Determining winning amount in Poker without creating side-pots

Question

I'm trying to run a poker simulation and have the following data about a poker table

• how much each player contributed to the pot
• a "hand score" (after flop) for each player (ie, if player[0].score == player[1].score, they tied)

I'm stuck calculating how much each player should win without needing to create sidepots and assigning players to each of them.

For example,

player[0].contributed = 100
player[1].contributed = 80
player[2].contributed = 20

player[0].score = 10
player[1].score = 2
player[2].score = 10

total_pot = 200;

In this example, do I first need to return player[0] 20 back and remove it from the pot?

Then, since player[0] and player[2] have tied for first spot, and player[1] has lost, should the pot be divided as:

player[0].received = 170
player[1].received = 0
player[2].received = 30

And subsequently, if player[1] had won, should the pot be divided as:

player[0].received = 20
player[1].received = 180
player[2].received = 0

Answer 1

First sort by score descending, so you'll end up with two groups: { 0, 2 }, { 1 }.

Then, sort each group by the order they have contributed ascending: { 2 (20), 0 (100) }, { 1 (80) }.

Now, divide the pot in that order:

1. First you'll take (max) 20 away from each players contributions to create the first pot. And divide it evenly to 2 and 0. The first pot will be (20 + 20 + 20 = 60. So both 0 and 2 will be given 30). After that, the first players winnings are done, and you are left with: { 0 (80) }, { 1 (60) }.

2. Now, you'll take (max) 80 away from each players contributions to create the next pot (80 + 60 = 140). And give it to 0 (no division needed as there are no longer more than one in the top group, so 0 will receive the whole 140). You'll be left with: { 1 (0) }.

3. No more contributions left, so you are done.

So, in total in your example, 0 would receive 170 and 2 would receive 30.