# Handicapping Draw Poker: seven vs. five cards odds

Let’s say you wanted to handicap a heads-up game of Draw Poker by giving one player seven cards at the start. Let’s suppose that at the draw that player must discard n+2 cards in order to receive n cards to make a five card hand.

I realize that there are easier ways to handicap a heads-up game, e.g. starting one player with more chips but I’m curious about the math.

1. How much of an edge does the 7-card player receive?

2. What if the handicap was six cards?

It’s my OP so I say any and all digressions are welcome. For example, chess is damned hard to handicap without fundamentally changing the game whereas Go is wonderful.

Here you go

This has all the probabilities for both 5 and 7 card hands, so you can get an idea of the odds of getting a particular hand dealt to you with 5 and with 7 cards.

Now, as far as the discarding stuff, and only ending up with 5, that’s a bit above my paygrade. Hopefully a smarter guy will come along to help flesh out the answer more!

In principle, you could compute the odds that the original 6 or 7 card hand would end up with the better hand, but the skill in poker really comes from reading the other player which handicapping wouldn’t do much to counteract. If you limit the amount or number or re-raises, then then better hand will win more often, because the reading skill will not be so important if you can’t do things like bet “all-in.”

You might possibly make the better player play without seeing the other, but allowing the inferior player to see his opponent – sort of one way on line poker. I don’t know how much that would help.

Chess isn’t hard to handicap. Just take anything from one pawn to the queen away from the better player. It doesn’t change the game that much. If two players have just the right difference in ability, counting a draw as a win for the lesser player can also be used. An even stronger handicap is to give the better player a capped piece that must be used to deliver checkmate. If the opponent can then capture that piece, at least a tie is assured.

Moved to the Game Room.

Colibri
General Questions Moderator