Arc, here's an easy point of yours to discuss:
You wrote: "Show me mathematically how they improve his chances of a "big win"."
Let's take this example of one of his special plays. When he is stuck playing 7/5 Bonus (I say "stuck" because ideally he wants to play 8/5) and he is dealt AAAKK he will hold only the 3 aces and goes for the quad aces and 2000 coins. If he held the full house, as you would because you are an APer, the chance of hitting quad aces is zero. But by breaking up the full house he has two chances to hit that one card.
Here is another example where his strategy improves his chances of a big win: Dealt AAA4K in triple double bonus. Your correct, AP strategy, is to hold AAA4 and draw the single card hoping the 1/47 shot for the ace and 4000 coins. His play is to hold AAA to give himself two chances to get the ace and 800 coins. His reasoning is that 800 coins is a big enough win for him. Or as I like to put it, 800 coins in the hand is worth 4000 coins in the bush.
(By the way at Caesars the other night I was dealt quad aces on a TDB $5 machine and the hand did not improve. But shortly after that I was dealt 33344 and I broke up the full house to hold 3334 hoping for the case 3 and the 2000 coin win. Yes, I played correct strategy. My hand did not improve.)
You wrote: "Show me mathematically how they improve his chances of a "big win"."
Let's take this example of one of his special plays. When he is stuck playing 7/5 Bonus (I say "stuck" because ideally he wants to play 8/5) and he is dealt AAAKK he will hold only the 3 aces and goes for the quad aces and 2000 coins. If he held the full house, as you would because you are an APer, the chance of hitting quad aces is zero. But by breaking up the full house he has two chances to hit that one card.
Here is another example where his strategy improves his chances of a big win: Dealt AAA4K in triple double bonus. Your correct, AP strategy, is to hold AAA4 and draw the single card hoping the 1/47 shot for the ace and 4000 coins. His play is to hold AAA to give himself two chances to get the ace and 800 coins. His reasoning is that 800 coins is a big enough win for him. Or as I like to put it, 800 coins in the hand is worth 4000 coins in the bush.
(By the way at Caesars the other night I was dealt quad aces on a TDB $5 machine and the hand did not improve. But shortly after that I was dealt 33344 and I broke up the full house to hold 3334 hoping for the case 3 and the 2000 coin win. Yes, I played correct strategy. My hand did not improve.)