Mark Gritter (markgritter) wrote,
Mark Gritter


I added pruning to my single-draw 2-7 calculator and as expected it sped things up quite a bit. If a choice of draw by player A leads to a worse EV for player A than some already-explored draws (which contains the opponents' best responses) then there is no sense exploring that branch any further. In particular, this can be determined while still enumerating the possible results--- we can calculate A's maximum EV as 1.0 - the partial EV's already calculated for the other players.

So if player A already has a draw that wins 80% of the time, we may only have to enumerate slightly more than 20% of the cases on a different draw to judge that it is inferior. We can then skip all the other possible draws the other players (B, C, etc.) could make as well. This is a pretty standard technique; it can be applied here because the EV for each player (and the total EV) is bounded so we don't run into some of the odd multi-player cases.

Example case:

Dead cards: 5s 5c
0: 3s5h7d9c/Qs 0.487821
1: 2s4s6s8c/Qc 0.512179

Draws examined: 72454441
Hand comparisons: 380306841

Draws examined: 50012
Hand comparisons: 81115
Pruned draws: 44

This hand is an example I came up with where even in the perfect-information game, position matters. If the players draw in reverse order, the Q8 should stand pat while the Q9 breaks, for 0.5 equity each.
Tags: lowball, poker, theory
  • Post a new comment


    default userpic

    Your reply will be screened

    Your IP address will be recorded 

    When you submit the form an invisible reCAPTCHA check will be performed.
    You must follow the Privacy Policy and Google Terms of use.