5CD odds

[XxPenguinxX]

I have just started playing 5CD after reading Murakawa's article in the March magazine, and various of MW's articles on CP. I'm really enjoying it, but I am conscious of having much less grounding in the odds of the game that I had in the other games I have played in more depth. Whilst I have been able to find the odds of my hand improving in the various different circumstances, what I haven't managed to get hold of is hand matchup odds (ie the chances of my hand still being ahead after the draw). Can any of you help? Or, of course, if it would take you too long to go through these questions, can you tell me how to work out the answers for myself? I'm assuming that there's no equivalent to twodimes etc for 5CD?

The situations that occur most frequently are:

1. I have AAxxx, and at the draw there are X players in with me. They all draw 3 (and we assume that they are all drawing to a smaller pair). How likely am I to have the best hand after the draw when X=

a) 1 player
b) 2 players
c) 3 players
d) 4 players

2. I have a TT44x, and at the draw there are X players in with me. They all draw 3 (and we assume that they are all drawing to Jacks or better). How likely am I to have the best hand after the draw when X=

a) 2 players
b) 3 players
c) 4 players

3. I have a AATTx, and at the draw there are X players in with me. They all draw 3 (and we assume that they are all drawing to a smaller pair). How likely am I to have the best hand after the draw when X=

a) 2 players
b) 3 players
c) 4 players

4. I have a KK88x, and at the draw there is one player in with me. How likely am I to have the best hand after the draw if he has:

a) AA77x
b) JJ44x
c) any two pair

4. I have a KK88x, and at the draw there is one player in with me. How likely am I to have the best hand after the draw if he draws 3 to:

a) AAxxx
b) JJxxx
c) any pair.

Thanks in advance!

[brian1175]

penquin, i think your going about it all wrong. If your going in the hand ahead against 1 player then yoiur probably ahead post draw. The secret is to watch your opp. and understand what there range is and if they are willing to bluff. Obv if your going gains multiple players your odss will decrease butt he pot will increase.
Get reads, get your money in when your ahead and you should do fine.

[mindflayer]

The only guy who would give you the EXACT answer is Bigpooch.
[ QUOTE ]
1. I have AAxxx, and at the draw there are X players in with me. They all draw 3 (and we assume that they are all drawing to a smaller pair). How likely am I to have the best hand after the draw when X=

a) 1 player
b) 2 players
c) 3 players
d) 4 players


[/ QUOTE ]
Here is a rough guide to go by.
When drawing 3
Case a)No improvement AAxyz 72%
Case b)approx odds to improve to AAXX 18%
case c)approx odds to improve to AAAxy or better 10%
for case a
odds that your 1 opponent does NOT improve 72%
odds that your 2 opponents do NOT improve 52% (.72x.72)
odds that your 3 opponents do NOT improve 37% (.72x.72x.72)

case b)
odds that your 1 opponent does NOT make trips 90%
odds that your 2 opponents do NOT make trips 81%
odds that your 3 opponents do NOT make trips 73%

case c) I think the odds of making a boat while
drawing three are something like 1/126 (not sure)
but lets say when you draw 3 and make AAA
odds that your 1 opponent did NOT make a boat 99%
odds that your 2 opponents did NOT make a boat 98%
odds that your 3 opponents did not make a boat 97%

Now vs 1: 72%(opponent does not improve)
case a+b+c win.. 72% x 100% = 72%
vs 1: 18% (opponent improves to two pair)
case b+c win 18% x 28% = 5%
vs 1: 10% opponent improves to trips
case c wins for you 10% x 10% = 1%
vs 1: 1% (or less) opponent improves to full house
case d wins for you 1% x 1% = (say zero)

72% + 5% + 1% - 1% = 77%
So vs 1 opponent you are approx 77% favourite after both draw 3 cards.

Ok now vs 2:
odds opponents did not improve 52% a+b+c win = 52%

odds at least ONE improved to two pair but NOT trips
(take a stab at it..) is
48% odds of at least one improvement minus the odds of at Least one improving to trips or better 19% total is 29%
out of 29% only b+c win for your 28%
29%x28% = 8%

odds of at least one of your opponents making trips but not full house (17%-25)17%
now 17% x 10% = 1.7% (say 2%)
odds of at least one of your opponents making a full house 2%
now 2% x 1% = (say zero)

so 52% + +8% +2% - 2% = 60%

So vs 2 opponents you are 60% favourite after Both draw 3

(let me know if i am way off BP)

[XxPenguinxX]

Mindflayer - cool, thanks for showing your working, gives me a way to approach it myself for other situations.

[mindflayer]

[ QUOTE ]
odds of at least one of your opponents making trips but not full house (17%-25)17%
now 17% x 10% = 1.7% (say 2%)


[/ QUOTE ]
should read (19%-2%)= 17%

[mindflayer]

Vs 3 opponents

none improve 37%..
you win a+b+c 37%

at least one improves 67% but not trips or better (25%)
(63 - 30) = 38%
you win b+c
38% x 28% = 9%

at least one improves to trips but not full house
27% x 10% = 3%

at least one improves to full house 3%
3% x 1% = say zero

now 37% +9% +3% - 3% = 46% to win vs 3 opponents drawing 3.

[mindflayer]

For question 2 it is much easier to calculate
Odds that neither improve
52%

Odds that at least one improves 48% (you lose unless you make a boat) say 8.5%
so 48% x 8.5% = 4%

52% + 4% = 56% minus the odds that one of them made a boat bigger than yours (say zero for that.. because 1)its a small number and 2)I have no idea how to split boats bigger and smaller than yours)

[bigpooch]

You can use twodimes for heads up. The trick is to use 2-7
results and invert the equities.

Some of the results posted in this thread are off by a bit,
but I won't elaborate. One key point: if someone holds AA
and one or players hold a distinct pocket pair, you can see
that each person's chances of any improvement is around 30%.
If you were to calculate the chances (without ANY
information about the distribution of cards due to action or
inaction of opposition) just based on your own cards, the
chances of improvement is only 4656/16215 or about 28.71%.

The more important question is how will the hands play out
in practice and what is the EV of playing the hand.

[Big Limpin]

[ QUOTE ]

The more important question is how will the hands play out
in practice and what is the EV of playing the hand.

[/ QUOTE ]

[mindflayer]

Now you have gone and done it..
Now I have to look it up.

AA vs 2 players drawing 3 says I win 71%.. (much higher than the 60% I calculated)

I have to check the basic assumptions of % improvement.
I went from memory for 10% trips and 18% two pairs.

I checked twodimes and it shows
AA drawing 3 quads 0.35%, boat 1.02%, trips 12.93%

(total improvement 33.175?!?)(But my drawing assumptions may skew the results so I will have to think about it for a while.

If I chose 2c 2d 3c 3d / 2h
vs Ac Ad / 2s 3h 3s
the "/" separates the discards.
to calculate the odds of improving Ac Ad to two pair or better to eliminate my opponent from making a full house
it shows that I win 33.17% BUT it also eliminates my chances of making AA22 and AA33.

If I use Ac Ad / 4c 5c 6c
vs 2c 2d 3c 3d / 7h

It shows I win 27.27% that is almost 6% so I will have to think about this for a while.