More meditations on pot limit Badugi

[*TT*]

Although I was crushing this game for a bit, the more I understand it the worse my results have been [img]/images/graemlins/smile.gif[/img] So I think its time to make my results really take a dive by evaluating some of the math endemic to a classic 1/2 pot limit game.

Lets assume the blinds are 50/100. Hero is in the big blind with A [img]/images/graemlins/spade.gif[/img]2 [img]/images/graemlins/diamond.gif[/img]3 [img]/images/graemlins/heart.gif[/img]x where x is any bad card of any suit. folds to SB who raises 1/2 the pot ($75), hero calls - the pot now stands at $300.

SB is of course pat. Hero assumes that he has 4 effective outs, the 4,5,6 or 7 of [img]/images/graemlins/club.gif[/img]. From past experience we know the SB will bet all streets 1/2 the pot. We will also assume the SB wont ever break, and will at a minimum call any raises.

There are 93 unseen cards in the remaining 2 draws and 4 cards twice that will improve the heros hand to what we will assume will be the winner (of course its impossible to know this, but for this post we can imply that the hand would be the winner). Therefore (if I did my math right) hero is 10.6:1 against improving his hand to a winner.

Since we know the villain will make a 1/2 pot sized bet after the first draw, the hero will have to call $150 to win $450 - meaning the pot is laying 3:1. From this information can we deduce if there is ever a time to call a 1/2 pot bet while still drawing heads up? From what I can see the answer is no.

TT [img]/images/graemlins/club.gif[/img]

[dibbs]

A good example of why this game seems pretty simplistic to me, most of your value seems to come from getting pat badugis early or betting it down with a very solid one card draw v. poorer draws, chasing seems just almost never correct in this game to me, especially headsup.

[MarkGritter]

I think you are way overestimating SB's hand. He would easily be correct to stand pat with a 9 or worse here. (And Hero should probably re-(half)-pot with this starter to discourage steals or rough pat hands, although that's probably limit thinking.) Let's say we need a 9 to win.

Hero bricks his first draw with a non-club. He needs 45678 or 9 of clubs. There are 52 cards in the deck. Hero has seen 5 non-club cards, and further knows that three of Villain's cards are not clubs.

Assuming Villain has an 9, there is 3/9 probability that he holds one of the clubs that pairs Hero (leaving Hero 6 outs) and 6/9 probability that he holds one of Hero's outs (so Hero has 5 outs.) In either case there are 43 cards remaining (52 - 5 observed hands - 3 inferred non-clubs - 1 club). This gives hero effectively 5+1/3 outs in 43 cards.

The odds are thus 37+2/3 to 5+1/3, or about 7:1.

If we assume Villain holds an 8 instead then Hero has effectively 3/8*5 + 5/8*4 outs = 4.375 outs, odds of 38.625:4.375 = 8.8:1. So things are a little better to improve on the next card than your calculations suggest.

Hero is getting immediate pot odds of 3:1. Villain has to half-pot after the 2nd draw as well, so Hero's implied odds are instead 5:1. This is obviously not favorable.

However, getting to 7:1 or even 9:1 is not impossible. If Villain is unwilling to fold then it is easy to pick up additional bets by raising the 'turn' or smooth-calling and betting the river.

I usually continued with a smooth draw against a pat player on the second draw, assuming stacks were both deep, but folded before the third draw, because it was less likely that I would get paid off.

Hero or Villain may be short-stacked as well, affecting the situation.

In the 8 or better case, Hero's draw comes in 4.375/43 + (38.865/43)(4.375/42) = 0.196 over two draws, so Hero needs odds of 4:1 to call an all-in raise.

[bugstud]

are you deep? If so, bluffing plays a very important part. Obv.

[*TT*]

[ QUOTE ]
are you deep? If so, bluffing plays a very important part. Obv.

[/ QUOTE ]

Bluffing never works in the online version of this game, nobody ever breaks except for me. That is also a good side effect of course, they will pay off handsomely because they are afraid of being bluffed with pat Q's for example

TT [img]/images/graemlins/club.gif[/img]

[*TT*]

[ QUOTE ]
I think you are way overestimating SB's hand. He would easily be correct to stand pat with a 9 or worse here. (And Hero should probably re-(half)-pot with this starter to discourage steals or rough pat hands, although that's probably limit thinking.) Let's say we need a 9 to win.

[/ QUOTE ]

I think its better to say we need a 7 or better to win 95% of the time, 8 to or 9 to win 50% of the time, T to win 25% of the time. Of course these are just estimates.

Do you care to continue extrapolating with this adjustment Mark? Your much better at the math behind the game than I am., I am better at applying the theory.

TT [img]/images/graemlins/club.gif[/img]