Nick, do you understand what a resplit is? It means you can split a second time only if you have a certain combination of cards. It’s a subgroup of hands… only those where you draw a pair of 10s after splitting. Your expected return for hands where you draw a 20 after splitting is higher than your overall average regardless of splitting or standing, but standing on 20 produces the highest overall return.
If you draw 20s on each of the 4 hands after splitting, then you can resplit to 8 hands (not 6). If you stand on the 4 20s, your expected gain is 4x 0.7 = 2.8x bet size per hand. If you split the 4 20s, your expected gains is 4x 0.56 = 2.24x bet size per hand (asumming only 1 resplit is allowed).
That’s half of the problem. Next you need to consider how often resplits occur. Let’s keep it simple and use the approximation that you’ll draw a 10 4/13 of the time (a 10, J, Q, K) as in an infinite deck (recall Wizard of Odd’s sim used infinite decks, mine did not)
So in any hand 4/13 of the time, we decrease the expected return by (0.7-0.56). The expected return decreases by (0.7-0.56) x 4/13 per hand = 0.043 per hand. If there are 2 hands with totals of 20 that can be resplit (as after splitting a single hand), the overall decrease is 2 x0.043 = .086. So we expect the overall expected return to decreaes by .086.
0.56 – 0.086 = ~0.47
We are using the infinite decks approximation as stated above, so we expect to get the same numbers listed at Wizard of Odds for infinite decks… http://wizardofodds.com/blackjack/appendix1.html He lists 0.47… the same number.
Once again, you have shown that you do not understand basic mathematics.[/CODE][CODE][/CODE]