Thanks for checking out our website and giving our Draw Poker Challenge a try!
Here's the solution:
The key to drawing the right hand is making sure that you cover the highest hand (a royal flush - Ace thru 10 in the same suit) in every suit - on your first draw.
- The winning hand is to draw all four 10’s, which prevents your opponent from drawing a royal flush (Ace - 10 straight flush). If your opponent then draws and leaves any open royal flush draw, you win.
- If your opponent instead prevents you from drawing a royal flush (for instance, by drawing all four aces), then you can draw to a 10-high straight flush and be assured of winning, as your opponent has no 10s.
For you statisticians (and card counters): technically, you can also accomplish this by drawing three tens and covering the fourth straight flush with a two card combo (such as K - 9). So in total, there are 88 winning first hands: 48 hands with four 10’s and any other card, and 40 with three 10’s and any other covering combination in the fourth suit. Whew!
Inspired by: Martin Gardner, “Draw Poker,” in My Best Mathematical and Logic Puzzles (New York: Dover Publications, 1994), 1 & 39.