Proposition bet being offered to me

[MinionOfNothing]

My friend has offered me the following proposition bet which I believe to be in my favour, but would like to hear some confirmation.

We each put up $100.

I get 5s 2s.
He gets Qs Qc.

We deal out 100 sets of 5 cards, and I need to win 14 times out of 100 to collect the $200.

If the odds are in my favour, by how much? I don't have any of the software that some of you guys have, so I can't get these numbers on my own.

Thanks.

[lorinda]

The 5s2s will win 18.36% of the trials.
It will win, or tie 18.86% (so maybe you want to change rules a little [img]/forums/images/icons/laugh.gif[/img] )
Now my binomial distribution is very rusty, but trying to decipher this table i have, you will win 7 or more out of 50 (as high as my tables go) 63.9% of the time if you have a 15% chance per hand and 89.7% of the time at 20% chance per hand. So some sort of guess gives you a 75% chance of winning 7/50 which i believe will go up for 14/100.
As I say, my probability is rusty, but for sure you will win 18.36% of the hands.

[lorinda]

Okay, I downloaded a b.d. simulator, and, if I have used it correctly, your friend only has a 10.12% chance of winning the bet, for your info, your chances of winning x times or less is as follows:

12 05.97 %
13 10.12 %
14 15.91 %
15 23.29 %
16 32.32 %
17 42.24 %
18 52.53 %
19 62.52 %
20 71.61 %

From this data, you can see that you can win the bet, and then give him a chance to win his money back by saying it will come up 15 times on the next bet ...16....17...18 :P

[MinionOfNothing]

Thank you very much for this!

That's about what I expected, but just wanted to make sure I wasn't crazy.

He's a very egotistical poker player that thinks every time he loses with a big pocket pair, it's a huge deal. He seems to think he's offering me an even money bet. I know it's in my favour, but just wanted to know by how much. Of course, this all comes from him losing a hand with QQ to 52s.

I don't know why he'd want to do it if he thought it was even money. But it's not, so I'll definately give him a call about it.

[Gabe]

Take the bet. you should on average win the bet after about 70 hands, so you'll have about 30 hands to go if you're unlucky.

[cardshark]

I’d be interested to find out what the outcome was (provided that you took the bet).