Golden Tower/Ultimate Weapon Plus

Ultimate Weapon Plus - Golden Combo

Ultimate Weapon Plus abilities can only be unlocked when all 9 Ultimate Weapons are unlocked. Golden Combo increases cash and coins earned after Golden Tower finishes by x% for each kill. The equation to determine the bonus is shown below:

Bonus multiplier = ((1 + 0.0003 x (Level + 1))^Kill) - 1

Golden Combo will only count killed enemies that spawned during the activation. Enemies that were alive before the current Golden tower activation will not be included in the kill count.

UW+ Cost Table
Level	0	1	2	3	4	5	6	7	8	9	10
Cost	Unlocked	300	360	430	510	620	750	900	1100	1350	1650
Value	0.03%	0.06%	0.09%	0.12%	0.15%	0.18%	0.21%	0.24%	0.27%	0.30%	0.33%

Final bonus

The final bonus received very much depends on the duration of the GT.

K = Kills during GT = Kills per second * duration = Kps * d

B = Bonus multiplier = ((1 + 0.0003 x (Level + 1))^K) - 1

I = Income during GT = K * income per mob

T = Number of GT activations = Total duration / GT CD

FI = Final income = T * (I + I * B) => T * I * (1 + B) => T * Kps * d * income per mob * ((1 + 0.0003 x (Level + 1))^(Kps * d))

We can solve for FI(d+1) vs FI(d) as

T * Kps * (d + 1) * income per mob * ((1 + 0.0003 x (Level + 1))^(Kps * (d+1)))
---------------------------------------------------------------------------
T * Kps * d * income per mob * ((1 + 0.0003 x (Level + 1))^(Kps * d))

Which reduces to

(d + 1)
------- * ((1 + 0.0003 x (Level + 1))^Kps)
   d

And thus we can make a table of the expected relative income when comparing both GT+ levels and duration.

Following table shows Relative income when comparing both GT+ levels and duration.Assumes 5s of mobs at the start of the GT+ that is not included the GT+ bonus and Kps=8.Numbers are relative to GT+10 at 60s.

Relative income when comparing both GT+ levels and duration.

Level/Duration	1	2	3	4	5	6	7	8	9	10
40	0,177	0,192	0,209	0,227	0,247	0,269	0,292	0,318	0,345	0,376
41	0,183	0,199	0,217	0,237	0,258	0,281	0,306	0,334	0,364	0,397
42	0,189	0,206	0,225	0,246	0,269	0,294	0,321	0,351	0,383	0,419
43	0,195	0,213	0,233	0,256	0,280	0,307	0,336	0,368	0,403	0,441
44	0,201	0,220	0,242	0,266	0,292	0,320	0,352	0,386	0,424	0,465
45	0,207	0,228	0,251	0,276	0,303	0,334	0,368	0,404	0,445	0,490
46	0,213	0,235	0,259	0,286	0,316	0,348	0,384	0,424	0,467	0,515
47	0,219	0,242	0,268	0,297	0,328	0,363	0,401	0,443	0,490	0,542
48	0,226	0,250	0,277	0,307	0,341	0,378	0,418	0,464	0,514	0,570
49	0,232	0,258	0,286	0,318	0,354	0,393	0,437	0,485	0,539	0,599
50	0,238	0,265	0,296	0,329	0,367	0,409	0,455	0,507	0,564	0,629
51	0,245	0,273	0,305	0,341	0,380	0,425	0,474	0,529	0,591	0,660
52	0,251	0,281	0,315	0,352	0,394	0,441	0,494	0,553	0,618	0,692
53	0,258	0,289	0,325	0,364	0,409	0,458	0,514	0,577	0,647	0,726
54	0,264	0,297	0,335	0,376	0,423	0,476	0,535	0,602	0,676	0,761
55	0,271	0,306	0,345	0,389	0,438	0,494	0,557	0,627	0,707	0,797
56	0,278	0,314	0,355	0,401	0,453	0,512	0,579	0,654	0,739	0,834
57	0,285	0,323	0,365	0,414	0,469	0,531	0,601	0,681	0,771	0,874
58	0,292	0,331	0,376	0,427	0,485	0,550	0,625	0,709	0,805	0,914
59	0,299	0,340	0,387	0,440	0,501	0,570	0,649	0,739	0,840	0,956
60	0,306	0,349	0,398	0,454	0,518	0,591	0,674	0,769	0,877	1,000
61	0,313	0,358	0,409	0,468	0,535	0,612	0,699	0,800	0,914	1,045
62	0,320	0,367	0,420	0,482	0,552	0,633	0,726	0,832	0,953	1,092
63	0,327	0,376	0,432	0,496	0,570	0,655	0,753	0,865	0,993	1,141
64	0,334	0,385	0,443	0,511	0,588	0,678	0,780	0,899	1,035	1,192
65	0,341	0,394	0,455	0,526	0,607	0,701	0,809	0,934	1,078	1,245
66	0,349	0,404	0,467	0,541	0,626	0,724	0,838	0,970	1,123	1,299
67	0,356	0,413	0,480	0,556	0,645	0,749	0,869	1,008	1,169	1,356
68	0,364	0,423	0,492	0,572	0,665	0,774	0,900	1,046	1,216	1,414
69	0,371	0,433	0,505	0,588	0,686	0,799	0,932	1,086	1,266	1,475
70	0,379	0,443	0,517	0,605	0,707	0,826	0,965	1,127	1,317	1,538
71	0,387	0,453	0,530	0,621	0,728	0,852	0,998	1,169	1,369	1,604
72	0,394	0,463	0,544	0,638	0,750	0,880	1,033	1,213	1,424	1,671
73	0,402	0,473	0,557	0,656	0,772	0,908	1,069	1,258	1,480	1,742
74	0,410	0,484	0,571	0,673	0,794	0,937	1,106	1,304	1,538	1,814
75	0,418	0,494	0,585	0,691	0,818	0,967	1,143	1,352	1,598	1,890
76	0,426	0,505	0,599	0,710	0,841	0,997	1,182	1,401	1,661	1,968
77	0,434	0,516	0,613	0,728	0,866	1,028	1,222	1,452	1,725	2,049
78	0,442	0,527	0,627	0,747	0,890	1,060	1,263	1,504	1,791	2,133
79	0,450	0,538	0,642	0,767	0,916	1,093	1,305	1,558	1,860	2,220
80	0,459	0,549	0,657	0,787	0,941	1,127	1,348	1,613	1,931	2,310

IE, at 40s duration a GT+10 is 213% better than a GT+1. At 80s duration it is 504% better income.

Similarly, a GT+10 at 80s duration is 231% better than the one at 60s.

100% GT uptime

If GT is already at 100% uptime (such as when using MVN or GC), the calculation changes a bit.

T = Number of GT activations = Total duration / d

FI = Final income =T * (I + I * B) => T * I * (1 + B) => Total duration * Kps * income per mob * ((1 + 0.0003 x (Level + 1))^(Kps * d)

Following table shows Relative income when comparing both GT+ levels and duration for GT duration >= 100%.Assumes 5s of mobs at the start of the GT+ that is not included the GT+ bonus and Kps=8.Numbers are relative to GT+10 at 60s.You CANNOT compare the numbers in the above table with numbers in this table. That's like comparing apples to oranges. The calculations are based on difference premises.

Relative income when comparing both GT+ levels and duration for 100% GT uptime

Level/Duration	1	2	3	4	5	6	7	8	9	10
60	0,306	0,349	0,398	0,454	0,518	0,591	0,674	0,769	0,877	1,000
61	0,307	0,351	0,402	0,459	0,525	0,601	0,687	0,785	0,898	1,027
62	0,308	0,354	0,405	0,465	0,533	0,611	0,700	0,802	0,920	1,054
63	0,310	0,356	0,409	0,470	0,541	0,621	0,714	0,820	0,942	1,082
64	0,311	0,359	0,413	0,476	0,548	0,632	0,727	0,838	0,965	1,111
65	0,313	0,361	0,417	0,482	0,556	0,642	0,742	0,856	0,988	1,141
66	0,314	0,364	0,421	0,488	0,564	0,653	0,756	0,875	1,012	1,171
67	0,316	0,367	0,425	0,494	0,573	0,664	0,771	0,894	1,037	1,203
68	0,317	0,369	0,429	0,499	0,581	0,675	0,785	0,913	1,062	1,235
69	0,319	0,372	0,434	0,506	0,589	0,687	0,801	0,933	1,088	1,268
70	0,321	0,375	0,438	0,512	0,598	0,699	0,816	0,954	1,114	1,302
71	0,322	0,377	0,442	0,518	0,606	0,710	0,832	0,974	1,141	1,336
72	0,324	0,380	0,446	0,524	0,615	0,722	0,848	0,996	1,169	1,372
73	0,325	0,383	0,451	0,530	0,624	0,735	0,865	1,017	1,197	1,409
74	0,327	0,386	0,455	0,537	0,633	0,747	0,881	1,040	1,226	1,446
75	0,328	0,388	0,459	0,543	0,642	0,760	0,898	1,062	1,256	1,485
76	0,330	0,391	0,464	0,550	0,652	0,773	0,916	1,085	1,286	1,525
77	0,332	0,394	0,468	0,556	0,661	0,786	0,933	1,109	1,318	1,565
78	0,333	0,397	0,473	0,563	0,671	0,799	0,952	1,133	1,350	1,607
79	0,335	0,400	0,477	0,570	0,680	0,812	0,970	1,158	1,382	1,650
80	0,336	0,403	0,482	0,577	0,690	0,826	0,989	1,183	1,416	1,694

As can be seen, the GT+ level scales the same, but the duration loses some efficacy.

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