Math - How often will I go to Vegas?

My brother and I have this deal in place. We start with $50 each, make one bet every February, one bet every August. If we can parlay three bets in a row for winners, we go to Vegas with the winnings. If we lose a bet, we start the 3 leg parlay over with $50 each.

How often on average will we be going to Vegas? (Oh, assume each bet is 50-50 to win)

P.S. - If the Patriots go 12-4 or better this year, we are going to Vegas.

In 60 years, you'll have 120 betting opportunities. Do you BOTH have to hit your trifecta to go. I calculate 1/64 chance per three consecutive bets, with 118 of those occurring. So, perhaps you'll get to go twice in the next 60 years.

How do you go to Vegas with just $400? Is that just the criteria for going, like you have other funds available?

Quote: ewjones080

In 60 years, you'll have 120 betting opportunities. Do you BOTH have to hit your trifecta to go. I calculate 1/64 chance per three consecutive bets, with 118 of those occurring. So, perhaps you'll get to go twice in the next 60 years.

How do you go to Vegas with just $400? Is that just the criteria for going, like you have other funds available?

Sorry, I knew I wasn't going to make it clear. We make the same bet. So we only have to hit 3 in a row.

The $400 will pay for our flight/hotel unless we can use points for that, then we'll use the $400 for our spending money. $400 isn't a lot, but if we're going sans spouses, it's a lot of sitting in the sportsbook and playing $10 pai gow, so it lasts.