TPFAP: When the blinds are coming up

[Losfer]

I'm having trouble with this chapter, and am hoping someone here will enlighten me.

He writes about being forced to make an even money bet tomorrow on a 20% shot meaning you should make a bet today for as low as 28.57% if losing means you won't have to make the bet tomorrow.

I don't understand why one wouldn't want to make the bet as long as it was anything over 20%. He references earlier in the book where he wrote about passing up good bets in order to make great bets later. However, I couldn't quite make the connection. Any help would be appreciated.

[Losfer]

Anyone?

[Nick C]

I don't have the book in front of me, but I believe this is the reason 25%, for instance, isn't good enough:

Most of the time (80%) when you win the initial bet, you'll lose back what you won on the second day when you're forced to make the second even-money bet against the odds, and you'll end up simply breaking even.

If you make that initial 25% bet 100 times, you'll instantly lose a bet 75 times. Of the 25 times you win initially, you'll lose back what you won 20 times. The other 5, you'll win both bets.
-75 + 0 + 10 = -65 bets.

If you passed on the 25% bet, you'd lose 80 times on the 20% bet and win 20 times.
-80 + 20 = -60.

If the first bet were at 30%, however, you'd lose initially 70 times, you'd end up breaking even 24 times, and you'd win twice 6 times. -70 + 0 + 12 = -58. So you'd have minimized your losses by taking that initial bet.

I haven't done the math for 28.57%, but that must be the break-even point for minimizing your losses.