Plugging f=1 into our first formula we see that the contemplation of insuring at least a portion of the bet should begin with values of p just above 1/3(1 + 1) = 1/6, or when just more than one out of six remaining cards is a ten. if it's a choice betien all or nothing, the critical fraction of
=. tens is, from our last formula, 1- log(1+1) 1 = 2435 or just
log (1+3/2)
less than one ten out of four cards.

Unfortunately our newly converted gambler has no money left to insure with. Will the casino accept his blackjack as security and mark it? is the pit boss the devil ?