#### Bloody Marvelous

##### 3 of a Kind

This is always a nice topic for discussion, and I've been collecting and reworking existing formulas for ages, trying to come up with something that works for me. I'm happy to say that I finally cracked it .

First let met start by listing some of the formulas that have been suggested, and that I've found along the way. (Sorry TexRex, I didn't include your points system because it's dependent on what happens during the game itself, which means there are too many variables to convert it to a formula.)

I've made graphs of the points distribution for the following 4 games:

I reworked

That's when I came across

First let met start by listing some of the formulas that have been suggested, and that I've found along the way. (Sorry TexRex, I didn't include your points system because it's dependent on what happens during the game itself, which means there are too many variables to convert it to a formula.)

I've made graphs of the points distribution for the following 4 games:

- $150 Freezeout with 24 players (Prize-pool: $3,600)
- $50 R+A with 24 players (Prize-pool: $3,600)
- $75 Freezeout with 24 Players (Prize-pool $1,800)
- $75 Freezeout with 12 Players (Prize-pool $900)

**Points = Cash**

This is very straightforward. Just add however much money the players have won, and that's the points they accumulated. Only ITM finishes receive points (obviously), and the points curve is identical to the payout curve. The bigger the Prize-pool and the higher you finish, the more points you get. Rank, Players, Buy-ins, Rebuys, and Add-ons are all factors in this simple formula. I haven't graphed points here, since they mimic what you're paying out to your players.

**Points = Players - Rank + 1**(by*Pltrgyst*)

This is a linear points system where last place finish receives 1 point, and every place you finish higher gets you an additional point. First place finisher receives as many points as there were players in the game. Buy-ins aren't a factor in this formula, so games 1-3 have an identical points spread.

**Points = LN((Players + 1) / Rank)**(by*Dr. Neau*)

This is an oldie by Dr. Neau. Probably one of his first attempts to apply a curve to the points distribution using Natural Logarithms. The curve is about halfway between the linear formula above, and the curves below. Last place points decrease as the fields get bigger. Dr. Neau has stepped away from this formula since, and created a new one which I'll go into later. Again, since Buy-ins don't factor in, games 1-3 are identical when it comes to the points.

**Points = 10 * SQRT(Players / Rank) - 5**(by*bpbenda**)

In this formula the points for last place are frozen at 5, regardless of the number of players. Points increase in a curve dictated by the 1/SQRT(Rank) in the formula. Extra points are awarded for larger fields by the square root of the field size ratio. Buy-ins don't factor in, so graphs 1-3 are identical.

* I'm crediting*bpbenda*but am not sure he created the formula. Feel free to let me know if I should change the credit on this.

**Points = SQRT(Prizemoney) / Rank^(3/5)**(by*PocketFives.com*)

The 1/Rank^(3/5) dictates the shape of the curve. The square root of the ratio of the Prize-pool and the number of players dictate the points increase. 4x as many players will give you 2x as many points, and the same goes for the size of the Prize-pool (observable in the graph where $150 / 24 players gets twice as many points as $75 / 12 players). Points for last place decrease as the number of players increases. Since the size of the Prize-pool is identical for games 1 and 2, the graphs are identical as well.

Simplified versions:

if you only run freezeout tournaments with identical buy-ins.**Points = SQRT(Players) / Rank^(3/5)**

**Points = 10 * SQRT(Players / Rank) * (1 + LOG(Buy-in + 0.25)**(by*Pokerstars*)

The points curve is dictated by 1/SQRT(Rank). The points are boosted for larger fields by the square root of the ratio of players. The points boost for higher buy-in tournaments is determined by the logarithm section. The Prize-pool doesn't factor in, so even if there are rebuys or add-ons, the points stay the same. Last place points are not affected by the field size, only by the amount of the buy-in.*Pokerstars*only awards points to the top 15% finishes, but I applied the formula to all players in this graph.

Simplified versions:

if buy-ins are identical for all your tournaments.**Points = SQRT(Players / Rank)**

**Points = Buy-in * SQRT(Players / (Buy-in + Rebuys + Add-ons)) / (1 + Rank)**(by*Dr. Neau*)

This formula has been adopted in one form or another by many poker leagues. This is the only formula I've come across which deducts points for having to rebuy or add-on to your chipstack. The curve is determined by the 1/(1+Rank) segment of the formula, and point boosts are given for larger fields and higher buy-ins at the square root of the ratio, like a lot of the other formulas above. The baseline for the points you receive is the buy-in from which points are deducted when you rebuy or add-on at the square root of the ratio to the buy-in. The size of the Prize-pool isn't factored in. This means that if you rebuy twice and add-on for the amount of the buy-in, your points will be halved. Points for last place decrease as the field size increases.

Simplified versions:

**Points = SQRT(Players * Buy-in) / (1 + Rank)**if you don't have rebuy tournaments.

**Points = SQRT(Players) / (1 + Rank)**if all your tournaments have identical buy-ins.

I reworked

*Dr. Neau's*formula to incorporate the size of the Prize-pool, and came up with the following:**Points = Prizemoney / SQRT(Players * (Buy-in + Rebuys + Add-ons)) / (1 + Rank)**

The characteristics of this formula are identical to Dr. Neau's formula except that I'm not using the buy-in as the baseline, but the average amount spent per player.

That's when I came across

*bpbenda's*formula which was elegant in its simplicity. The points for last place were the same regardless of the field size, and the curve of the graph was similar. It was the points for last place that drew me to this formula because I believe you didn't play any better if you finish last out of 10 than if you finish last out of 1,000. Last is last. However, there was no provision for buy-in or rebuys in the formula. So reworking ensued:**Points = (10 * SQRT(Players / Rank) - 5) * SQRT(Prizemoney / Players / SQRT(Buy-in + Rebuys + Add-ons))**

Yeah, I basically added part of*Dr. Neau's*formula to*bpbenda's*, and threw in an extra square root to reduce the points boost for higher buy-ins and flatten out the effects of rebuys and add-ons.

*Pokerstars'*points, except the buy-in boosts are smaller in*Pokerstars'*formula. I want that. I need that. OK, let's see what we can do with Pokerstars' system here:**Points = 10 * SQRT(Players / Rank) * (1 + LOG(Prizemoney / Players + 0.25))^2 / (1 + LOG(Buy-in + Rebuys + Add-ons + 0.25))**

Yes, I'm probably making everything way more complicated than it really needs to be, but this is exactly what I was looking for. It has the fixed points for last place, the curve, the points boost for larger fields, and the reduced points boost for higher buy-ins, and it's got the punish/reward system for rebuys and add-ons. Did it really need a square root, a power, and two logarithms in a single formula? Well, yes, I guess it did for me.

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