Say, in a tournament of N hands, that you need a royal (4000 coins) or
equivalent to get into the money. The chances of getting one royal in N
hands of play is Pr x (1-Pr)^(N-1) x N. Let's assume double-double
bonus and max-er strategy for starters. Well, two aces with kicker is
also 4000 coins, and the chances of getting that in N hands is Pak^2 x
(1-Pak)^(N-2) x N!/(2!x(N-2)!). The ratio of those two probabilities
gives you the ratio of their values. For example, for DDB max-er
strategy, Pr=.000025, Pak=.00006, chances of getting one royal in 500
hands is 1.2%, chances of getting two aces with kicker is 0.04%, ratio
is 1.2/0.04=30; repeat for other paying hands; to get the strategy,
take FVP or VPSM and set royal win to 4000, aces with kicker to
4000/30, etc. If you hit a royal in play, you should switch to a
strategy that optimizes the chances of getting any winning hand, if you
hit one aces with kicker, you should switch to a strategy that values a
royal or aces with kicker equally, etc. Very roughly speaking, a royal
only strategy doubles your chances of getting a royal over max-er
strategy. That doesn't mean you will win the tournament, but doubling
your odds of winning over a max-er or similar player ain't bad.