The Mathematics of a Lowball Sidebet

This month I have gone ahead and gone along with the other Lowball players wishes and played the “gidgets and gadgets” of Lowball sidebets. I figure it doesn’t cost me anything, it’s good for my image, and it pays to be liked by the other players which will tend to happen when they go along with their stupid bets.

A younger player has learned the game and proposed a new side bet. He was open to taking either side of the bet. The bet is that one player will pay another play $20 if he doesn’t have a King. However, if that player does have at least one King, then he will be paid $35 per King by the other player.

Let’s take a look at the math on that. Since we’re dealing with a 53 card deck using the Joker, the total number of five card hand combinations are 53 choose 5 which total 2,869,685. The total number of hands which involve no Kings are 49 choose 5 which equals 1,906,884. So the odds of getting a hand without a single King are 66.4%. We can alos tell that there are exactly 2,869,685 – 1,906,884 = 962,801 hands containing a King.

The total number of hands which involve getting one King are 4 choose 1 times 49 choose 4 which is: 4 x 211876 = 847504.
Divided by the original 2,869,685 we see that the chances of getting a hand containing a single King are 29.5%.

For a hand with two Kings, it is 4 choose 2 multiplied by 49 choose 3: 6 x 18424= 110,554
For a hand with three Kings, it is 4 choose 3 multiplied by 49 choose 2: 4 x 1176 = 4704
For all four Kings, there is only one combination for the four multiplied by 49 = 49

So if we add up all of the the hands with Kings, we get 962,811 hands containing a King: ten more than we were expecting. I’m guessing there we some rounding errors in dealing with these large numbers. When we’re accounting for close to 3 million hands, having a 10 hand discrepancy ain’t too bad. So I’m just going to convert to percentages.

66.4% of hands contain no King. 29.5% contain 1 King. 3.8% of hands contain two Kings. .16% contain three Kings, and .002% containing 4 Kings.

Going back to the original wager, if we play out 10,000 hands, then we’d have:
10,000 x 66.4% = 6640 No Kings receiving $20 = $132,800
10,000 x 29.5% = 2950 with one King receiving $35 = -$103250
10000 x 3.8% = 380 with two Kings receiving $70 = -$26,000
10000 x .16% = 16 with three Kings receiving $105= -$1680
And quad Kings being such a rare event that it doesn’t figure into 10,000 hands.
So if we do the math, over 10000 hands, the person buying the Kings will reap a profit of
$1870 which amounts to 19 cents a hand or so.

Nothing to get excited about, but the kind of stuff that gets the chips flying.

Pathfinder RPG PFS Build for a Gnome Dr. Strangelob/Poisoner

The Alchemist is one of the more flexible character classes in the Pathfinder RPG: his extracts function as spells, his bombs function as arcane blasts that ignore Spell Resistance, and he can function as a skill monkey whose talents can include finding and disarming traps.

The class is so flexible that Ogre proposed three distinct builds for the Alchemist: a bomb thrower (Dr. Strangelob), a melee build (Mr. Hyde), and a poisoner build. I’ve only played a bomb specialist, but I found that there were enough feat and discover spaces left over to add a separate element to the character. I decided to go with the poisoner, because certain feats the bomb chucker would already have such as Point Black Shot and Rapid Shot or Two-Weapon Fighting, would have natural synergy with the poisoner.

I decided to go with the Two-Weapon Fighting model instead of the Point Blank Shot and Rapid Shot model because it’s very difficult to make use of the sticky poison discovery when dealing with ammunition. They only way around it would be to use multiple daggers of throwing, but coming across such things in a Pathfinder Society setting can be rather daunting. In order to maximize the effectiveness of poison, you need to hit the target multiple times in a round. Each hit adds a +2 to the DC save versus the poison and increases it’s total duration by half. The sticky poison discovery, meanwhile, allows one dose of poison to be stretched to a number of hits equal to your Intelligence modifier- which is quite a cost saver for the poisoner.
Continue reading Pathfinder RPG PFS Build for a Gnome Dr. Strangelob/Poisoner

Ronda Rousey Uses Judo to Become Strikeforce MMA Champion

Ronda Rousey, who trained a Venice Judo back in her earlier years, used her Judo skills to become the Bantam Weight Women’s Champion over the weekend. You can see the entire fight here. I’ve also made a playlist of all her Strikeforce fights. Each is an incredible testament to real life Judo application to win a fight.