Can I make money in the betting markets based on what i ``know'' about the Republican VP choice

The betting markets for the Republican VP are here.

Assume that I am very confident that the VP won't be Nikki Haley. I can buy a NO share for 90 cents (that may change by the time you read this). If I buy 1 shares of NO for Haley for 90 cents then

IF she is NOT the nominee I get 100 cents, so a profit of 100-90= 10 cents. 

IF she IS the nominee I lose the 90 cents.

More generally, if I buy x shares then 

IF she is NOT the nominee I get 100x cents so, so a profit of 100x-90x=10x cents.

IF she IS the nominee then I lose the 90x cents. 

SO, if I am so confident, why not buy x shares of NO on Haley where x is large?

That depends on how confident I am. 

I am VERY CONFIDENT that if Trump is the Nominee then Haley is NOT the VP. Say I think the probability of this is \( p_1\) (very close to 1. \(p_1\) could be 0.999).

I am CONFIDENT that Trump will be the nominee.  Note that I didn't say ``VERY''. I think the probability of this is \(p_2\) (not as confident- say 0.95). 

So my expected value is (ignoring some other cases)

\(10xp_1p_2 - 90(1-p_1p_2)x = x(10p_1p_2 - 90(1-p_1p_2))\).

So to make a profit I  need \(p_1p_2 > \frac{9}{10} \). 

With my estimates \(p_1=0.999\) and \(p_2=0.95\) I should make the bet. But I won't.

1) I can imagine a world where Trump does not get the nomination- health or legal problem. Legal might not stop him--- recall that Eugene Debs ran for president while in jail, as the socialist candidate (a third party) and got 3.4% of the vote. When I google list all of the people who ran for president from jail Eugene Debs is the only person I found. I suspect there are others but they were fourth party candidates. Trump  might be ineligible to run based on some interpretation of the 14th amendment, though I doubt that will happen.

2) I cannot imagine a world where Trump gets the nomination and picks Haley as his VP. So if I could make an IF-THEN bet that it WON"T be the case that Trump is the nominee and Haley is VP, I might do that. But again, weird things can happen--- what if  (say) at the convention Kristi Noem is picked for VP (she is on some lists of possible running mates for Trump) but then after that Trump has a health problem and withdraws and after the dust settles, Haley is VP. So I need to word the bet carefully so that I don't lose in that case. 

3) NOT-Haley is now at 88 cents so I may make more of a profit!

4) Some of my thoughts on Trump's possible running mates come from this article on Nate Silver's website: here.  (ADDED LATER: One of my astute readers left a comment that informed me that it should not be called Nate Silver's website.) 

5) NO-PENCE is selling for 99 cents. I am sure Pence won't be VP in any world, but to make any real money on that you would need to buy A LOT of shares.

6) Tim Scott and Nikki Haley both said they are not interested in the VP job. People running for prez always say that. It has no information value since often they end up on the ticket anyway. Well--- not that often since lately its not that often that a primary opponent is VP. (Kamala Harris was one, but before that you need to go all the way back to 2004 Kerry-Edwards. One of my astute readers points out that Biden ran for prez in 2008, though I didn't count that since he dropped out after the Iowa Caucus where he got less than 1% of the vote. So this depends on what you mean by `running for prez'.) 

7) Winning X dollars will make me feel good. Losing Y dollars will make me feel VERY BAD. So emotionally I shouldn't be betting. And I don't. My non-math friends (I have some!) ask me why  don't go to Las Vegas and clean up, using my knowledge of Ramsey Theory. Um.... The odd thing is that even if I was really good at Probability its still hard to make money in Vegas. As the saying goes: the money you gamble in Vegas, stays in Vegas.

8) I have blogged before about gambling. One theme is that there is no such thing as a sure thing. Here are the links:

Betting on who will win the Superb Owl if one team is undefeated here. (Superb Owl is not a typo, see next link for why I am calling that big football game the Superb Owl.)

Betting on weird things in the Superb Owl: see here

Betting on long shots in the Kentucky Derby: see  here

Betting on VP in 2008: see here

 Betting on Cash Cab: Part of this post here