basic triple draw probability questions

[Chris Daddy Cool]

1. suppose before the first draw i have a hand like 2357K and i want to get rid of the K, thinking a 4,6 or 8 is likely to win it for me for the duration of the draws.

a) what is the chance of me getting a 4,6, or 8 on an individual draw?

b) what is the chance of me improving by the third draw?


2. I am heads up on the last draw and draw one card and pair up for a final holding of 22357. my opponent drew one card as well and bets 4 dollars into me. basically i can only beat a bluff. how big must the pot be for me to correctly call?

[jason_t]

1a) 12/47 or about 25% of the time.
1b) 1-(35/47) * (34/46) * (33/45) or about 60% of the time.

2) This is covered in a chapter in TOP. I haven't read it in awhile and don't have it handy. I'll post again later if no one else has. I'd say at least $40.

[jason_t]

Is this triple draw game a low hand game?

[BluffTHIS!]

[ QUOTE ]
Is this triple draw game a low hand game?

[/ QUOTE ]

Yes it is, with ace to five lowball having the wheel as the best hand, aces counting as low cards, and flushes having no meaning, whereas in deuce to seven lowball the best hand is 75432 with aces counting as a high card and straights and flushes are losers.

As far as lowballs odds, on a draw by draw basis you could probably just use the single draw odds given by Caro in the back of Super System.

[jason_t]

1a) On the first draw, 12/47 or about 25%. On the second, assuming you didn't improve on the first draw, 12/46 or about 26%. On the third draw, assuming that you didn't improve on the first two draws, 12/45 or about 27%.

[Cobra]

There are 47 unseen cards 12 help you and 35 do not.

The probability of getting at least one of those 12 cards on the next three cards is the same as 1 - the probability of not getting any of them on the next three cards.

1 - (35 choose 3)/(47 choose 3) = 59.6 %

From your post I don't understand how an Ace does not help you. If you include an Ace as well as the other cards the probability becomes.

1 - (31 choose 3)/(47 choose 3) = 72.3%

Cobra

[Yads]

[ QUOTE ]
From your post I don't understand how an Ace does not help you. If you include an Ace as well as the other cards the probability becomes.

1 - (31 choose 3)/(47 choose 3) = 72.3%


[/ QUOTE ]

Because an Ace is high only so 2345K beats 2345A (2345A is not a straight btw since Ace is only high.)

[Chris Daddy Cool]

sorry i forgot to mention in my post that this is triple draw deuce to seven, where A is high only.

however i'm really curious about question 2, because that situation seems to come up a lot where i catch bad and he bets into me.

[maurile]

[ QUOTE ]
2. I am heads up on the last draw and draw one card and pair up for a final holding of 22357. my opponent drew one card as well and bets 4 dollars into me. basically i can only beat a bluff. how big must the pot be for me to correctly call?

[/ QUOTE ]
It depends on your opponent's bluffing frequency. If he never bluffs, you should call 0% of the time. [img]/images/graemlins/wink.gif[/img]

If he draws one card, his chance of pairing up is about 25%.

If he bluffs every time he pairs up on the end (and value bets every time he doesn't), that makes you a 3-1 dog to be ahead whenever he bets (assuming your pair of twos will beat any pair he has). So the pot would only have to be $12 for you to call.

If he bluffs half the time on the end after pairing, that means you can beat him 12.5/(75+12.5) = 14% of the time that he bets, making you a 6-1 dog. So you'd need the pot to be $24 in order to call.

If he bluffs 10% of the time that he pairs up on the end, that means you can beat him 2.5/77.5 = 3.2% of the time that he bets, making you a 30-1 dog. So the pot would have to have $120 in it before you should call.

(These figures naively assume that your opponent would value bet every time he doesn't pair up on the end. If he'd value bet a lesser fraction of the time -- say, only when he draws a jack or better -- the pot doesn't have to be as big to call.)

[Chris Daddy Cool]

heh i feel so stupid for asking this, but how big does the pot have to be for me to draw 2 cards on the last draw heads up asssuming my opponent is standing pat on a rough 8 or even a 9, and i had say, 234KK?

a) assume i had discarded a 2,3 before.
b) assume i had discarded two blanks.