The Average Winning Hold’em Hand
It is commonly said that the average winning Hold’em hand is 2 pair, which, to me, seems reasonable. I have not seen any analytical basis for this so I attempted one.
I assigned ranks to the 9 hand types, 1 for a straight flush, 2 for quads, … , 9 for high card. I then used Wiki showdown probabilities and determined the win probability for each hand type. These were then used as weights to calculate the average win rank.
For two players, the average rank was 6.75, fairly close to the 7 ranking for 2 pair. For 3 players, however, the average rank was 6.30, closer to the 6 ranking for 3 of a kind. The results lend support to the logical supposition that the greater the number of players in showdown, the more likely a higher ranked hand is the winner.
Yes, the analysis has issues. It assumes independence, which is not the case and more importantly, it does not consider folds. Perhaps the best way to determine the average winning hand type is analyses of very large samples for various game situations. If anyone knows of such analysis, please post a reference.
1 Reply
Here is the winning hand distribution in 6-max (all hands go to showdown) I found in a 10 million deal simulation. I did this as a comparison to the distribution in Short Deck.
The Triton poker series has popularized short deck hold-em. I am sure that everyone knows by now that Short Deck is played with a 36-card deck since all the 2's, 3's, 4's, and 5's have been removed (of course, this is why Short Deck is also called Six-Plus poker).
Short Deck is a wildly fast-moving game with frequent large pots and tons of action. Pre-flop equities run much tighter than in Long Deck (regular 52-card NLHE poker). Similar to PLO, the in-hand swings in Short Deck are wild it being c
