted on all tables while pocket calculators are brought into play, diagrams are drawn and outstandingly large side bets are made on the result

please tell me this is what happened....

*Counterfeit*

Apologies here on my reply, I should have pointed out that the article I read on this issue (and it dealt specifically with QQ) counted the chances of an A or K appearing on the flop without the opponent holding that overcard, but using that overcard to make a better hand, such as straights and flushes. It also counted the complete board as opposed to just the flop. Very interesting article, will try and find an online link, but it was in a recent issue of the WPT mag.

Glowingmind

just to be different i came up with 48.98%

Lafortezza

There are 8 overcards to your Queens so there is obviously an 80% chance of an over card!! Maths is eazy!

malinh

i came up with the 48.98%. all tho that is taking the the other player doesnt have a a or k in their hand!

EDIT: this def wrong, worked out 41% that there is at least one over on the flop

Linford

Glowingmind wrote:

just to be different i came up with 48.98%

I came up with same as you.

48.98% for A or K on flop
42.85% for A or K on flop if you hold an A or a K
36.73% for A or K on flop if you hold an A and a K

Hitman Actual

Linford wrote:

I came up with same as you.

48.98% for A or K on flop

At least an A or a K, what you have is probably for exactly one A or one K (I think).

Sangre

lafortezza wrote:

There are 8 overcards to your Queens so there is obviously an 80% chance of an over card!! Maths is eazy!

rofl, nearly knocked drink over with that one.

Hmm, I ruled the world of probability back in the LC days. Should actually try one of theses one day.

Question needs clarification a bit, does opponent have AK or some such. How many cards are we assuming are in the deck etc?

Heads up, against an unknown opponent, with 48 cards available for the flop. I worked out the odds of at least an A or a K on the flop as roughly 43% (don't know how to do fractions on computer cal.)

fuzzbox

37%

Linford

lenny_leonard wrote:

At least an A or a K, what you have is probably for exactly one A or one K (I think).

Maybe my maths is off, I calculated 8/50 + 8/49 + 8/48 and I got .4898 or 48.98%.

Should it be 8/50 + 7/49 + 6/48 which would reach your figure. If so why?

Danny Rafferty

I have work to do so I'm not going to work it out for the full board.

Assuming all 8 overcards are available to flop.........

Exactly one ace or king: 35%
Exactly Two over cards: 3.4%
Exactly Three overcards: 2.8%

So the total probability would be approx 41.2% accepting rounding errors.

But the real question is "does this probabliltiy really matter?"

I'm re-raising and getting my chips into the middle if I catch QQ.

Knowing that the opponent always has odds to call in particular limit scenarios just gives calling stations an excuse for all those bad beats.

Hitman Actual

Linford wrote:

Maybe my maths is off, I calculated 8/50 + 8/49 + 8/48 and I got .4898 or 48.98%.

Should it be 8/50 + 7/49 + 6/48 which would reach your figure. If so why?

I always work with combs (I find it easier), so I'm not sure exactly what's wrong here. Spectre's probability calculation is easier to follow, cos he removes the aces and kings from the calculation, and then just uses 1-p to get the answer. But I'm sure ~41% is correct.

Hitman Actual

fuzzbox wrote:

37%

Now there's a first; fuzzbox is wrong.

Sangre

Cards: QQ
HU opponent: Unknown
And first burn card means there are 48 cards available for the flop.

The odds of an A or K not hitting (assuming all 8 are in play) is:

40/48 * 39/47 * 38/46 ~ .5688

So 56% they won't hit at all.

The odds of at least one hitting is 1 - .5688 ~ 43%

Very rough calculation.

Hitman Actual

Sangre wrote:

HU opponent: Unknown
And first burn card means there are 48 cards available for the flop.

Neither of these matter though. The calcs are done for 50 unknown cards.

Linford

lenny_leonard wrote:

I always work with combs (I find it easier), so I'm not sure exactly what's wrong here. Spectre's probability calculation is easier to follow, cos he removes the aces and kings from the calculation, and then just uses 1-p to get the answer. But I'm sure ~41% is correct.

When I calculate the way you did and the way spectre- i.e. odds of there not being an overcard on board - I get the same figure as you and that makes sense. Just trying to work out how to get the same figure working the other way.

5starpool

odds of A or K on the flop:

87% if I have QQ
8.7% if I have AK

On a less woe is me note, I tend to trust Lennys calculations in these things.

spectre

Linford wrote:

Maybe my maths is off, I calculated 8/50 + 8/49 + 8/48 and I got .4898 or 48.98%.

Should it be 8/50 + 7/49 + 6/48 which would reach your figure. If so why?

You can't just add these three together. In order to calculate the answer using OR instead of AND (way longer), you have to factor in more possibilities

i.e. Pr[Over under under] or p[under over under] or ...... p[over over over]
(8/50 * 42/49 * 41/48) + (42/50 * 8/49 * 41/48) + ... (8/50 * 7/49 * 6/48)

So, neither 8/50 + 8/49 + 8/48
nor 8/50 + 7/49 + 6/48 make any sense

It is much quicker to calculate for all unders as already shown.

Linford

spectre wrote:

You can't just add these three together. In order to calculate the answer using OR instead of AND (way longer), you have to factor in more possibilities

i.e. Pr[Over under under] or p[under over under] or ...... p[over over over]
(8/50 * 42/49 * 41/48) + (42/50 * 8/49 * 41/48) + ... (8/50 * 7/49 * 6/48)

So, neither 8/50 + 8/49 + 8/48
nor 8/50 + 7/49 + 6/48 make any sense

It is much quicker to calculate for all unders as already shown.

Cheers Spectre, that makes sense.

goldilocked

There's also the point that you're (probably) really only worried if someone else has one of the over cards..which of course reduces the probability of the flop being hit by one...

oldboy

Hi all,

I read way more here than I ever post (still swimming in the little pond with the fish) but I'm just getting clarification on how to work this one out as being a noob its hard to keep up when getting to grips with the probabilities.

Heads up - 2 cards each so 48 cards left, there will be 1 burnt so there are 47 cards remaining in the dealers hand which the flop will come from.

When doing the probabilities is it a given that you work out the odds based only on those 47 cards or do you treat the deck as a whole and work it out from 50 disregarding the other players cards and the burnt cards etc ??

Apologies for what may seem a stupid post

Thanks

spectre

oldboy wrote:

Hi all,

I read way more here than I ever post (still swimming in the little pond with the fish) but I'm just getting clarification on how to work this one out as being a noob its hard to keep up when getting to grips with the probabilities.

Heads up - 2 cards each so 48 cards left, there will be 1 burnt so there are 47 cards remaining in the dealers hand which the flop will come from.

When doing the probabilities is it a given that you work out the odds based only on those 47 cards or do you treat the deck as a whole and work it out from 50 disregarding the other players cards and the burnt cards etc ??

Apologies for what may seem a stupid post

Thanks

The calculations are done against 50 cards because the only information you have about the distribution of the deck is your own hole cards. Everything else is unknown. The fact that the burn card can't come out on the flop is irrelavent (the cards at the bottom of the deck can't come out on the flop either).

charlesanto

spectre wrote:

The calculations are done against 50 cards because the only information you have about the distribution of the deck is your own hole cards. Everything else is unknown. The fact that the burn card can't come out on the flop is irrelavent (the cards at the bottom of the deck can't come out on the flop either).

But the question is regarding QQ, so in this example you gotta work for a deck of 48 unknowns !

eggie

spectre wrote:

Lenny is right. Interestingly, this means that in PLHE, AK always has the odds to call a Preflop raise from QQ.

For the non-believers: The Maths

50 unseen cards (8 overs)

Probability of no overs is 42/50 * 41/49 * 40/48 = 0.5857

Therefore Probability of at least one over is 1 - 0.5857 = 41%

Correct.

The probability of an event happening is equal to 1 minus the the probability of the event not happening.

the only way there wil be no over card is if all 3 flop cards are:

under - AND - under - AND - under. calculation as above.

fuzzbox

charlesanto wrote:

But the question is regarding QQ, so in this example you gotta work for a deck of 48 unknowns !

Is this statement due to the fact that you hold 2 aces up your sleeve?

tricky D

Of course by this stage, you would have run out of time or had 'clock' called.

Goodluck2me

charlesanto wrote:

But the question is regarding QQ, so in this example you gotta work for a deck of 48 unknowns !

yeah but you have QQ, so its 50 cards remaining. if you knew your opponents cards you would only need to calculate the possibilities of them being ahead on the flop.

The Bollox

I am surpried 2 and a half pages of replies and not one person said 42, the answer to life, the universe and everything (they'd be pretty damn close too)