Badugi Math

Here's my 0.009% from few years ago

Sweet!
I've had two that I can remember -- one was fairly recently in a streamer's home game.

All the best,
VS

Originally posted by VorpalF2F

Comments appreciated...

I think it's worth mentioning that even tho the average dealt badugi is a decent Q, people usually only play that from late positions.
If average player opens from EP and pats, you should probably expect to see a J or a T

Hi adasko99,
Very good point!
Like all lowball games position is extremely important.

It's easy to see why:
Let's assume you have 60% chance of winning and you're in the small blind and it checks to you.
This means that BB has a 60% chance of losing.

Backup up one position, and assume that each of SB and BB hold hands with with a 60% chance of losing.
The chances of both of them losing are 60% x 60% or 36% -- in other words, there is a 72% chance that 1 of them will win.

and so on.

Cheers,
VS

Assume we have been dealt a 3-card hand:
3,2,A

Thus we are drawing 1 card from a pool of 48 cards.
There are 10 cards that give us a Badugi -- the 13 cards of the missing suit leaving out the 3 ranks we hold of other suits.
Note that all 10 cards do not give us equal chances of a winning hand -- we may get outdrawn

When figuring chances on multiple streets, it is better to look at the chances of missing the draw on each street.
Then multiplying the chances of missing together we get the effective chance overall of missing on all three streets.

1st draw:
Chance of missing: (48-10)/48 = 0.792

2nd Draw:
Chance of missing: (47-10)/47 = 0.787
Cumulative: 0.792 * 0.787 = 0.623

3rd Draw:
Chance of missing: (46-10)/46 = 0.783
Cumulative: 0.792 * 0.787 * 0.783 = 0.488

Overall chances of making any Badugi in 3 draws:
1 - 0.487 = 0.512

If you want to leave out the K,Q & J and only shoot for 10-Badugis or better, then the calculations become:
1st draw:
Chance of missing: (48-7)/48 = 0.854

2nd Draw:
Chance of missing: (47-7)/47 = 0.851
Cumulative: 0.854 * 0.851 = 0.0.727

3rd Draw:
Chance of missing: (46-7)/46 = 0.848
Cumulative: 0.854 * 0.851 * 0.848 = 0.616

Overall chances of making any Badugi in 3 draws:
1 - 0.616 = 0.383

Here is the table that shows the above calculations all the way down to a single out
(good luck with that)

Except for the right-most column, the numbers represent the chance of missing the draw
  Outs      1st      2nd      Cum      3rd      Cum    % Hit  
    10    0.792    0.787    0.623    0.783    0.488     51.2  
     9    0.813    0.809    0.657    0.804    0.528     47.2  
     8    0.833    0.830    0.691    0.826    0.571     42.9  
     7    0.854    0.851    0.727    0.848    0.616     38.4  
     6    0.875    0.872    0.763    0.870    0.664     33.6  
     5    0.896    0.894    0.801    0.891    0.714     28.6  
     4    0.917    0.915    0.839    0.913    0.766     23.4  
     3    0.938    0.936    0.878    0.935    0.820     18.0  
     2    0.958    0.957    0.918    0.957    0.878     12.2  
     1    0.979    0.979    0.958    0.978    0.938      6.3  

For an example of what this looks like in real life, take a look at this Hand of the Day. In that hand, Harrier88 has but 1 out -- the A♦:
Since this is his 2nd draw, the pool is down to 47 cards. So the chances of getting just that 1 card are 1/47 or 2.1%

Easy Game!

Next -- 2-Card draws

I kinda get the idea but personally, when trying to determine whether I'm priced in or not, I'd rather look at chances to hit instead of chances to miss

Hi adasko99,
Fair point...
The chance of hitting is just 1 minus the chance of missing.

The last column shows the overall chance of making your badugi in 3 draws.
When you do a calculation like this, it is easier to calculate the misses, then subtract the answer from 1 to get the hit %

There is another piece of the picture missing, though...
The table shows the chance that you will hit your draw in 3 tries, but what is the chance that will hit it in the first two draws?
What about the times when you throw 2 cards first, then want to know what are your chances of hitting a 1-card draw on the second and third draws?

I'll do that table before I tackle 2-card draws...

Cheers,
VS

There is a formula to quickly estimate your chances of hitting a draw with surprising accuracy.
It's pretty simple and it takes number of draws into consideration.
You can do it in your head, in-game.
I will only post it if more people will show interest in this whole thread

Is that the one that says:

Outs * Draws * 2 = Chances of hitting

For example, with 5 outs, and 3 draws, your chances of hitting using the estimate is 5 * 3 * 2 = 30%
Using the table, it is 28.6%

Pretty good estimate!
The more outs there are, the less accurate, but still within range (for 3 draws).

Later,
VS

Yeah hehe
I guess this thread is just you and me pal

The thread has had 442 views, so there are either quite a few people who just read it, or one person who reads it a lot over and over

hello not among the 442 visualizations there are also 'I am of the Italian forum and passionate of variants and I often read your contributions trying to learn we have equipped ourselves in home games to be able to play tournaments 8 game h.o.r.s.e and other variants.
on .it only PokerStars schedules mixed tournaments and games like 2/7 treple draws and badugi are limited to a handful of a few amateurs.
GL.

Hi anem804,
It is rather sad that we cannot all play together.

maybe one day again...
VS

Good day I come to see you again with my contribution and advice.
would you recommend a converter that supports badugi and other variants?
and how did I play this hand?

PokerStars Home Game Hand #199373274342: Tournament #2584822611, 17000+25 Badugi Limit - Level VIII (300/600) - 2019/04/16 22:35:50 CET [2019/04/16 16:35:50 ET]
Table '2584822611 1' 8-max Seat #5 is the button
Seat 1: angela328 (915 in chips)
Seat 3: ucciopoker60 (6175 in chips)
Seat 4: anem804 (2605 in chips)
Seat 5: sulley501 (3960 in chips)
Seat 6: Garasmir (2990 in chips)
Seat 7: gammon51 (1720 in chips)
Seat 8: artemisia66 (5725 in chips)
Garasmir: posts small blind 150
gammon51: posts big blind 300
DEALING HANDS
Dealt to anem804 [As 9c 7d 5h]
artemisia66: calls 300
angela328: folds
Garasmir said, "ho avuto paura"
ucciopoker60: folds
Garasmir said, "avevo un brutto badugi"
anem804: raises 300 to 600
sulley501: folds
Garasmir: folds
Garasmir said, "ma dovevo per forza chiamare"
gammon51: folds
artemisia66: calls 300
FIRST DRAW
artemisia66: discards 1 card
anem804: stands pat on [As 9c 7d 5h]
artemisia66: checks
anem804: bets 300
artemisia66: calls 300
SECOND DRAW
artemisia66: discards 1 card
anem804: stands pat on [As 9c 7d 5h]
angela328 said, "<3"
artemisia66: bets 600
anem804: raises 600 to 1200
artemisia66: raises 600 to 1800
anem804: calls 505 and is all-in
Uncalled bet (95) returned to artemisia66
THIRD DRAW
artemisia66: stands pat
anem804: stands pat on [As 9c 7d 5h]
SHOW DOWN
artemisia66: shows [Ah 7c 2d 5s] (Badugi: 7,5,2,A)
anem804: shows [As 9c 7d 5h] (Badugi: 9,7,5,A)
artemisia66 collected 5660 from pot
SUMMARY
Total pot 5660 | Rake 0
Seat 1: angela328 folded before the Draw (didn't bet)
Seat 3: ucciopoker60 folded before the Draw (didn't bet)
Seat 4: anem804 showed [As 9c 7d 5h] and lost with a Badugi: 9,7,5,A
Seat 5: sulley501 (button) folded before the Draw (didn't bet)
Seat 6: Garasmir (small blind) folded before the Draw
Seat 7: gammon51 (big blind) folded before the Draw
Seat 8: artemisia66 showed [Ah 7c 2d 5s] and won (5660) with a Badugi: 7,5,2,A

I don't know much about Fixed Limit Badugi (I only play Pot Limit), but considering the stack sizes on the 2nd draw, I believe it's fair to go all-in.

If this was Pot Limit, both players were deep stacked, and villain would either lead with a big bet or check-raise in that situation, I would consider folding and looking for a better spot.

In this situation, though, I believe it was fine.

Originally posted by anem804
Good day I come to see you again with my contribution and advice.
would you recommend a converter that supports badugi and other variants?
and how did I play this hand?

Hi anem804,
The only converter I know of that supports (most) non-hold'em games is Feral Cow Poker I say "most" because it can't do PKO hand histories properly. I have a script that removes the bounty information, and after running that Feral Cow works fine.

I always choose the output format option "Two Plus Two - emoticons" , since it pastes into PokerStrategy.com forum posts directly.

Here is the result of your hand history as converted by Feral Cow:
Converting hands till the cows come home
PokerStars Limit Badugi t300/t600 - 7 players

UTG+1: t915
HJ: t6,175
CO: t2,605 (Hero)
Button: t3,960
SB: t2,990
BB: t1,720
UTG: t5,725

Dealing Hands: (t450) A♠ 9♣ 7♦ 5♥ (7 players)
UTG calls t300, UTG+1 folds, HJ folds, Hero raises to t600, 2 folds, BB folds, UTG calls t300

First Draw: (t1,650) (2 players)
UTG discards 1, Hero stands,
A♠ 9♣ 7♦ 5♥
UTG checks, Hero bets t300, UTG calls t300

Second Draw: (t2,250) (2 players)
UTG discards 1, Hero stands,
A♠ 9♣ 7♦ 5♥
UTG bets t600, Hero raises to t1200, UTG raises to t1800, Hero calls t505 and is all-in

Third Draw: (t5,660) (2 players)
UTG stands, Hero stands

Hero showed A♠ 9♣ 7♦ 5♥, a Badugi: 9,7,5,A
UTG showed A♥ 7♣ 2♦ 5♠, a Badugi: 7,5,2,A
UTG won t5660

Note also that it is sometimes necessary to manually enter a mucked hand in the showdown section.

All the best,
VS