Re: Pre-millenial post: 27 lowball research problems
 

[ QUOTE ]
1. (TD) Nontrivial 1st-round hand equities, hot + cold. For example, if you push all-in with 23xxx, what are your chances of winning the pot vs. a player who calls with a range of two-card draws?

[/ QUOTE ]

This is fairly easy to sim, but you would have to stipulate what each player would draw-to/stand-with on each of the drawing rounds.

I think I've asked this before, but what do you mean by hot+cold?

Re: Pre-millenial post: 27 lowball research problems
 

[ QUOTE ]
[ QUOTE ]
1. (TD) Nontrivial 1st-round hand equities, hot + cold. For example, if you push all-in with 23xxx, what are your chances of winning the pot vs. a player who calls with a range of two-card draws?

[/ QUOTE ]

This is fairly easy to sim, but you would have to stipulate what each player would draw-to/stand-with on each of the drawing rounds.

I think I've asked this before, but what do you mean by hot+cold?

[/ QUOTE ]

I think the right way to approach this is for the players to draw to their "best" draws. "Best" is unambiguous if you play face-up. It requires a little more definition if you want to play with cards hidden. (For example, does the player with 23 know what the player drawing two has to start? Or at least put him on a range?)

"Hot + cold" just means no further bets go in. From the pokerstove FAQ:

[ QUOTE ]

Q13. PokerStove is a hot and cold simulator, what does that mean?

It means that all hands are simulated through showdown. No one is allowed to bet, raise or fold. Because of this, there are a lot of unrealistic situations that might get included in the equity calculation if you are using PokerStove to evaluate scenarious where there is still betting to occur. If you have a good understanding of implied odds, effective odds, and reverse implied odds, you should be able to benefit from the equity calculations. But any time you use PokerStove in this manner, you should be careful about drawing strong conclusions about how you should play the hand.


[/ QUOTE ]

Re: Pre-millenial post: 27 lowball research problems
 

[ QUOTE ]
I think the right way to approach this is for the players to draw to their "best" draws. "Best" is unambiguous if you play face-up. It requires a little more definition if you want to play with cards hidden. (For example, does the player with 23 know what the player drawing two has to start? Or at least put him on a range?)

[/ QUOTE ]

Let's say that both players start by drawing 3 to 23xxx. Player 1 hits K7532 and draws 1. Player 2 hits K 7632 and draws 2?

This is a little different than I imagined. I wonder if "best" draws could become ambiguous as the number of players increases.

Re: Pre-millenial post: 27 lowball research problems
 

[ QUOTE ]
[ QUOTE ]
I think the right way to approach this is for the players to draw to their "best" draws. "Best" is unambiguous if you play face-up. It requires a little more definition if you want to play with cards hidden. (For example, does the player with 23 know what the player drawing two has to start? Or at least put him on a range?)

[/ QUOTE ]

Let's say that both players start by drawing 3 to 23xxx. Player 1 hits K7532 and draws 1. Player 2 hits K 7632 and draws 2?

This is a little different than I imagined. I wonder if "best" draws could become ambiguous as the number of players increases.

[/ QUOTE ]

I think in the example you give it is quite likely that it is still correct to draw to 7632. But what about 9632? T632? It's not immediately obvious (though we generally think keeping the 9 is better than discarding it.)

There are some very non-intuitive last-round draws that can occur if one player is drawing two. (For example, the suit of a discarded K can switch a draw from one card to two cards.)

The best (highest-expectation) draw will always be unambiguous when you know all the cards, even multiway, but it might be position-dependent. I came up with a couple examples a while back where the best draws depended on who drew first for the same set of cards.

Re: Pre-millenial post: 27 lowball research problems
 

[ QUOTE ]
[ QUOTE ]
[ QUOTE ]
I think the right way to approach this is for the players to draw to their "best" draws. "Best" is unambiguous if you play face-up. It requires a little more definition if you want to play with cards hidden. (For example, does the player with 23 know what the player drawing two has to start? Or at least put him on a range?)

[/ QUOTE ]

Let's say that both players start by drawing 3 to 23xxx. Player 1 hits K7532 and draws 1. Player 2 hits K 7632 and draws 2?

This is a little different than I imagined. I wonder if "best" draws could become ambiguous as the number of players increases.

[/ QUOTE ]

I think in the example you give it is quite likely that it is still correct to draw to 7632. But what about 9632? T632? It's not immediately obvious (though we generally think keeping the 9 is better than discarding it.)

There are some very non-intuitive last-round draws that can occur if one player is drawing two. (For example, the suit of a discarded K can switch a draw from one card to two cards.)

The best (highest-expectation) draw will always be unambiguous when you know all the cards, even multiway, but it might be position-dependent. I came up with a couple examples a while back where the best draws depended on who drew first for the same set of cards.

[/ QUOTE ]

I thought about this some more today. I am assuming that the composition of the deck is always known. I couldn't immediately come up with an ambiguous situation, but I believe I could come up with a situation where it didn't matter if the first player drew one or stood pat (in other words, his win% in either case would be identical).

I think having the players play "face up" might provide the easiest-to-define drawing strategies, but the results could be trivialized. It seems that specific drawing stategies could be identified (for example, drawing to the 9632 and T632 you mention above), simmed, benchmarked, and then compared to come up with the pre-drawing EVs. I have to think about this some more.

Re: Pre-millenial post: 27 lowball research problems
 

[ QUOTE ]
12. (Studugi) Quantify how likely you are to get a badugi in 7 cards. What is the median strength of this badugi?

[/ QUOTE ]

I've tried calculating this and have never been completely satisfied with my work, but I've simmed this in a couple of different ways for different projects, and always came close to ~ .53.

A typical sim result: 100,000 hands; 52,953 had badugis; of 52,953 badugis, median badugi was T983 (#206); of 100,000 7-card hands, median badugi was KT73 (#588).

I'm lobbying for a studugi tourney in Vegas this summer. Will keep you informed if you're interested. (All the cool kids play studugi. [img]/images/graemlins/smile.gif[/img] )

[ QUOTE ]
25. (Chinese Poker - Badugi) Invent and solve a Chinese Poker variant using badugi rankings in the middle.

[/ QUOTE ]

There is a 3-person, 17 card CP variant that is best 5-card high, best 2-7, best badugi, best 3-card high. In the Raymer variant, the 52nd card is turned over and the 2-7 hand with the highest ranked card of the same suit wins all ties. If you solve this variant, PM me; I know where we can get rich.

Re: Pre-millenial post: 27 lowball research problems
 

[ QUOTE ]
[ QUOTE ]
25. (Chinese Poker - Badugi) Invent and solve a Chinese Poker variant using badugi rankings in the middle.

[/ QUOTE ]

There is a 3-person, 17 card CP variant that is best 5-card high, best 2-7, best badugi, best 3-card high. In the Raymer variant, the 52nd card is turned over and the 2-7 hand with the highest ranked card of the same suit wins all ties. If you solve this variant, PM me; I know where we can get rich.

[/ QUOTE ]

I thought of a 4-player, 13-card version: 5-card high in back; 4-card badugi in the middle; 4-card cribbage hand in front. Game is played with the bug, so a 53 card deck. After the hands are set, 53rd card is turned over and plays as part of the cribbage hands.

Re: Pre-millenial post: 27 lowball research problems
 

[ QUOTE ]

I thought of a 4-player, 13-card version: 5-card high in back; 4-card badugi in the middle; 4-card cribbage hand in front. Game is played with the bug, so a 53 card deck. After the hands are set, 53rd card is turned over and plays as part of the cribbage hands.

[/ QUOTE ]

Nice. Who gets extra points if it's a jack?

Re: Pre-millenial post: 27 lowball research problems
 

[ QUOTE ]
[ QUOTE ]

I thought of a 4-player, 13-card version: 5-card high in back; 4-card badugi in the middle; 4-card cribbage hand in front. Game is played with the bug, so a 53 card deck. After the hands are set, 53rd card is turned over and plays as part of the cribbage hands.

[/ QUOTE ]

Nice. Who gets extra points if it's a jack?

[/ QUOTE ]

Heh, I actually gave this some thought. In a self-dealt game, it should be the dealer, but I was thinking of reducing it to 1 point. Nah, let it stay 2.

Re: Pre-millenial post: 27 lowball research problems
 

bump b/c i just found this via lowballgurus and think it's pretty cool.

Progress?

I've been doing some td and badugi research, will add some of these to the list.